update project notes

project.org

@@ -86,7 +86,7 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] =>  4:12
 **** DONE TeX interaction energy
 **** DONE Implement interaction energy for multiple baths.
 - plot it for tal
-**** TODO Test it with the two-qubit model
+**** DONE Test it with the two-qubit model
 **** TODO Initial Slip
 - [[file:calca/heat_flow/initial_slip_zero_int.xopp][see notes on zero interaction]]
 - for self adj -> apparently tempertature independent
@@ -94,9 +94,10 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] =>  4:12
   proportional to integral of imag part of BCF -> normalizing to one
   is helpful: explains why ω_c has influence on coupling strength (as
   seen in the new trunc scheme)
-***** NEXT Adjust normalization of model
-***** TODO Verify that this works
-**** TODO Q-Trid -> how non-thermal?
+***** DONE Adjust normalization of model
+***** DONE Verify that this works
+***** TODO Verify time dependent
+**** HOLD Q-Trid -> how non-thermal?
 **** DONE Influence ω_c on initial slip and shape
 - see [[file:calca/heat_flow/initial_slip_zero_int.xopp][the notes]]
 - without non-zero system: generally enhanced flow (why?)
@@ -123,7 +124,8 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] =>  4:12
 - fit quality
 - switched to fitting 2/3 where bcf is big and the rest on the tail
 
-******  TODO Try less symmetric
+****** TODO Port to new system
+****** TODO Try less symmetric
 
 *** DONE figure out why means involving the stoch. process are so bad
 - maybe y is wrong -> no
@@ -142,11 +144,12 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] =>  4:12
 - Properties
 - Initial time: \(E_{\text {int }}(0):=\operatorname{Tr}\left[\rho_{\mathrm{S}}(0) H_{\mathrm{S}}\right] \quad\left(H_{\mathrm{S}}^{\circledast}(0, \beta)=H_{\mathrm{S}}\right)\)
 **** DONE Find Rivas Paper
-*** TODO Physical Implication Single Bath
+*** HOLD Physical Implication Single Bath
 - how far away from thermal state
 - exponential decay for markov case?
 *** TODO Think about Higher moments
-*** TODO Why does the expression containing the first hier. states converging faster.
+- see [[file:calca/heat_flow/higher_order.xopp][notes]]
+*** HOLD Why does the expression containing the first hier. states converging faster.
 ** HOLD Steady State Methods
 - [[file:python/energy_flow_proper/05_gaussian_two_baths/longhopsidea.org][cholesky transform]] seems to provide us with the posibility of
   generating tree like processes
@@ -165,7 +168,7 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] =>  4:12
   - negative thermal conductance at low coupling strenght between
     qubit and mode
   - thermal transistor with two qubits and one mode
-*** TODO Two Qubits
+*** HOLD Two Qubits
 **** NEXT Hamiltonian
 - [[file:calca/qubit_model/general_model.xopp][see notes]]
 - look at cite:Kato2015Aug
@@ -223,7 +226,7 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] =>  4:12
 - cite:Aurell2019Apr -> jump processes, one bath
 - effective description
 - rate/kinetic equations
-*** TODO Three Bath Fridge
+*** HOLD Three Bath Fridge
 
 here is the paper I had in mind when we talked about the three-bath fridge.
 
@@ -238,9 +241,146 @@ This fridge is working continuously. Maybe for HOPS a stroke-based model could b
 https://link.springer.com/article/10.1140%2Fepjs%2Fs11734-021-00094-0
 
 - cite:Karimi2016Nov -> one HO and two resonators
-*** TODO Realistic Models
+- cite:Mu2017Dec, cite:Binder2018 -> linear additive coupling can't be used to attain cooling
+*** HOLD Realistic Models
 - ask Kimmo about quantum dots
 - look at prof. strunzs paper again
+*** TODO Heat Engines
+See cite:Binder2018.
+- our strengths lie in medium/fast non-periodic driving
+- carnot maybe good idea: expansion and coupling at the same time
+- we need at least two baths -> non passive
+- stronger coupling + coherence should decrease
+- interesting effects if H(t) does not commute for different times
+- adiabaticity still present even with stronger coupling?
+- monotonic convergence to steady state is guaranteed cite:Feldmann2004Oct
+  - distance measure is the relative entropy: not symmetric
+- shortcut to adiabaticity -> performance boost
+**** TODO Ref 92
+- convergence to limit cycle only for weak?
+- I don't think so
+**** TODO Look at 105
+**** TODO Chapter Two: How applicable to our case?
+**** DONE Single Bath Time Dependence
+- no energy extraction due to passivity
+  - WRONG!, indeed you can, but it's likely bounded
+  - N - times the same HO definitely is, see [[file:python/energy_flow_proper/ergo_stuff/ergotropy_bath_qubit.org][my ergotropy experiments]] and [[file:calca/qubit_model/passive_states_once_more.xopp][calculations]]
+    - small but finite changes let things blow up. i suspect this was a waste of time
+
+- see also [[file:calca/heat_flow/initial_slip_zero_int.xopp][my notes on pure dephasing]] -> no energy transfer dephasing at all
+- see [[file:python/energy_flow_proper/08_dynamic_one_bath/coupling_modulation.org][modulation experiments]] and cite:Binder2018
+  - as far away from dephasing as is possible
+
+**** TODO Connection to Prior Art
+- find out how much theorems are violated
+- are there STIRUP-like surprises: overlapping and swapping stages
+***** TODO Find results to reproduce
+- strong coupling with HO WM: cite:Wiedmann2021Jun
+- stirling: non-markovian cite:Raja2021Mar
+  - strokes separate, no overlap
+  - apparently higher eff than quasistat -> but only without thermalization
+  - only qubits
+  - second order in coupling -> born approx, no bath change cite:Kofman2004Sep
+- carnot-like: cite:Scopa2018Jun uses GKSL-Floquet
+
+****** (old) spin-1/2 in weak-coupling: cite:Geva1992Feb
+  - refers to laser with semigroup model: Curzon-Ahlborn efficiency (in classical limit)
+    - speaks of endoreversibility
+    - irreverisibility through coupling
+  - this work: more easily compared with classical, b.c. no simultaneous heat contact
+  - qubit: no classical analog, simple
+  - questions: curzon-ahlborn still valid, approaching equilibrium
+    limit?, effect of quantum mechanics per-se
+
+******* Model
+- **many** non interacting spins as working fluid (multiply everything by N)
+  - **does this make a difference?**
+- carnot cycle: two isothermal br., two adiabatic
+- modulation has no zero, simpliy magnitude of magnetic field, commutes with \(H\)
+  - effecive diagonality
+
+******* Work, Heat, Temp
+- power and heat naively defined by instantaneous limits
+  #+DOWNLOADED: screenshot @ 2022-05-09 15:22:34
+  [[file:Tasks/2022-05-09_15-22-34_screenshot.png]]
+
+#+DOWNLOADED: screenshot @ 2022-05-09 15:22:54
+[[file:Tasks/2022-05-09_15-22-54_screenshot.png]]
+- cite:Binder2018 says this is problematic outside the limit cycle if
+  modulation is fast: work vs. internal energy (do we have this problem?)
+- Modulating H does not change population
+- negative Temperatures as artifact of non-positive
+******* Cycles
+- temperature equilibration is performed
+- sudden limit: otto cycle efficiency upper bound for all
+- step cycle converges onto reversible
+- final cycle: detailed balance for the gksl -> time dependent coefficients (but ok if slow-varying)
+  otherwise problematic
+- non-equilibrium -> "temperatures of the working fluid not the same as the baths"
+******* Striking Findings
+- different heat transfer law
+- high temperature limit:
+  - times for isothermal branches
+  - at maximum power: times independent of the isotherm temperatures
+    - explicit modulation
+  - maximum power at curzon-ahlborn eff, effectiveness 1/2
+  - similar to newton but need not be close to eq.
+****** General Notions in cite:Kurizki2021Dec
+- continous
+******* Reciprocating Engines
+- adiabatic limit: wm state diagonal, efficiency 1-ω_c/ω_h
+- coherence generated when hamiltonian (system driving) does not
+  commute with itself: extra (external) work
+  - making the state non-passive is costing work
+- in sudden limit: cohorence gives work extraciton, *markov*
+  - non-passivity for unitary extraction from the work medium
+  - all engine types are equivalent (map over one cycle) when action small cite:Uzdin2015Sep
+    - equivalence of map, but not state inside cycle
+    - thermodynamic heat/power also converge to same
+    - continous engines only extrac work from coherences
+******* TODO 18, 22 -> ergotropy
+- tighter bound p. 268 for entropy change
+- 18: nonthermal baths are special and may perform work
+- 22: nonpassivity of piston states -> work
+  - maybe later: *implement machine proposed in HOPS*
+
+***** TODO Find Theorems to break
+- quantum speed limit
+- quantum friction
+- stochastic cycles: efficiency limit cite:Binder2018
+- symmetry of expansion and compression
+- modulating the nature of the coupling may be interesting
+- fast driving + overlap of strokes
+- level of non-adiabaticity
+- how much is spohn violated
+- ergotropy production
+- dependence on cutoff
+- limit-cycle: constant energy and entropy? (probably)
+- fast modulation: more complicated "einschwingen", energy exchange
+  with external source not to be neglected
+- sudden limit->finite work? and adiabatic limit.
+  (maybe even easier to define with finite memory)
+- reversibility? how to define?
+- *sudden limit*: equivalence of continous and stroke broken with a lot of memory?
+  - may need big actions
+- detect signatures from cite:Uzdin2015Sep
+  - *continous engines*: coherences are only source of work
+  - defines a classical engine
+- cite:Kurizki2021Dec: p. 268 -> heat and entropy inequalities may be
+  broken, gives concrete conditions
+
+***** TODO Model Ideas
+- for starters: qubit
+- two coupled qubits also nice
+- non-scalar time dependence
+- period of high int-strength followed by period of low for thermalization
+- maybe extra dephasing step -> should remove power output
+- notion of instantaneous temperature? cite:Geva1992Feb
+- continous cycle machines: may have quantum advantage cite:Kurizki2021Dec
+  - coherence work extraction
+  - maybe contrast stroke vs continous?
+**** NEXT Implement Two-Bath Qubit
+
 ** DONE Talk
 *** DONE Plan
 **** RESOLVED How much introduction
@@ -257,11 +397,12 @@ https://link.springer.com/article/10.1140%2Fepjs%2Fs11734-021-00094-0
 - intesting: anti-herm part is probability decay
 - decay is stronger the higher the depth
 **** DONE TeX it
-**** TODO Truncation scheme
+**** HOLD Truncation scheme
 - what does it mean if the norms are small?
 - apparently with coupling it still works
 - maybe dynamic truncation
-**** TODO TeX It
+**** DONE TeX It
+*** TODO Hopsflow Power
 ** Quantum Thermo
 *** How is heat flow measured?
 - cite:Stevens2021Sep energy change in qubit drive field conditioned on measurement outcome
@@ -301,7 +442,7 @@ https://link.springer.com/article/10.1140%2Fepjs%2Fs11734-021-00094-0
 *** Thermal Operations
 ** Entropy Dynamics
 ** Effective thermal states (forget coherences)
-*** ASK what is eigenstate thermalization
+*** DONE what is eigenstate thermalization
 
 *** Preferred Basis
 ** Automatic definition of interaction so that interaction energy stays zero
@@ -317,9 +458,10 @@ https://link.springer.com/article/10.1140%2Fepjs%2Fs11734-021-00094-0
 ** cite:Esposito2015Dec exclude definitions because not exact differential
 ** What happens to the interaction H in steady state
 ** Why does everything come to a halt except the bath?
+** ASK General Coupling Operators?
 * Questions
 ** RESOLVED what is a kinetic equation
-** ASK what is feschbach projection
+** DONE what is feschbach projection
 ** DONE Look up Michele Campisi
 - identify heat source first: then definition :)
 - entropy production positive not quite second law: not thermodynamic entropy