diff --git a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/first_experiments.org b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/first_experiments.org
index 9ae47c5..6d58ed7 100644
--- a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/first_experiments.org
+++ b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/first_experiments.org
@@ -1,28 +1,29 @@
-#+PROPERTY: header-args :session 09_one_qubit_otto :kernel python :pandoc no :async yes :tangle no
+#+PROPERTY: header-args :session 09_one_qubit_otto :kernel python :pandoc no :async yes :tangle otto_motor.py
 Herein I'll try to get a basic two-bath cycle running and touch base
 with the markovian result.
 
 * Boilerplate
 #+begin_src jupyter-python :results none
   import figsaver as fs
+  import plot_utils as pu
   from hiro_models.one_qubit_model import QubitModelMutliBath, StocProcTolerances
   import hiro_models.model_auxiliary as aux
   import numpy as np
   import qutip as qt
+  import utilities as ut
+  import stocproc
 #+end_src
 
 Init ray and silence stocproc.
 #+begin_src jupyter-python
   import ray
   ray.shutdown()
-  ray.init(address='auto')
+  #ray.init(address='auto')
+  ray.init()
 #+end_src
 
 #+RESULTS:
-:RESULTS:
-: 2022-07-13 14:56:26,440       INFO worker.py:956 -- Connecting to existing Ray cluster at address: 141.30.17.16:6379
-: RayContext(dashboard_url='', python_version='3.9.13', ray_version='1.13.0', ray_commit='e4ce38d001dbbe09cd21c497fedd03d692b2be3e', address_info={'node_ip_address': '141.30.17.225', 'raylet_ip_address': '141.30.17.225', 'redis_address': None, 'object_store_address': '/tmp/ray/session_2022-07-07_19-11-40_930040_398742/sockets/plasma_store.6', 'raylet_socket_name': '/tmp/ray/session_2022-07-07_19-11-40_930040_398742/sockets/raylet.2', 'webui_url': '', 'session_dir': '/tmp/ray/session_2022-07-07_19-11-40_930040_398742', 'metrics_export_port': 53497, 'gcs_address': '141.30.17.16:6379', 'address': '141.30.17.16:6379', 'node_id': 'a1b9acc4f221cb88f7c445762b2f1afb56a05388fd4a986377513e20'})
-:END:
+: RayContext(dashboard_url='', python_version='3.9.13', ray_version='1.13.0', ray_commit='e4ce38d001dbbe09cd21c497fedd03d692b2be3e', address_info={'node_ip_address': '192.168.100.170', 'raylet_ip_address': '192.168.100.170', 'redis_address': None, 'object_store_address': '/tmp/ray/session_2022-08-15_11-00-55_094481_7214/sockets/plasma_store', 'raylet_socket_name': '/tmp/ray/session_2022-08-15_11-00-55_094481_7214/sockets/raylet', 'webui_url': '', 'session_dir': '/tmp/ray/session_2022-08-15_11-00-55_094481_7214', 'metrics_export_port': 57106, 'gcs_address': '192.168.100.170:59797', 'address': '192.168.100.170:59797', 'node_id': '9026d4f7c22bee0643e9faa61b56e25e2a8eed0568554be81b1fafe2'})
 
 #+begin_src jupyter-python :results none
   from hops.util.logging_setup import logging_setup
@@ -39,162 +40,197 @@ Now we build a basic otto cycle.
 Let's lay down some basic functionality.
 
 #+begin_src jupyter-python
-  H_op = (1/2 * (qt.sigmaz() + qt.identity(2))).full()
+  H_op = 2*(1/2 * (qt.sigmaz() + qt.identity(2))).full()
   L_op = (1/2 * qt.sigmax()).full()
-  L_op_2 = (1/2 * qt.sigmay()).full()
+  L_op_2 = (1/2 * qt.sigmax()).full()
   print(H_op, L_op, sep="\n")
 #+end_src
 
 #+RESULTS:
-: [[1.+0.j 0.+0.j]
+: [[2.+0.j 0.+0.j]
 :  [0.+0.j 0.+0.j]]
 : [[0. +0.j 0.5+0.j]
 :  [0.5+0.j 0. +0.j]]
 
 #+begin_src jupyter-python :results none
-  comp_ratio = .1
-  t_exp_end = .1
-  t_hot_modulation = .1
-  t_hot_end = .5
-  t_comp_end = .6
-  t_cold_modulation = .1
-  t_cold_end = 1
+  t_compression = .1
+  t_expansion = .1
+  comp_ratio = .5
+  hot_switch_ratio = .8
+  cold_switch_ratio = .8
+
+  t_hot = (1 - t_expansion - t_compression) / 2
+  t_hot_switch = t_hot * hot_switch_ratio / 2
+  t_cold = (1 - t_expansion - t_compression) / 2
+  t_cold_switch = t_cold * cold_switch_ratio / 2
   t = np.linspace(0, 10, 1000)
 #+end_src
 
 ** Expansion
 #+begin_src jupyter-python
   %matplotlib inline
-  H_exp = SmoothStep(comp_ratio * H_op, 0, t_exp_end, 3) + H_op * (1 - comp_ratio)
+  H_exp = SmoothStep(comp_ratio * H_op, 0, t_expansion, 2) + H_op * (1 - comp_ratio)
   tt = np.linspace(0, 1, 1000)
-  plt.plot(tt, H_exp.derivative().operator_norm(tt))
+  plt.plot(tt, H_exp.operator_norm(tt))
 #+end_src
 
 #+RESULTS:
 :RESULTS:
-| <matplotlib.lines.Line2D | at | 0x7f92066c9e50> |
-[[file:./.ob-jupyter/586c97bae17d5d7684ecc3f9937e8183a3f3d3e1.svg]]
+| <matplotlib.lines.Line2D | at | 0x7f4fcc5ac130> |
+[[file:./.ob-jupyter/7d4003fe9d7b0b9dffdf0ac550823de40c40b89d.svg]]
 :END:
 
 ** Hot Thermalization
 #+begin_src jupyter-python
-  L_hot = SmoothStep(L_op, t_exp_end, t_exp_end + t_hot_modulation, 3) - SmoothStep(
-      L_op, t_hot_end - t_hot_modulation, t_hot_end, 3
-  )
+  L_hot = SmoothStep(L_op, t_expansion, t_expansion + t_hot_switch, 2) - SmoothStep(
+        L_op, t_expansion + t_hot - t_hot_switch, t_expansion + t_hot, 2
+    )
   plt.plot(tt, L_hot.operator_norm(tt))
 #+end_src
 
 #+RESULTS:
 :RESULTS:
-| <matplotlib.lines.Line2D | at | 0x7f9206382070> |
-[[file:./.ob-jupyter/7bed2d851ddc1cfc55317d2dff986662f609ca88.svg]]
+| <matplotlib.lines.Line2D | at | 0x7f4fcbdd7cd0> |
+[[file:./.ob-jupyter/34a09437b2b74d4bbe12efc5c9a3e868bd7ef7e5.svg]]
 :END:
 
 ** Compression
 #+begin_src jupyter-python
-  H_comp = ConstantMatrix(H_op) - SmoothStep(comp_ratio * H_op, t_hot_end, t_comp_end, 3)
+  H_comp = ConstantMatrix(H_op) - SmoothStep(comp_ratio * H_op, t_expansion + t_hot, t_expansion + t_hot + t_compression, 2)
   plt.plot(tt, H_comp.operator_norm(tt))
 #+end_src
 
 #+RESULTS:
 :RESULTS:
-| <matplotlib.lines.Line2D | at | 0x7f9205fe38e0> |
-[[file:./.ob-jupyter/e6b4df328725cf5e6fca48e4d52a890dafefb35e.svg]]
+| <matplotlib.lines.Line2D | at | 0x7f4fb41475b0> |
+[[file:./.ob-jupyter/6a32491bdbf52e88d8447cd4e1175d3f8e13a426.svg]]
 :END:
 
 ** Cold Thermalization
 #+begin_src jupyter-python
-  L_cold = SmoothStep(L_op_2, t_comp_end, t_comp_end + t_cold_modulation, 3) - SmoothStep(
-      L_op_2, t_cold_end - t_cold_modulation, t_cold_end, 3
+  L_cold = SmoothStep(L_op_2, t_expansion + t_hot + t_compression, t_expansion + t_hot + t_compression + t_cold_switch, 3) - SmoothStep(
+      L_op_2, t_expansion + t_hot + t_compression + t_cold - t_cold_switch, 1, 2
   )
   plt.plot(tt, L_cold.operator_norm(tt))
 #+end_src
 
 #+RESULTS:
 :RESULTS:
-| <matplotlib.lines.Line2D | at | 0x7f9205f7c3d0> |
-[[file:./.ob-jupyter/a4b3dcee48e76c03405b365f1513fae0fb337d47.svg]]
+| <matplotlib.lines.Line2D | at | 0x7f4fb4128c40> |
+[[file:./.ob-jupyter/e4d12af68c3403047d6de687c0d98e22db4b026c.svg]]
 :END:
 
 ** Full Cycle
 Now we turn the system around after each fill-cycle.
 #+begin_src jupyter-python
-  H_cyc = Periodic(Piecewise([H_exp, H_comp], [0, t_exp_end, 1]), 1)
+  H_cyc = Periodic(Piecewise([H_exp, H_comp], [0, t_expansion, 1]), 1)
   L = [Periodic(L_i, 1) for L_i in (L_cold, L_hot)]
-  H_cyc, *L = [ScaleTime(op, 2) for op in [H_cyc, *L]]
+  period = 1
+  scale = .1
+  H_cyc, *L = [ScaleTime(op, scale) for op in [H_cyc, *L]]
 
+  ω_mod = 2*np.pi / (period) * scale
   plt.plot(t, H_cyc.operator_norm(t))
   plt.plot(t, L[0].operator_norm(t))
   plt.plot(t, L[1].operator_norm(t))
+  ω_mod
+  t_cycle = period/scale
+  periods = 20
+  t_max = t_cycle * periods
+  dt = .01
 #+end_src
 
 #+RESULTS:
-:RESULTS:
-| <matplotlib.lines.Line2D | at | 0x7f9205edbca0> |
-[[file:./.ob-jupyter/bafb9c982efbee26edc0e3e20cd25059793ee4f3.svg]]
-:END:
+[[file:./.ob-jupyter/9fe28aca2667d52381ce08ef48407c6dca2028fb.svg]]
 
 * Model
 #+begin_src jupyter-python :results none
   model = QubitModelMutliBath(
-      δ=[1, 1],
+      δ=[.5, .1],
       ω_c=[1] * 2,
-      ω_s=[0, 10],
-      t=np.arange(0, 60, .01),
-      ψ_0=(qt.basis([2], [0])  + qt.basis([2], [1])*0),
+      ω_s=[H_cyc.operator_norm(0) - 1, H_cyc.operator_norm(t_expansion/scale) - 1],
+      t=ut.linspace_with_strobe(0, t_max, int(t_max // dt), ω_mod),
+      ψ_0=(qt.basis([2], [0])*0  + qt.basis([2], [1])*1),
       description=f"A simple otto cycle.",
-      k_max=5,
-      bcf_terms=[5]*2,
+      k_max=4,
+      bcf_terms=[6]*2,
       truncation_scheme="simplex",
       driving_process_tolerances=[StocProcTolerances(1e-3, 1e-3)] * 2,
       thermal_process_tolerances=[StocProcTolerances(1e-3, 1e-3)] * 2,
-      T = [0, 2],
+      T = [1, 20],
       L = L,
-      H = H_cyc * 10,
+      H = H_cyc,
       therm_methods=["tanhsinh", "fft"],
   )
 #+end_src
 
 
 #+begin_src jupyter-python
-  aux.integrate(model, 100)
+  aux.integrate(model, 200)
 #+end_src
 
 #+RESULTS:
-: fc74a430-fac5-467e-ab88-1bb8c9da7e74
+: [INFO    hops.core.integration     7214] Choosing the nonlinear integrator.
+: [INFO    hops.core.integration     7214] Using 8 integrators.
+: [INFO    hops.core.integration     7214] Some 151 trajectories have to be integrated.
+: [INFO    hops.core.integration     7214] Using 1820 hierarchy states.
+: 100% 151/151 [19:43<00:00,  7.84s/it]
 
 
 #+begin_src jupyter-python
   %matplotlib inline
+  f, a = pu.plot_energy_overview(model, strobe_frequency=ω_mod)
+  a.plot(model.t, model.H.operator_norm(model.t))
+  a.plot(model.t, model.L[0].operator_norm(model.t))
+  a.plot(model.t, model.L[1].operator_norm(model.t))
+  a.legend()
+#+end_src
+
+#+RESULTS:
+:RESULTS:
+: <matplotlib.legend.Legend at 0x7f4f97d30be0>
+[[file:./.ob-jupyter/dcb781a84fce870deba7b071bc96c4e16b39e164.svg]]
+:END:
+
+#+begin_src jupyter-python
   fig, ax = plt.subplots()
   with aux.get_data(model) as data:
-      fs.plot_with_σ(model.t, model.total_energy_from_power(data), ax=ax, label=r"$\langle H(t)\rangle$")
-      fs.plot_with_σ(model.t, model.bath_energy(data).for_bath(0), ax=ax, label=r"$\langle H_{B}^{(1)}\rangle$")
-      fs.plot_with_σ(model.t, model.bath_energy(data).for_bath(1), ax=ax, label=r"$\langle H_{B}^{(2)}\rangle$")
-      fs.plot_with_σ(model.t, model.system_energy(data), ax=ax, label=r"$\langle H_{S}\rangle$")
-      # fs.plot_with_σ(model.t, model.total_power(data), ax=ax, label=r"Power")
-  # ax.plot(model.t, model.H(model.t)[:,0,0].real, label="$H_{\mathrm{sys}}(t)$")
-  # ax.plot(model.t, model.L[0](model.t)[:,0,1].real, label="$L_C(t)$")
-  # ax.plot(model.t, model.L[1](model.t)[:,0,1].real, label="$L_H(t)$")
+        power = model.interaction_power(data).sum_baths()
+        power_sys = model.system_power(data).sum_baths()
+        energy = model.total_energy_from_power(data).sum_baths()
+        pu.plot_with_σ(model.t, power, ax=ax)
+        pu.plot_with_σ(model.t, power_sys, ax=ax, label="sys")
+        pu.plot_with_σ(model.t, energy, ax=ax)
 
   ax.legend()
 #+end_src
 
 #+RESULTS:
-: 5179bed6-d693-43de-8969-bf0dedacc8f3
+:RESULTS:
+: <matplotlib.legend.Legend at 0x7f4f974eff10>
+[[file:./.ob-jupyter/c08974c4e215e1890b26e9fc9a31a376b518bfe1.svg]]
+:END:
 
-#+begin_src jupyter-python :results none
+
+#+begin_src jupyter-python
   with aux.get_data(model) as data:
       ρ = data.rho_t_accum.mean[:]
       σ_ρ = data.rho_t_accum.ensemble_std[:]
+      plt.plot(model.t, ρ[:, 1, 1])
       xs = np.einsum("tij,ji->t", ρ, qt.sigmax().full())
       ys = np.einsum("tij,ji->t", ρ, qt.sigmay().full())
       zs = np.einsum("tij,ji->t", ρ, qt.sigmaz().full())
 #+end_src
 
+#+RESULTS:
+:RESULTS:
+: /nix/store/yf7vf1pic6xfwr035xywcczjm08psvpa-python3-3.9.13-env/lib/python3.9/site-packages/matplotlib/cbook/__init__.py:1298: ComplexWarning: Casting complex values to real discards the imaginary part
+:   return np.asarray(x, float)
+[[file:./.ob-jupyter/5dec5cced33bb9d2ede9b8805dd77daf9dfc5a24.svg]]
+:END:
+
 
 #+begin_src jupyter-python
-  %matplotlib tk
   b = qt.Bloch()
   b.add_points([xs, ys, zs])
   b.view = [20, 20]
@@ -207,4 +243,10 @@ Now we turn the system around after each fill-cycle.
 
 
 #+RESULTS:
-[[file:./.ob-jupyter/ceddb27aeff1174b98ec49f0d1e712f58591b14c.svg]]
+:RESULTS:
+: /nix/store/yf7vf1pic6xfwr035xywcczjm08psvpa-python3-3.9.13-env/lib/python3.9/site-packages/qutip/bloch.py:639: UserWarning: There are no gridspecs with layoutgrids. Possibly did not call parent GridSpec with the "figure" keyword
+:   self.fig.canvas.draw()
+: /nix/store/yf7vf1pic6xfwr035xywcczjm08psvpa-python3-3.9.13-env/lib/python3.9/site-packages/IPython/core/pylabtools.py:151: UserWarning: There are no gridspecs with layoutgrids. Possibly did not call parent GridSpec with the "figure" keyword
+:   fig.canvas.print_figure(bytes_io, **kw)
+[[file:./.ob-jupyter/b356a7697a8328d1eb85611295a8b5bfbff2e66b.svg]]
+:END:
diff --git a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/flake.lock b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/flake.lock
index d18e3ec..762fce6 100644
--- a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/flake.lock
+++ b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/flake.lock
@@ -2,11 +2,11 @@
   "nodes": {
     "flake-utils": {
       "locked": {
-        "lastModified": 1656065134,
-        "narHash": "sha256-oc6E6ByIw3oJaIyc67maaFcnjYOz1mMcOtHxbEf9NwQ=",
+        "lastModified": 1656928814,
+        "narHash": "sha256-RIFfgBuKz6Hp89yRr7+NR5tzIAbn52h8vT6vXkYjZoM=",
         "owner": "numtide",
         "repo": "flake-utils",
-        "rev": "bee6a7250dd1b01844a2de7e02e4df7d8a0a206c",
+        "rev": "7e2a3b3dfd9af950a856d66b0a7d01e3c18aa249",
         "type": "github"
       },
       "original": {
@@ -17,11 +17,11 @@
     },
     "flake-utils_2": {
       "locked": {
-        "lastModified": 1656065134,
-        "narHash": "sha256-oc6E6ByIw3oJaIyc67maaFcnjYOz1mMcOtHxbEf9NwQ=",
+        "lastModified": 1656928814,
+        "narHash": "sha256-RIFfgBuKz6Hp89yRr7+NR5tzIAbn52h8vT6vXkYjZoM=",
         "owner": "numtide",
         "repo": "flake-utils",
-        "rev": "bee6a7250dd1b01844a2de7e02e4df7d8a0a206c",
+        "rev": "7e2a3b3dfd9af950a856d66b0a7d01e3c18aa249",
         "type": "github"
       },
       "original": {
@@ -32,11 +32,11 @@
     },
     "nixpkgs": {
       "locked": {
-        "lastModified": 1657533762,
-        "narHash": "sha256-/cxTFSMmpAb8tBp1yVga1fj+i8LB9aAxnMjYFpRMuVs=",
+        "lastModified": 1660305968,
+        "narHash": "sha256-r0X1pZCSEA6mzt5OuTA7nHuLmvnbkwgpFAh1iLIx4GU=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "38860c9e91cb00f4d8cd19c7b4e36c45680c89b5",
+        "rev": "c4a0efdd5a728e20791b8d8d2f26f90ac228ee8d",
         "type": "github"
       },
       "original": {
@@ -47,11 +47,11 @@
     },
     "nixpkgs_2": {
       "locked": {
-        "lastModified": 1656492412,
-        "narHash": "sha256-CdTRqPFyE/t/nRfnfN3fxm+OOKjeJdaDbXm7E7k+Fxc=",
+        "lastModified": 1658311025,
+        "narHash": "sha256-GqagY5YmaZB3YaO41kKcQhe5RcpS83wnsW8iCu5Znqo=",
         "owner": "NixOS",
         "repo": "nixpkgs",
-        "rev": "72f17cca89ec773e5845f5fa1bffcf0b7a4e2094",
+        "rev": "cd8d1784506a7c7eb0796772b73437e0b82fad57",
         "type": "github"
       },
       "original": {
@@ -66,11 +66,11 @@
         "nixpkgs": "nixpkgs_2"
       },
       "locked": {
-        "lastModified": 1656405165,
-        "narHash": "sha256-p2c9QAnKsiUu0a3iHAkpHkO9jAkMWCbG1HCU7/TrYc0=",
+        "lastModified": 1657626303,
+        "narHash": "sha256-O/JJ0hSBCmlx0oP8QGAlRrWn0BvlC5cj7/EZ0CCWHTU=",
         "owner": "nix-community",
         "repo": "poetry2nix",
-        "rev": "abc47c71a4920e654e7b2e4261e3e6399bbe2be6",
+        "rev": "920ba682377d5c0d87945c5eb6141ab8447ca509",
         "type": "github"
       },
       "original": {
@@ -94,11 +94,11 @@
         "poetry2nix": "poetry2nix"
       },
       "locked": {
-        "lastModified": 1656499586,
-        "narHash": "sha256-tx99W8VI8xxsnPRK0zZs5V2xFo5/hfhxhrTxCQi/mQ8=",
+        "lastModified": 1658314126,
+        "narHash": "sha256-rEoZSb8bBafEd6m3xu/yQtSFlP8GZxKN15YqMZkeMaQ=",
         "owner": "vale981",
         "repo": "hiro-flake-utils",
-        "rev": "3c96df6681a2475d131a5f30e7cb02c223b7c567",
+        "rev": "316cd25ffd9d7afd331cbbc1429f62f30567e288",
         "type": "github"
       },
       "original": {
diff --git a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/flake.nix b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/flake.nix
index 4506867..f2fb887 100644
--- a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/flake.nix
+++ b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/flake.nix
@@ -12,7 +12,10 @@
       name = "09_dynamic_two_bath_one_qubit";
       shellPackages = (pkgs:
         (with pkgs;
-          [ pyright python39Packages.jupyter sshfs arb]));
+          [ pyright python39Packages.jupyter sshfs arb (pkgs.texlive.combine {
+          inherit (pkgs.texlive) scheme-medium
+          type1cm unicode-math;
+      })]));
 
       python = pkgs: pkgs.python39Full;
       shellOverride = (pkgs: oldAttrs: {
diff --git a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/otto_motor.py b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/otto_motor.py
new file mode 100644
index 0000000..ef6eb54
--- /dev/null
+++ b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/otto_motor.py
@@ -0,0 +1,125 @@
+import figsaver as fs
+import plot_utils as pu
+from hiro_models.one_qubit_model import QubitModelMutliBath, StocProcTolerances
+import hiro_models.model_auxiliary as aux
+import numpy as np
+import qutip as qt
+import utilities as ut
+import stocproc
+
+import ray
+ray.shutdown()
+#ray.init(address='auto')
+ray.init()
+
+from hops.util.logging_setup import logging_setup
+import logging
+logging_setup(logging.INFO)
+
+from hops.util.dynamic_matrix import SmoothStep, Periodic, ConstantMatrix, ScaleTime, Shift, Piecewise
+
+H_op = 2*(1/2 * (qt.sigmaz() + qt.identity(2))).full()
+L_op = (1/2 * qt.sigmax()).full()
+L_op_2 = (1/2 * qt.sigmax()).full()
+print(H_op, L_op, sep="\n")
+
+t_compression = .1
+t_expansion = .1
+comp_ratio = .5
+hot_switch_ratio = .8
+cold_switch_ratio = .8
+
+t_hot = (1 - t_expansion - t_compression) / 2
+t_hot_switch = t_hot * hot_switch_ratio / 2
+t_cold = (1 - t_expansion - t_compression) / 2
+t_cold_switch = t_cold * cold_switch_ratio / 2
+t = np.linspace(0, 10, 1000)
+
+%matplotlib inline
+H_exp = SmoothStep(comp_ratio * H_op, 0, t_expansion, 2) + H_op * (1 - comp_ratio)
+tt = np.linspace(0, 1, 1000)
+plt.plot(tt, H_exp.operator_norm(tt))
+
+L_hot = SmoothStep(L_op, t_expansion, t_expansion + t_hot_switch, 2) - SmoothStep(
+      L_op, t_expansion + t_hot - t_hot_switch, t_expansion + t_hot, 2
+  )
+plt.plot(tt, L_hot.operator_norm(tt))
+
+H_comp = ConstantMatrix(H_op) - SmoothStep(comp_ratio * H_op, t_expansion + t_hot, t_expansion + t_hot + t_compression, 2)
+plt.plot(tt, H_comp.operator_norm(tt))
+
+L_cold = SmoothStep(L_op_2, t_expansion + t_hot + t_compression, t_expansion + t_hot + t_compression + t_cold_switch, 3) - SmoothStep(
+    L_op_2, t_expansion + t_hot + t_compression + t_cold - t_cold_switch, 1, 2
+)
+plt.plot(tt, L_cold.operator_norm(tt))
+
+H_cyc = Periodic(Piecewise([H_exp, H_comp], [0, t_expansion, 1]), 1)
+L = [Periodic(L_i, 1) for L_i in (L_cold, L_hot)]
+period = 1
+scale = .1
+H_cyc, *L = [ScaleTime(op, scale) for op in [H_cyc, *L]]
+
+ω_mod = 2*np.pi / (period) * scale
+plt.plot(t, H_cyc.operator_norm(t))
+plt.plot(t, L[0].operator_norm(t))
+plt.plot(t, L[1].operator_norm(t))
+ω_mod
+t_cycle = period/scale
+periods = 20
+t_max = t_cycle * periods
+dt = .01
+
+model = QubitModelMutliBath(
+    δ=[.5, .1],
+    ω_c=[1] * 2,
+    ω_s=[H_cyc.operator_norm(0) - 1, H_cyc.operator_norm(t_expansion/scale) - 1],
+    t=ut.linspace_with_strobe(0, t_max, int(t_max // dt), ω_mod),
+    ψ_0=(qt.basis([2], [0])*0  + qt.basis([2], [1])*1),
+    description=f"A simple otto cycle.",
+    k_max=4,
+    bcf_terms=[6]*2,
+    truncation_scheme="simplex",
+    driving_process_tolerances=[StocProcTolerances(1e-3, 1e-3)] * 2,
+    thermal_process_tolerances=[StocProcTolerances(1e-3, 1e-3)] * 2,
+    T = [1, 20],
+    L = L,
+    H = H_cyc,
+    therm_methods=["tanhsinh", "fft"],
+)
+
+aux.integrate(model, 200)
+
+%matplotlib inline
+f, a = pu.plot_energy_overview(model, strobe_frequency=ω_mod)
+a.plot(model.t, model.H.operator_norm(model.t))
+a.plot(model.t, model.L[0].operator_norm(model.t))
+a.plot(model.t, model.L[1].operator_norm(model.t))
+a.legend()
+
+fig, ax = plt.subplots()
+with aux.get_data(model) as data:
+      power = model.interaction_power(data).sum_baths()
+      power_sys = model.system_power(data).sum_baths()
+      energy = model.total_energy_from_power(data).sum_baths()
+      pu.plot_with_σ(model.t, power, ax=ax)
+      pu.plot_with_σ(model.t, power_sys, ax=ax, label="sys")
+      pu.plot_with_σ(model.t, energy, ax=ax)
+
+ax.legend()
+
+with aux.get_data(model) as data:
+    ρ = data.rho_t_accum.mean[:]
+    σ_ρ = data.rho_t_accum.ensemble_std[:]
+    plt.plot(model.t, ρ[:, 1, 1])
+    xs = np.einsum("tij,ji->t", ρ, qt.sigmax().full())
+    ys = np.einsum("tij,ji->t", ρ, qt.sigmay().full())
+    zs = np.einsum("tij,ji->t", ρ, qt.sigmaz().full())
+
+b = qt.Bloch()
+b.add_points([xs, ys, zs])
+b.view = [20, 20]
+b.point_size = [0.1]
+b.sphere_alpha = 0.1
+b.size = [20, 20]
+b.render()
+b.fig
diff --git a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/plot_utils.py b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/plot_utils.py
new file mode 120000
index 0000000..dc76007
--- /dev/null
+++ b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/plot_utils.py
@@ -0,0 +1 @@
+../plot_utils.py
\ No newline at end of file
diff --git a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/poetry.lock b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/poetry.lock
index 490c0d7..58cf922 100644
--- a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/poetry.lock
+++ b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/poetry.lock
@@ -29,9 +29,9 @@ python-versions = ">=3.6"
 argon2-cffi-bindings = "*"
 
 [package.extras]
-dev = ["pre-commit", "cogapp", "tomli", "coverage[toml] (>=5.0.2)", "hypothesis", "pytest", "sphinx", "sphinx-notfound-page", "furo"]
-docs = ["sphinx", "sphinx-notfound-page", "furo"]
-tests = ["coverage[toml] (>=5.0.2)", "hypothesis", "pytest"]
+tests = ["pytest", "hypothesis", "coverage[toml] (>=5.0.2)"]
+docs = ["furo", "sphinx-notfound-page", "sphinx"]
+dev = ["furo", "sphinx-notfound-page", "sphinx", "pytest", "hypothesis", "coverage[toml] (>=5.0.2)", "tomli", "cogapp", "pre-commit"]
 
 [[package]]
 name = "argon2-cffi-bindings"
@@ -57,14 +57,14 @@ optional = false
 python-versions = ">=3.7"
 
 [package.extras]
-all = ["build", "twine", "coverage", "pytest", "pytest-cov", "sphinx"]
-dev = ["build", "twine"]
+test = ["pytest-cov", "pytest", "coverage"]
 doc = ["sphinx"]
-test = ["coverage", "pytest", "pytest-cov"]
+dev = ["twine", "build"]
+all = ["sphinx", "pytest-cov", "pytest", "coverage", "twine", "build"]
 
 [[package]]
 name = "asttokens"
-version = "2.0.5"
+version = "2.0.7"
 description = "Annotate AST trees with source code positions"
 category = "main"
 optional = false
@@ -74,21 +74,21 @@ python-versions = "*"
 six = "*"
 
 [package.extras]
-test = ["astroid", "pytest"]
+test = ["pytest", "astroid (<=2.5.3)"]
 
 [[package]]
 name = "attrs"
-version = "21.4.0"
+version = "22.1.0"
 description = "Classes Without Boilerplate"
 category = "main"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+python-versions = ">=3.5"
 
 [package.extras]
-dev = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins", "zope.interface", "furo", "sphinx", "sphinx-notfound-page", "pre-commit", "cloudpickle"]
-docs = ["furo", "sphinx", "zope.interface", "sphinx-notfound-page"]
-tests = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins", "zope.interface", "cloudpickle"]
-tests_no_zope = ["coverage[toml] (>=5.0.2)", "hypothesis", "pympler", "pytest (>=4.3.0)", "six", "mypy", "pytest-mypy-plugins", "cloudpickle"]
+tests_no_zope = ["cloudpickle", "pytest-mypy-plugins", "mypy (>=0.900,!=0.940)", "pytest (>=4.3.0)", "pympler", "hypothesis", "coverage[toml] (>=5.0.2)"]
+tests = ["cloudpickle", "zope.interface", "pytest-mypy-plugins", "mypy (>=0.900,!=0.940)", "pytest (>=4.3.0)", "pympler", "hypothesis", "coverage[toml] (>=5.0.2)"]
+docs = ["sphinx-notfound-page", "zope.interface", "sphinx", "furo"]
+dev = ["cloudpickle", "pre-commit", "sphinx-notfound-page", "sphinx", "furo", "zope.interface", "pytest-mypy-plugins", "mypy (>=0.900,!=0.940)", "pytest (>=4.3.0)", "pympler", "hypothesis", "coverage[toml] (>=5.0.2)"]
 
 [[package]]
 name = "backcall"
@@ -107,11 +107,11 @@ optional = false
 python-versions = ">=3.6.0"
 
 [package.extras]
-all = ["typing-extensions (>=3.10.0.0)"]
-dev = ["coverage (>=5.5)", "sphinx", "pytest (>=4.0.0)", "tox (>=3.20.1)", "sphinx (>=4.1.0)", "mypy (>=0.800)", "typing-extensions", "numpy"]
-doc-rtd = ["sphinx (==4.1.0)", "sphinx-rtd-theme (==0.5.1)"]
-test-tox = ["sphinx", "pytest (>=4.0.0)", "mypy (>=0.800)", "typing-extensions", "numpy"]
+test-tox = ["numpy", "typing-extensions", "mypy (>=0.800)", "pytest (>=4.0.0)", "sphinx"]
 test-tox-coverage = ["coverage (>=5.5)"]
+doc-rtd = ["sphinx-rtd-theme (==0.5.1)", "sphinx (==4.1.0)"]
+dev = ["numpy", "typing-extensions", "mypy (>=0.800)", "sphinx (>=4.1.0)", "tox (>=3.20.1)", "pytest (>=4.0.0)", "sphinx", "coverage (>=5.5)"]
+all = ["typing-extensions (>=3.10.0.0)"]
 
 [[package]]
 name = "beautifulsoup4"
@@ -125,12 +125,12 @@ python-versions = ">=3.6.0"
 soupsieve = ">1.2"
 
 [package.extras]
-html5lib = ["html5lib"]
 lxml = ["lxml"]
+html5lib = ["html5lib"]
 
 [[package]]
 name = "binfootprint"
-version = "0.1.0"
+version = "0.2.0"
 description = "binary representation for simple data structures"
 category = "main"
 optional = false
@@ -144,7 +144,7 @@ numpy = "^1.5.1"
 type = "git"
 url = "https://github.com/vale981/binfootprint"
 reference = "master"
-resolved_reference = "f30a9691a5dab1c288b0fafb95ce35c686e1aa29"
+resolved_reference = "e12ecdc74677e3d21b3114850bb1f7899683d70a"
 
 [[package]]
 name = "black"
@@ -161,20 +161,20 @@ pathspec = ">=0.9.0,<1"
 platformdirs = ">=2"
 tomli = ">=0.2.6,<2.0.0"
 typing-extensions = [
-    {version = ">=3.10.0.0", markers = "python_version < \"3.10\""},
     {version = "!=3.10.0.1", markers = "python_version >= \"3.10\""},
+    {version = ">=3.10.0.0", markers = "python_version < \"3.10\""},
 ]
 
 [package.extras]
-colorama = ["colorama (>=0.4.3)"]
-d = ["aiohttp (>=3.7.4)"]
-jupyter = ["ipython (>=7.8.0)", "tokenize-rt (>=3.2.0)"]
-python2 = ["typed-ast (>=1.4.3)"]
 uvloop = ["uvloop (>=0.15.2)"]
+python2 = ["typed-ast (>=1.4.3)"]
+jupyter = ["tokenize-rt (>=3.2.0)", "ipython (>=7.8.0)"]
+d = ["aiohttp (>=3.7.4)"]
+colorama = ["colorama (>=0.4.3)"]
 
 [[package]]
 name = "bleach"
-version = "5.0.0"
+version = "5.0.1"
 description = "An easy safelist-based HTML-sanitizing tool."
 category = "main"
 optional = false
@@ -185,8 +185,8 @@ six = ">=1.9.0"
 webencodings = "*"
 
 [package.extras]
-css = ["tinycss2 (>=1.1.0)"]
-dev = ["pip-tools (==6.5.1)", "pytest (==7.1.1)", "flake8 (==4.0.1)", "tox (==3.24.5)", "sphinx (==4.3.2)", "twine (==4.0.0)", "wheel (==0.37.1)", "hashin (==0.17.0)", "black (==22.3.0)", "mypy (==0.942)"]
+dev = ["mypy (==0.961)", "black (==22.3.0)", "wheel (==0.37.1)", "twine (==4.0.1)", "tox (==3.25.0)", "Sphinx (==4.3.2)", "pytest (==7.1.2)", "pip-tools (==6.6.2)", "hashin (==0.17.0)", "flake8 (==4.0.1)", "build (==0.8.0)"]
+css = ["tinycss2 (>=1.1.0,<1.2)"]
 
 [[package]]
 name = "certifi"
@@ -198,7 +198,7 @@ python-versions = ">=3.6"
 
 [[package]]
 name = "cffi"
-version = "1.15.0"
+version = "1.15.1"
 description = "Foreign Function Interface for Python calling C code."
 category = "main"
 optional = false
@@ -209,11 +209,11 @@ pycparser = "*"
 
 [[package]]
 name = "charset-normalizer"
-version = "2.0.12"
+version = "2.1.0"
 description = "The Real First Universal Charset Detector. Open, modern and actively maintained alternative to Chardet."
 category = "main"
 optional = false
-python-versions = ">=3.5.0"
+python-versions = ">=3.6.0"
 
 [package.extras]
 unicode_backport = ["unicodedata2"]
@@ -238,7 +238,7 @@ optional = false
 python-versions = "*"
 
 [package.extras]
-test = ["click", "pytest", "six"]
+test = ["six", "pytest", "click"]
 
 [[package]]
 name = "colorama"
@@ -270,9 +270,17 @@ category = "main"
 optional = false
 python-versions = ">=3.6"
 
+[[package]]
+name = "cython"
+version = "0.29.32"
+description = "The Cython compiler for writing C extensions for the Python language."
+category = "main"
+optional = false
+python-versions = ">=2.6, !=3.0.*, !=3.1.*, !=3.2.*"
+
 [[package]]
 name = "debugpy"
-version = "1.6.0"
+version = "1.6.2"
 description = "An implementation of the Debug Adapter Protocol for Python"
 category = "main"
 optional = false
@@ -296,7 +304,7 @@ python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
 
 [[package]]
 name = "distlib"
-version = "0.3.4"
+version = "0.3.5"
 description = "Distribution utilities"
 category = "main"
 optional = false
@@ -312,7 +320,7 @@ python-versions = ">=3.6"
 
 [[package]]
 name = "executing"
-version = "0.8.3"
+version = "0.10.0"
 description = "Get the currently executing AST node of a frame, and other information"
 category = "main"
 optional = false
@@ -320,7 +328,7 @@ python-versions = "*"
 
 [[package]]
 name = "fastjsonschema"
-version = "2.15.3"
+version = "2.16.1"
 description = "Fastest Python implementation of JSON schema"
 category = "main"
 optional = false
@@ -350,41 +358,41 @@ resolved_reference = "c979361a3e7d3d0eb7f16b99cb58b424156fd788"
 
 [[package]]
 name = "filelock"
-version = "3.7.1"
+version = "3.8.0"
 description = "A platform independent file lock."
 category = "main"
 optional = false
 python-versions = ">=3.7"
 
 [package.extras]
-docs = ["furo (>=2021.8.17b43)", "sphinx (>=4.1)", "sphinx-autodoc-typehints (>=1.12)"]
-testing = ["covdefaults (>=1.2.0)", "coverage (>=4)", "pytest (>=4)", "pytest-cov", "pytest-timeout (>=1.4.2)"]
+testing = ["pytest-timeout (>=2.1)", "pytest-cov (>=3)", "pytest (>=7.1.2)", "coverage (>=6.4.2)", "covdefaults (>=2.2)"]
+docs = ["sphinx-autodoc-typehints (>=1.19.1)", "sphinx (>=5.1.1)", "furo (>=2022.6.21)"]
 
 [[package]]
 name = "fonttools"
-version = "4.33.3"
+version = "4.34.4"
 description = "Tools to manipulate font files"
 category = "main"
 optional = false
 python-versions = ">=3.7"
 
 [package.extras]
-all = ["fs (>=2.2.0,<3)", "lxml (>=4.0,<5)", "zopfli (>=0.1.4)", "lz4 (>=1.7.4.2)", "matplotlib", "sympy", "skia-pathops (>=0.5.0)", "uharfbuzz (>=0.23.0)", "brotlicffi (>=0.8.0)", "scipy", "brotli (>=1.0.1)", "munkres", "unicodedata2 (>=14.0.0)", "xattr"]
-graphite = ["lz4 (>=1.7.4.2)"]
-interpolatable = ["scipy", "munkres"]
-lxml = ["lxml (>=4.0,<5)"]
-pathops = ["skia-pathops (>=0.5.0)"]
-plot = ["matplotlib"]
-repacker = ["uharfbuzz (>=0.23.0)"]
-symfont = ["sympy"]
-type1 = ["xattr"]
-ufo = ["fs (>=2.2.0,<3)"]
+woff = ["brotli (>=1.0.1)", "brotlicffi (>=0.8.0)", "zopfli (>=0.1.4)"]
 unicode = ["unicodedata2 (>=14.0.0)"]
-woff = ["zopfli (>=0.1.4)", "brotlicffi (>=0.8.0)", "brotli (>=1.0.1)"]
+ufo = ["fs (>=2.2.0,<3)"]
+type1 = ["xattr"]
+symfont = ["sympy"]
+repacker = ["uharfbuzz (>=0.23.0)"]
+plot = ["matplotlib"]
+pathops = ["skia-pathops (>=0.5.0)"]
+lxml = ["lxml (>=4.0,<5)"]
+interpolatable = ["munkres", "scipy"]
+graphite = ["lz4 (>=1.7.4.2)"]
+all = ["xattr", "unicodedata2 (>=14.0.0)", "munkres", "brotli (>=1.0.1)", "scipy", "brotlicffi (>=0.8.0)", "uharfbuzz (>=0.23.0)", "skia-pathops (>=0.5.0)", "sympy", "matplotlib", "lz4 (>=1.7.4.2)", "zopfli (>=0.1.4)", "lxml (>=4.0,<5)", "fs (>=2.2.0,<3)"]
 
 [[package]]
 name = "frozenlist"
-version = "1.3.0"
+version = "1.3.1"
 description = "A list-like structure which implements collections.abc.MutableSequence"
 category = "main"
 optional = false
@@ -444,7 +452,7 @@ qutip = "^4.6.3"
 type = "git"
 url = "git@github.com:vale981/two_qubit_model.git"
 reference = "main"
-resolved_reference = "b15aa6d77d9c2c5b772e4130365a22e06e53e343"
+resolved_reference = "8eacadd55220871f94be2f9e19604fbe546dc45d"
 
 [[package]]
 name = "hops"
@@ -478,11 +486,11 @@ plotting = ["matplotlib (>=3.5.0,<4.0.0)"]
 type = "git"
 url = "git@gitlab.hrz.tu-chemnitz.de:s8896854--tu-dresden.de/hops.git"
 reference = "time_dep_coupling"
-resolved_reference = "b2856eed49cd72e65b6d7ef6ec385e664f759725"
+resolved_reference = "7688249fa8d9e296e416c8fe347ad6e71f0469d5"
 
 [[package]]
 name = "hopsflow"
-version = "1.3.0"
+version = "1.4.2"
 description = "Calculating open system bath energy changes with HOPS and analytically."
 category = "main"
 optional = false
@@ -504,7 +512,7 @@ tqdm = "^4.62.3"
 type = "git"
 url = "https://github.com/vale981/hopsflow"
 reference = "main"
-resolved_reference = "b7940c1d805b4d9f3a64e9d0fce44398032d6cd7"
+resolved_reference = "b6512624cb8bc66e4ae532475cbf91820564c6ec"
 
 [[package]]
 name = "humanfriendly"
@@ -527,7 +535,7 @@ python-versions = ">=3.5"
 
 [[package]]
 name = "ipykernel"
-version = "6.15.0"
+version = "6.15.1"
 description = "IPython Kernel for Jupyter"
 category = "main"
 optional = false
@@ -547,7 +555,7 @@ tornado = ">=6.1"
 traitlets = ">=5.1.0"
 
 [package.extras]
-test = ["flaky", "ipyparallel", "pre-commit", "pytest-cov", "pytest-timeout", "pytest (>=6.0)"]
+test = ["pytest (>=6.0)", "pytest-timeout", "pytest-cov", "pre-commit", "ipyparallel", "flaky"]
 
 [[package]]
 name = "ipython"
@@ -572,17 +580,17 @@ stack-data = "*"
 traitlets = ">=5"
 
 [package.extras]
-all = ["black", "Sphinx (>=1.3)", "ipykernel", "nbconvert", "nbformat", "ipywidgets", "notebook", "ipyparallel", "qtconsole", "pytest (<7.1)", "pytest-asyncio", "testpath", "curio", "matplotlib (!=3.2.0)", "numpy (>=1.19)", "pandas", "trio"]
-black = ["black"]
-doc = ["Sphinx (>=1.3)"]
-kernel = ["ipykernel"]
-nbconvert = ["nbconvert"]
-nbformat = ["nbformat"]
-notebook = ["ipywidgets", "notebook"]
-parallel = ["ipyparallel"]
+test_extra = ["trio", "pandas", "numpy (>=1.19)", "nbformat", "matplotlib (!=3.2.0)", "curio", "testpath", "pytest-asyncio", "pytest (<7.1)"]
+test = ["testpath", "pytest-asyncio", "pytest (<7.1)"]
 qtconsole = ["qtconsole"]
-test = ["pytest (<7.1)", "pytest-asyncio", "testpath"]
-test_extra = ["pytest (<7.1)", "pytest-asyncio", "testpath", "curio", "matplotlib (!=3.2.0)", "nbformat", "numpy (>=1.19)", "pandas", "trio"]
+parallel = ["ipyparallel"]
+notebook = ["notebook", "ipywidgets"]
+nbformat = ["nbformat"]
+nbconvert = ["nbconvert"]
+kernel = ["ipykernel"]
+doc = ["Sphinx (>=1.3)"]
+black = ["black"]
+all = ["trio", "pandas", "numpy (>=1.19)", "matplotlib (!=3.2.0)", "curio", "testpath", "pytest-asyncio", "pytest (<7.1)", "qtconsole", "ipyparallel", "notebook", "ipywidgets", "nbformat", "nbconvert", "ipykernel", "Sphinx (>=1.3)", "black"]
 
 [[package]]
 name = "ipython-genutils"
@@ -609,7 +617,7 @@ traitlets = ">=4.3.1"
 widgetsnbextension = ">=3.6.0,<3.7.0"
 
 [package.extras]
-test = ["pytest (>=3.6.0)", "pytest-cov", "mock"]
+test = ["mock", "pytest-cov", "pytest (>=3.6.0)"]
 
 [[package]]
 name = "jedi"
@@ -623,8 +631,8 @@ python-versions = ">=3.6"
 parso = ">=0.8.0,<0.9.0"
 
 [package.extras]
-qa = ["flake8 (==3.8.3)", "mypy (==0.782)"]
-testing = ["Django (<3.1)", "colorama", "docopt", "pytest (<7.0.0)"]
+testing = ["pytest (<7.0.0)", "docopt", "colorama", "Django (<3.1)"]
+qa = ["mypy (==0.782)", "flake8 (==3.8.3)"]
 
 [[package]]
 name = "jinja2"
@@ -642,7 +650,7 @@ i18n = ["Babel (>=2.7)"]
 
 [[package]]
 name = "jsonschema"
-version = "4.6.0"
+version = "4.9.1"
 description = "An implementation of JSON Schema validation for Python"
 category = "main"
 optional = false
@@ -653,8 +661,8 @@ attrs = ">=17.4.0"
 pyrsistent = ">=0.14.0,<0.17.0 || >0.17.0,<0.17.1 || >0.17.1,<0.17.2 || >0.17.2"
 
 [package.extras]
-format = ["fqdn", "idna", "isoduration", "jsonpointer (>1.13)", "rfc3339-validator", "rfc3987", "uri-template", "webcolors (>=1.11)"]
-format-nongpl = ["fqdn", "idna", "isoduration", "jsonpointer (>1.13)", "rfc3339-validator", "rfc3986-validator (>0.1.0)", "uri-template", "webcolors (>=1.11)"]
+format-nongpl = ["webcolors (>=1.11)", "uri-template", "rfc3986-validator (>0.1.0)", "rfc3339-validator", "jsonpointer (>1.13)", "isoduration", "idna", "fqdn"]
+format = ["webcolors (>=1.11)", "uri-template", "rfc3987", "rfc3339-validator", "jsonpointer (>1.13)", "isoduration", "idna", "fqdn"]
 
 [[package]]
 name = "jupyter"
@@ -690,8 +698,8 @@ tornado = ">=6.0"
 traitlets = "*"
 
 [package.extras]
-doc = ["ipykernel", "myst-parser", "sphinx-rtd-theme", "sphinx (>=1.3.6)", "sphinxcontrib-github-alt"]
-test = ["codecov", "coverage", "ipykernel (>=6.5)", "ipython", "mypy", "pre-commit", "pytest", "pytest-asyncio (>=0.18)", "pytest-cov", "pytest-timeout"]
+test = ["pytest-timeout", "pytest-cov", "pytest-asyncio (>=0.18)", "pytest", "pre-commit", "mypy", "ipython", "ipykernel (>=6.5)", "coverage", "codecov"]
+doc = ["sphinxcontrib-github-alt", "sphinx (>=1.3.6)", "sphinx-rtd-theme", "myst-parser", "ipykernel"]
 
 [[package]]
 name = "jupyter-console"
@@ -713,7 +721,7 @@ test = ["pexpect"]
 
 [[package]]
 name = "jupyter-core"
-version = "4.10.0"
+version = "4.11.1"
 description = "Jupyter core package. A base package on which Jupyter projects rely."
 category = "main"
 optional = false
@@ -724,7 +732,7 @@ pywin32 = {version = ">=1.0", markers = "sys_platform == \"win32\" and platform_
 traitlets = "*"
 
 [package.extras]
-test = ["ipykernel", "pre-commit", "pytest", "pytest-cov", "pytest-timeout"]
+test = ["pytest-timeout", "pytest-cov", "pytest", "pre-commit", "ipykernel"]
 
 [[package]]
 name = "jupyterlab-pygments"
@@ -744,7 +752,7 @@ python-versions = ">=3.6"
 
 [[package]]
 name = "kiwisolver"
-version = "1.4.3"
+version = "1.4.4"
 description = "A fast implementation of the Cassowary constraint solver"
 category = "main"
 optional = false
@@ -764,6 +772,20 @@ numpy = ">=1.18"
 scipy = ">=1.4"
 uncertainties = ">=3.0.1"
 
+[[package]]
+name = "lxml"
+version = "4.9.1"
+description = "Powerful and Pythonic XML processing library combining libxml2/libxslt with the ElementTree API."
+category = "main"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, != 3.4.*"
+
+[package.extras]
+source = ["Cython (>=0.29.7)"]
+htmlsoup = ["beautifulsoup4"]
+html5 = ["html5lib"]
+cssselect = ["cssselect (>=0.7)"]
+
 [[package]]
 name = "markupsafe"
 version = "2.1.1"
@@ -774,7 +796,7 @@ python-versions = ">=3.7"
 
 [[package]]
 name = "matplotlib"
-version = "3.5.2"
+version = "3.5.3"
 description = "Python plotting package"
 category = "main"
 optional = false
@@ -789,7 +811,7 @@ packaging = ">=20.0"
 pillow = ">=6.2.0"
 pyparsing = ">=2.2.1"
 python-dateutil = ">=2.7"
-setuptools_scm = ">=4"
+setuptools_scm = ">=4,<7"
 
 [[package]]
 name = "matplotlib-inline"
@@ -802,17 +824,6 @@ python-versions = ">=3.5"
 [package.dependencies]
 traitlets = "*"
 
-[[package]]
-name = "memory-profiler"
-version = "0.60.0"
-description = "A module for monitoring memory usage of a python program"
-category = "main"
-optional = false
-python-versions = ">=3.4"
-
-[package.dependencies]
-psutil = "*"
-
 [[package]]
 name = "mistune"
 version = "0.8.4"
@@ -830,8 +841,8 @@ optional = false
 python-versions = "*"
 
 [package.extras]
-develop = ["pytest (>=4.6)", "pycodestyle", "pytest-cov", "codecov", "wheel"]
 tests = ["pytest (>=4.6)"]
+develop = ["wheel", "codecov", "pytest-cov", "pycodestyle", "pytest (>=4.6)"]
 
 [[package]]
 name = "msgpack"
@@ -851,7 +862,7 @@ python-versions = "*"
 
 [[package]]
 name = "nbclient"
-version = "0.6.4"
+version = "0.6.3"
 description = "A client library for executing notebooks. Formerly nbconvert's ExecutePreprocessor."
 category = "main"
 optional = false
@@ -861,15 +872,15 @@ python-versions = ">=3.7.0"
 jupyter-client = ">=6.1.5"
 nbformat = ">=5.0"
 nest-asyncio = "*"
-traitlets = ">=5.2.2"
+traitlets = ">=5.0.0"
 
 [package.extras]
-sphinx = ["autodoc-traits", "mock", "moto", "myst-parser", "Sphinx (>=1.7)", "sphinx-book-theme"]
-test = ["black", "check-manifest", "flake8", "ipykernel", "ipython (<8.0.0)", "ipywidgets (<8.0.0)", "mypy", "pip (>=18.1)", "pre-commit", "pytest (>=4.1)", "pytest-asyncio", "pytest-cov (>=2.6.1)", "setuptools (>=60.0)", "testpath", "twine (>=1.11.0)", "xmltodict"]
+test = ["xmltodict", "twine (>=1.11.0)", "testpath", "setuptools (>=60.0)", "pytest-cov (>=2.6.1)", "pytest-asyncio", "pytest (>=4.1)", "pre-commit", "pip (>=18.1)", "mypy", "ipywidgets (<8.0.0)", "ipython (<8.0.0)", "ipykernel", "flake8", "check-manifest", "black"]
+sphinx = ["sphinx-book-theme", "Sphinx (>=1.7)", "myst-parser", "moto", "mock", "autodoc-traits"]
 
 [[package]]
 name = "nbconvert"
-version = "6.5.0"
+version = "6.5.3"
 description = "Converting Jupyter Notebooks"
 category = "main"
 optional = false
@@ -883,6 +894,7 @@ entrypoints = ">=0.2.2"
 jinja2 = ">=3.0"
 jupyter-core = ">=4.7"
 jupyterlab-pygments = "*"
+lxml = "*"
 MarkupSafe = ">=2.0"
 mistune = ">=0.8.1,<2"
 nbclient = ">=0.5.0"
@@ -894,11 +906,11 @@ tinycss2 = "*"
 traitlets = ">=5.0"
 
 [package.extras]
-all = ["pytest", "pytest-cov", "pytest-dependency", "ipykernel", "ipywidgets (>=7)", "pre-commit", "pyppeteer (>=1,<1.1)", "tornado (>=6.1)", "sphinx (>=1.5.1)", "sphinx-rtd-theme", "nbsphinx (>=0.2.12)", "ipython"]
-docs = ["sphinx (>=1.5.1)", "sphinx-rtd-theme", "nbsphinx (>=0.2.12)", "ipython"]
-serve = ["tornado (>=6.1)"]
-test = ["pytest", "pytest-cov", "pytest-dependency", "ipykernel", "ipywidgets (>=7)", "pre-commit", "pyppeteer (>=1,<1.1)"]
 webpdf = ["pyppeteer (>=1,<1.1)"]
+test = ["pyppeteer (>=1,<1.1)", "pre-commit", "ipywidgets (>=7)", "ipykernel", "pytest-dependency", "pytest-cov", "pytest"]
+serve = ["tornado (>=6.1)"]
+docs = ["ipython", "nbsphinx (>=0.2.12)", "sphinx-rtd-theme", "sphinx (>=1.5.1)"]
+all = ["ipython", "nbsphinx (>=0.2.12)", "sphinx-rtd-theme", "sphinx (>=1.5.1)", "tornado (>=6.1)", "pyppeteer (>=1,<1.1)", "pre-commit", "ipywidgets (>=7)", "ipykernel", "pytest-dependency", "pytest-cov", "pytest"]
 
 [[package]]
 name = "nbformat"
@@ -915,7 +927,7 @@ jupyter-core = "*"
 traitlets = ">=5.1"
 
 [package.extras]
-test = ["check-manifest", "testpath", "pytest", "pre-commit"]
+test = ["pre-commit", "pytest", "testpath", "check-manifest"]
 
 [[package]]
 name = "nest-asyncio"
@@ -951,13 +963,13 @@ tornado = ">=6.1"
 traitlets = ">=4.2.1"
 
 [package.extras]
-docs = ["sphinx", "nbsphinx", "sphinxcontrib-github-alt", "sphinx-rtd-theme", "myst-parser"]
+test = ["requests-unixsocket", "pytest-cov", "selenium", "nbval", "testpath", "requests", "coverage", "pytest"]
 json-logging = ["json-logging"]
-test = ["pytest", "coverage", "requests", "testpath", "nbval", "selenium", "pytest-cov", "requests-unixsocket"]
+docs = ["myst-parser", "sphinx-rtd-theme", "sphinxcontrib-github-alt", "nbsphinx", "sphinx"]
 
 [[package]]
 name = "numpy"
-version = "1.23.0"
+version = "1.23.2"
 description = "NumPy is the fundamental package for array computing with Python."
 category = "main"
 optional = false
@@ -975,8 +987,8 @@ python-versions = ">=3.5"
 numpy = ">=1.7"
 
 [package.extras]
-docs = ["sphinx (==1.2.3)", "sphinxcontrib-napoleon", "sphinx-rtd-theme", "numpydoc"]
-tests = ["pytest", "pytest-cov", "pytest-pep8"]
+tests = ["pytest-pep8", "pytest-cov", "pytest"]
+docs = ["numpydoc", "sphinx-rtd-theme", "sphinxcontrib-napoleon", "sphinx (==1.2.3)"]
 
 [[package]]
 name = "packaging"
@@ -999,16 +1011,16 @@ python-versions = ">=3.8"
 
 [package.dependencies]
 numpy = [
-    {version = ">=1.18.5", markers = "platform_machine != \"aarch64\" and platform_machine != \"arm64\" and python_version < \"3.10\""},
-    {version = ">=1.19.2", markers = "platform_machine == \"aarch64\" and python_version < \"3.10\""},
-    {version = ">=1.20.0", markers = "platform_machine == \"arm64\" and python_version < \"3.10\""},
     {version = ">=1.21.0", markers = "python_version >= \"3.10\""},
+    {version = ">=1.20.0", markers = "platform_machine == \"arm64\" and python_version < \"3.10\""},
+    {version = ">=1.19.2", markers = "platform_machine == \"aarch64\" and python_version < \"3.10\""},
+    {version = ">=1.18.5", markers = "platform_machine != \"aarch64\" and platform_machine != \"arm64\" and python_version < \"3.10\""},
 ]
 python-dateutil = ">=2.8.1"
 pytz = ">=2020.1"
 
 [package.extras]
-test = ["hypothesis (>=5.5.3)", "pytest (>=6.0)", "pytest-xdist (>=1.31)"]
+test = ["pytest-xdist (>=1.31)", "pytest (>=6.0)", "hypothesis (>=5.5.3)"]
 
 [[package]]
 name = "pandocfilters"
@@ -1027,8 +1039,8 @@ optional = false
 python-versions = ">=3.6"
 
 [package.extras]
-qa = ["flake8 (==3.8.3)", "mypy (==0.782)"]
-testing = ["docopt", "pytest (<6.0.0)"]
+testing = ["pytest (<6.0.0)", "docopt"]
+qa = ["mypy (==0.782)", "flake8 (==3.8.3)"]
 
 [[package]]
 name = "pathspec"
@@ -1051,7 +1063,7 @@ numpy = ">=1.4"
 six = "*"
 
 [package.extras]
-test = ["pytest", "pytest-cov", "scipy"]
+test = ["scipy", "pytest-cov", "pytest"]
 
 [[package]]
 name = "pexpect"
@@ -1074,15 +1086,15 @@ python-versions = "*"
 
 [[package]]
 name = "pillow"
-version = "9.1.1"
+version = "9.2.0"
 description = "Python Imaging Library (Fork)"
 category = "main"
 optional = false
 python-versions = ">=3.7"
 
 [package.extras]
-docs = ["olefile", "sphinx (>=2.4)", "sphinx-copybutton", "sphinx-issues (>=3.0.1)", "sphinx-removed-in", "sphinx-rtd-theme (>=1.0)", "sphinxext-opengraph"]
-tests = ["check-manifest", "coverage", "defusedxml", "markdown2", "olefile", "packaging", "pyroma", "pytest", "pytest-cov", "pytest-timeout"]
+tests = ["pytest-timeout", "pytest-cov", "pytest", "pyroma", "packaging", "olefile", "markdown2", "defusedxml", "coverage", "check-manifest"]
+docs = ["sphinxext-opengraph", "sphinx-removed-in", "sphinx-issues (>=3.0.1)", "sphinx-copybutton", "sphinx (>=2.4)", "olefile", "furo"]
 
 [[package]]
 name = "platformdirs"
@@ -1093,8 +1105,8 @@ optional = false
 python-versions = ">=3.7"
 
 [package.extras]
-docs = ["furo (>=2021.7.5b38)", "proselint (>=0.10.2)", "sphinx-autodoc-typehints (>=1.12)", "sphinx (>=4)"]
-test = ["appdirs (==1.4.4)", "pytest-cov (>=2.7)", "pytest-mock (>=3.6)", "pytest (>=6)"]
+test = ["pytest (>=6)", "pytest-mock (>=3.6)", "pytest-cov (>=2.7)", "appdirs (==1.4.4)"]
+docs = ["sphinx (>=4)", "sphinx-autodoc-typehints (>=1.12)", "proselint (>=0.10.2)", "furo (>=2021.7.5b38)"]
 
 [[package]]
 name = "prettytable"
@@ -1108,7 +1120,7 @@ python-versions = ">=3.7"
 wcwidth = "*"
 
 [package.extras]
-tests = ["pytest", "pytest-cov", "pytest-lazy-fixture"]
+tests = ["pytest-lazy-fixture", "pytest-cov", "pytest"]
 
 [[package]]
 name = "prometheus-client"
@@ -1123,7 +1135,7 @@ twisted = ["twisted"]
 
 [[package]]
 name = "prompt-toolkit"
-version = "3.0.29"
+version = "3.0.30"
 description = "Library for building powerful interactive command lines in Python"
 category = "main"
 optional = false
@@ -1149,7 +1161,7 @@ optional = false
 python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*"
 
 [package.extras]
-test = ["ipaddress", "mock", "enum34", "pywin32", "wmi"]
+test = ["wmi", "pywin32", "enum34", "mock", "ipaddress"]
 
 [[package]]
 name = "ptyprocess"
@@ -1203,7 +1215,7 @@ optional = false
 python-versions = ">=3.6.8"
 
 [package.extras]
-diagrams = ["railroad-diagrams", "jinja2"]
+diagrams = ["jinja2", "railroad-diagrams"]
 
 [[package]]
 name = "pyreadline3"
@@ -1234,7 +1246,7 @@ six = ">=1.5"
 
 [[package]]
 name = "pytz"
-version = "2022.1"
+version = "2022.2.1"
 description = "World timezone definitions, modern and historical"
 category = "main"
 optional = false
@@ -1250,7 +1262,7 @@ python-versions = "*"
 
 [[package]]
 name = "pywinpty"
-version = "2.0.5"
+version = "2.0.7"
 description = "Pseudo terminal support for Windows from Python."
 category = "main"
 optional = false
@@ -1266,7 +1278,7 @@ python-versions = ">=3.6"
 
 [[package]]
 name = "pyzmq"
-version = "23.2.0"
+version = "23.2.1"
 description = "Python bindings for 0MQ"
 category = "main"
 optional = false
@@ -1295,12 +1307,12 @@ qtpy = ">=2.0.1"
 traitlets = "<5.2.1 || >5.2.1,<5.2.2 || >5.2.2"
 
 [package.extras]
+test = ["pytest-qt", "pytest", "flaky"]
 doc = ["Sphinx (>=1.3)"]
-test = ["flaky", "pytest", "pytest-qt"]
 
 [[package]]
 name = "qtpy"
-version = "2.1.0"
+version = "2.2.0"
 description = "Provides an abstraction layer on top of the various Qt bindings (PyQt5/6 and PySide2/6)."
 category = "main"
 optional = false
@@ -1310,7 +1322,7 @@ python-versions = ">=3.7"
 packaging = "*"
 
 [package.extras]
-test = ["pytest (>=6,!=7.0.0,!=7.0.1)", "pytest-cov (>=3.0.0)", "pytest-qt"]
+test = ["pytest-qt", "pytest-cov (>=3.0.0)", "pytest (>=6,!=7.0.0,!=7.0.1)"]
 
 [[package]]
 name = "qutip"
@@ -1326,11 +1338,11 @@ packaging = "*"
 scipy = ">=1.0"
 
 [package.extras]
-full = ["matplotlib (>=1.2.1)", "cython (>=0.29.20)", "cvxpy (>=1.0)", "cvxopt", "pytest (>=5.2)", "pytest-rerunfailures"]
-graphics = ["matplotlib (>=1.2.1)"]
+tests = ["pytest-rerunfailures", "pytest (>=5.2)"]
+semidefinite = ["cvxopt", "cvxpy (>=1.0)"]
 runtime_compilation = ["cython (>=0.29.20)"]
-semidefinite = ["cvxpy (>=1.0)", "cvxopt"]
-tests = ["pytest (>=5.2)", "pytest-rerunfailures"]
+graphics = ["matplotlib (>=1.2.1)"]
+full = ["pytest-rerunfailures", "pytest (>=5.2)", "cvxopt", "cvxpy (>=1.0)", "cython (>=0.29.20)", "matplotlib (>=1.2.1)"]
 
 [[package]]
 name = "ray"
@@ -1356,19 +1368,19 @@ requests = "*"
 virtualenv = "*"
 
 [package.extras]
-all = ["aiohttp-cors", "opentelemetry-api (==1.1.0)", "scikit-image", "pyyaml", "aiorwlock", "kubernetes", "requests", "fastapi", "kopf", "dm-tree", "ray-cpp (==1.13.0)", "tensorboardX (>=1.9)", "prometheus-client (>=0.7.1,<0.14.0)", "pyarrow (>=6.0.1,<7.0.0)", "colorful", "starlette", "opentelemetry-sdk (==1.1.0)", "py-spy (>=0.2.0)", "scipy", "lz4", "aiohttp (>=3.7)", "smart-open", "tabulate", "gpustat (>=1.0.0b1)", "gym (<0.22)", "opentelemetry-exporter-otlp (==1.1.0)", "fsspec", "opencensus", "urllib3", "numpy (>=1.20)", "pandas", "uvicorn (==0.16.0)", "matplotlib (!=3.4.3)"]
+tune = ["requests", "tensorboardX (>=1.9)", "tabulate", "pandas"]
+serve = ["gpustat (>=1.0.0b1)", "py-spy (>=0.2.0)", "smart-open", "starlette", "fastapi", "requests", "uvicorn (==0.16.0)", "colorful", "aiorwlock", "aiohttp (>=3.7)", "prometheus-client (>=0.7.1,<0.14.0)", "aiohttp-cors", "opencensus"]
+rllib = ["scipy", "pyyaml", "scikit-image", "matplotlib (!=3.4.3)", "lz4", "gym (<0.22)", "dm-tree", "requests", "tensorboardX (>=1.9)", "tabulate", "pandas"]
+observability = ["opentelemetry-exporter-otlp (==1.1.0)", "opentelemetry-sdk (==1.1.0)", "opentelemetry-api (==1.1.0)"]
+k8s = ["kopf", "urllib3", "kubernetes"]
+default = ["smart-open", "prometheus-client (>=0.7.1,<0.14.0)", "opencensus", "gpustat (>=1.0.0b1)", "requests", "py-spy (>=0.2.0)", "colorful", "aiohttp-cors", "aiohttp (>=3.7)"]
+data = ["numpy (>=1.20)", "fsspec", "pyarrow (>=6.0.1,<7.0.0)", "pandas"]
 cpp = ["ray-cpp (==1.13.0)"]
-data = ["pandas", "pyarrow (>=6.0.1,<7.0.0)", "fsspec", "numpy (>=1.20)"]
-default = ["aiohttp (>=3.7)", "aiohttp-cors", "colorful", "py-spy (>=0.2.0)", "requests", "gpustat (>=1.0.0b1)", "opencensus", "prometheus-client (>=0.7.1,<0.14.0)", "smart-open"]
-k8s = ["kubernetes", "urllib3", "kopf"]
-observability = ["opentelemetry-api (==1.1.0)", "opentelemetry-sdk (==1.1.0)", "opentelemetry-exporter-otlp (==1.1.0)"]
-rllib = ["pandas", "tabulate", "tensorboardX (>=1.9)", "requests", "dm-tree", "gym (<0.22)", "lz4", "matplotlib (!=3.4.3)", "scikit-image", "pyyaml", "scipy"]
-serve = ["opencensus", "aiohttp-cors", "prometheus-client (>=0.7.1,<0.14.0)", "aiohttp (>=3.7)", "aiorwlock", "colorful", "uvicorn (==0.16.0)", "requests", "fastapi", "starlette", "smart-open", "py-spy (>=0.2.0)", "gpustat (>=1.0.0b1)"]
-tune = ["pandas", "tabulate", "tensorboardX (>=1.9)", "requests"]
+all = ["matplotlib (!=3.4.3)", "uvicorn (==0.16.0)", "pandas", "numpy (>=1.20)", "urllib3", "opencensus", "fsspec", "opentelemetry-exporter-otlp (==1.1.0)", "gym (<0.22)", "gpustat (>=1.0.0b1)", "tabulate", "smart-open", "aiohttp (>=3.7)", "lz4", "scipy", "py-spy (>=0.2.0)", "opentelemetry-sdk (==1.1.0)", "starlette", "colorful", "pyarrow (>=6.0.1,<7.0.0)", "prometheus-client (>=0.7.1,<0.14.0)", "tensorboardX (>=1.9)", "ray-cpp (==1.13.0)", "dm-tree", "kopf", "fastapi", "requests", "kubernetes", "aiorwlock", "pyyaml", "scikit-image", "opentelemetry-api (==1.1.0)", "aiohttp-cors"]
 
 [[package]]
 name = "requests"
-version = "2.28.0"
+version = "2.28.1"
 description = "Python HTTP for Humans."
 category = "main"
 optional = false
@@ -1376,24 +1388,24 @@ python-versions = ">=3.7, <4"
 
 [package.dependencies]
 certifi = ">=2017.4.17"
-charset-normalizer = ">=2.0.0,<2.1.0"
+charset-normalizer = ">=2,<3"
 idna = ">=2.5,<4"
 urllib3 = ">=1.21.1,<1.27"
 
 [package.extras]
+use_chardet_on_py3 = ["chardet (>=3.0.2,<6)"]
 socks = ["PySocks (>=1.5.6,!=1.5.7)"]
-use_chardet_on_py3 = ["chardet (>=3.0.2,<5)"]
 
 [[package]]
 name = "scipy"
-version = "1.8.1"
+version = "1.9.0"
 description = "SciPy: Scientific Library for Python"
 category = "main"
 optional = false
-python-versions = ">=3.8,<3.11"
+python-versions = ">=3.8,<3.12"
 
 [package.dependencies]
-numpy = ">=1.17.3,<1.25.0"
+numpy = ">=1.18.5,<1.25.0"
 
 [[package]]
 name = "send2trash"
@@ -1404,26 +1416,25 @@ optional = false
 python-versions = "*"
 
 [package.extras]
-nativelib = ["pyobjc-framework-cocoa", "pywin32"]
-objc = ["pyobjc-framework-cocoa"]
 win32 = ["pywin32"]
+objc = ["pyobjc-framework-cocoa"]
+nativelib = ["pywin32", "pyobjc-framework-cocoa"]
 
 [[package]]
 name = "setuptools-scm"
-version = "7.0.2"
+version = "6.4.2"
 description = "the blessed package to manage your versions by scm tags"
 category = "main"
 optional = false
-python-versions = ">=3.7"
+python-versions = ">=3.6"
 
 [package.dependencies]
 packaging = ">=20.0"
 tomli = ">=1.0.0"
-typing-extensions = "*"
 
 [package.extras]
-test = ["pytest (>=6.2)", "virtualenv (>20)"]
 toml = ["setuptools (>=42)"]
+test = ["virtualenv (>20)", "pytest (>=6.2)"]
 
 [[package]]
 name = "six"
@@ -1451,7 +1462,7 @@ python-versions = "*"
 
 [[package]]
 name = "stack-data"
-version = "0.3.0"
+version = "0.4.0"
 description = "Extract data from python stack frames and tracebacks for informative displays"
 category = "main"
 optional = false
@@ -1463,7 +1474,7 @@ executing = "*"
 pure-eval = "*"
 
 [package.extras]
-tests = ["pytest", "typeguard", "pygments", "littleutils", "cython"]
+tests = ["cython", "littleutils", "pygments", "typeguard", "pytest"]
 
 [[package]]
 name = "statsmodels"
@@ -1487,7 +1498,7 @@ docs = ["sphinx", "nbconvert", "jupyter-client", "ipykernel", "matplotlib", "nbf
 
 [[package]]
 name = "stocproc"
-version = "1.1.2"
+version = "1.1.3"
 description = "Generate continuous time stationary stochastic processes from a given auto correlation function."
 category = "main"
 optional = false
@@ -1504,7 +1515,18 @@ scipy = "^1.7.3"
 type = "git"
 url = "https://github.com/vale981/stocproc"
 reference = "master"
-resolved_reference = "0035c0185a1dbc717d30ac22485020d59c865094"
+resolved_reference = "52d642c95741b0e8257e807555288cd8da425b63"
+
+[[package]]
+name = "tabulate"
+version = "0.8.10"
+description = "Pretty-print tabular data"
+category = "main"
+optional = false
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*"
+
+[package.extras]
+widechars = ["wcwidth"]
 
 [[package]]
 name = "terminado"
@@ -1520,7 +1542,7 @@ pywinpty = {version = ">=1.1.0", markers = "os_name == \"nt\""}
 tornado = ">=6.1.0"
 
 [package.extras]
-test = ["pre-commit", "pytest-timeout", "pytest (>=6.0)"]
+test = ["pytest (>=6.0)", "pytest-timeout", "pre-commit"]
 
 [[package]]
 name = "tinycss2"
@@ -1534,8 +1556,8 @@ python-versions = ">=3.6"
 webencodings = ">=0.4"
 
 [package.extras]
-doc = ["sphinx", "sphinx-rtd-theme"]
-test = ["pytest", "pytest-cov", "pytest-flake8", "pytest-isort", "coverage"]
+test = ["coverage", "pytest-isort", "pytest-flake8", "pytest-cov", "pytest"]
+doc = ["sphinx-rtd-theme", "sphinx"]
 
 [[package]]
 name = "tomli"
@@ -1547,11 +1569,11 @@ python-versions = ">=3.6"
 
 [[package]]
 name = "tornado"
-version = "6.1"
+version = "6.2"
 description = "Tornado is a Python web framework and asynchronous networking library, originally developed at FriendFeed."
 category = "main"
 optional = false
-python-versions = ">= 3.5"
+python-versions = ">= 3.7"
 
 [[package]]
 name = "tqdm"
@@ -1565,15 +1587,15 @@ python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,>=2.7"
 colorama = {version = "*", markers = "platform_system == \"Windows\""}
 
 [package.extras]
-dev = ["py-make (>=0.1.0)", "twine", "wheel"]
-notebook = ["ipywidgets (>=6)"]
-slack = ["slack-sdk"]
 telegram = ["requests"]
+slack = ["slack-sdk"]
+notebook = ["ipywidgets (>=6)"]
+dev = ["wheel", "twine", "py-make (>=0.1.0)"]
 
 [[package]]
 name = "traitlets"
-version = "5.3.0"
-description = ""
+version = "5.2.0"
+description = "Traitlets Python configuration system"
 category = "main"
 optional = false
 python-versions = ">=3.7"
@@ -1583,7 +1605,7 @@ test = ["pre-commit", "pytest"]
 
 [[package]]
 name = "typer"
-version = "0.4.1"
+version = "0.4.2"
 description = "Typer, build great CLIs. Easy to code. Based on Python type hints."
 category = "main"
 optional = false
@@ -1593,16 +1615,16 @@ python-versions = ">=3.6"
 click = ">=7.1.1,<9.0.0"
 
 [package.extras]
-all = ["colorama (>=0.4.3,<0.5.0)", "shellingham (>=1.3.0,<2.0.0)"]
-dev = ["autoflake (>=1.3.1,<2.0.0)", "flake8 (>=3.8.3,<4.0.0)"]
-doc = ["mkdocs (>=1.1.2,<2.0.0)", "mkdocs-material (>=8.1.4,<9.0.0)", "mdx-include (>=1.4.1,<2.0.0)"]
-test = ["shellingham (>=1.3.0,<2.0.0)", "pytest (>=4.4.0,<5.4.0)", "pytest-cov (>=2.10.0,<3.0.0)", "coverage (>=5.2,<6.0)", "pytest-xdist (>=1.32.0,<2.0.0)", "pytest-sugar (>=0.9.4,<0.10.0)", "mypy (==0.910)", "black (>=22.3.0,<23.0.0)", "isort (>=5.0.6,<6.0.0)"]
+test = ["isort (>=5.0.6,<6.0.0)", "black (>=22.3.0,<23.0.0)", "mypy (==0.910)", "pytest-sugar (>=0.9.4,<0.10.0)", "pytest-xdist (>=1.32.0,<2.0.0)", "coverage (>=5.2,<6.0)", "pytest-cov (>=2.10.0,<3.0.0)", "pytest (>=4.4.0,<5.4.0)", "shellingham (>=1.3.0,<2.0.0)"]
+doc = ["mdx-include (>=1.4.1,<2.0.0)", "mkdocs-material (>=8.1.4,<9.0.0)", "mkdocs (>=1.1.2,<2.0.0)"]
+dev = ["pre-commit (>=2.17.0,<3.0.0)", "flake8 (>=3.8.3,<4.0.0)", "autoflake (>=1.3.1,<2.0.0)"]
+all = ["shellingham (>=1.3.0,<2.0.0)", "colorama (>=0.4.3,<0.5.0)"]
 
 [[package]]
 name = "typing-extensions"
-version = "4.2.0"
+version = "4.3.0"
 description = "Backported and Experimental Type Hints for Python 3.7+"
-category = "main"
+category = "dev"
 optional = false
 python-versions = ">=3.7"
 
@@ -1618,41 +1640,40 @@ python-versions = "*"
 future = "*"
 
 [package.extras]
-all = ["sphinx", "nose", "numpy"]
-docs = ["sphinx"]
+tests = ["numpy", "nose"]
 optional = ["numpy"]
-tests = ["nose", "numpy"]
+docs = ["sphinx"]
+all = ["numpy", "nose", "sphinx"]
 
 [[package]]
 name = "urllib3"
-version = "1.26.9"
+version = "1.26.11"
 description = "HTTP library with thread-safe connection pooling, file post, and more."
 category = "main"
 optional = false
-python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, <4"
+python-versions = ">=2.7, !=3.0.*, !=3.1.*, !=3.2.*, !=3.3.*, !=3.4.*, !=3.5.*, <4"
 
 [package.extras]
-brotli = ["brotlicffi (>=0.8.0)", "brotli (>=1.0.9)", "brotlipy (>=0.6.0)"]
-secure = ["pyOpenSSL (>=0.14)", "cryptography (>=1.3.4)", "idna (>=2.0.0)", "certifi", "ipaddress"]
 socks = ["PySocks (>=1.5.6,!=1.5.7,<2.0)"]
+secure = ["ipaddress", "certifi", "idna (>=2.0.0)", "cryptography (>=1.3.4)", "pyOpenSSL (>=0.14)"]
+brotli = ["brotlipy (>=0.6.0)", "brotli (>=1.0.9)", "brotlicffi (>=0.8.0)"]
 
 [[package]]
 name = "virtualenv"
-version = "20.14.1"
+version = "20.16.3"
 description = "Virtual Python Environment builder"
 category = "main"
 optional = false
-python-versions = "!=3.0.*,!=3.1.*,!=3.2.*,!=3.3.*,!=3.4.*,>=2.7"
+python-versions = ">=3.6"
 
 [package.dependencies]
-distlib = ">=0.3.1,<1"
-filelock = ">=3.2,<4"
-platformdirs = ">=2,<3"
-six = ">=1.9.0,<2"
+distlib = ">=0.3.5,<1"
+filelock = ">=3.4.1,<4"
+platformdirs = ">=2.4,<3"
 
 [package.extras]
-docs = ["proselint (>=0.10.2)", "sphinx (>=3)", "sphinx-argparse (>=0.2.5)", "sphinx-rtd-theme (>=0.4.3)", "towncrier (>=21.3)"]
-testing = ["coverage (>=4)", "coverage-enable-subprocess (>=1)", "flaky (>=3)", "pytest (>=4)", "pytest-env (>=0.6.2)", "pytest-freezegun (>=0.4.1)", "pytest-mock (>=2)", "pytest-randomly (>=1)", "pytest-timeout (>=1)", "packaging (>=20.0)"]
+testing = ["pytest-timeout (>=2.1)", "pytest-randomly (>=3.10.3)", "pytest-mock (>=3.6.1)", "pytest-freezegun (>=0.4.2)", "pytest-env (>=0.6.2)", "pytest (>=7.0.1)", "packaging (>=21.3)", "flaky (>=3.7)", "coverage-enable-subprocess (>=1)", "coverage (>=6.2)"]
+docs = ["towncrier (>=21.9)", "sphinx-rtd-theme (>=1)", "sphinx-argparse (>=0.3.1)", "sphinx (>=5.1.1)", "proselint (>=0.13)"]
 
 [[package]]
 name = "wcwidth"
@@ -1684,7 +1705,7 @@ notebook = ">=4.4.1"
 [metadata]
 lock-version = "1.1"
 python-versions = ">=3.9,<3.11"
-content-hash = "87822aa4f245ff657f068df77d57bd02e0e94e46b43f01b53750342876094e3b"
+content-hash = "4b5b6426183fa06685f983bed6f531ea00715816ad42f9faf630bfff5d866083"
 
 [metadata.files]
 aiosignal = [
@@ -1727,12 +1748,12 @@ asteval = [
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+    {file = "asttokens-2.0.7.tar.gz", hash = "sha256:8444353e4e2a99661c8dfb85ec9c02eedded08f0006234bff7db44a06840acc2"},
 ]
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+    {file = "attrs-22.1.0-py2.py3-none-any.whl", hash = "sha256:86efa402f67bf2df34f51a335487cf46b1ec130d02b8d39fd248abfd30da551c"},
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@@ -1752,68 +1773,82 @@ black = [
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diff --git a/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/stocproc.ini b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/stocproc.ini
new file mode 100644
index 0000000..8ee5cfa
--- /dev/null
+++ b/python/energy_flow_proper/09_dynamic_two_bath_one_qubit/stocproc.ini
@@ -0,0 +1,2 @@
+[FFT]
+use_normalized_diff = True