project updates

project.org

@@ -63,6 +63,11 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] =>  4:12
 - see my notes. just calculate the time derivative of the bath energy
   expectation
 - [[file:python/billohops/test_billohops.org][my first experiments]] yield bogus numerics...
+- richards code makes it work
+- for derivations see
+   - [[file:calca/heat_flow/nonlinear_hops.xoj][nonlinear]]
+   - [[file:tex/energy_transfer/main.pdf][TeXed notes]]
+- the energy balance checks out [[id:cbc95df0-609d-4b1f-a51d-ebca7b680ec7][System + Interaction Energy]] and [[file:calca/heat_flow/hsi.xoj][my notes]]
 *** TODO TeX notes
 - done with nonlinear
 *** TODO verify that second hops state vanishes
@@ -71,13 +76,23 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] =>  4:12
 - it works see [[file:python/richard_hops/energy_flow.org][Energy Flow]]
 - interestingly with this model: only one aux state
 *** TODO Test Nonlinear hops
+- see [[file:python/richard_hops/energy_flow_nonlinear.org][here]]
 *** TODO Generalize to two Baths
 *** TODO Generalize to Nonzero Temp
 - in cite:RichardDiss the noise hamiltonian method is described
 - b.c. only on system -> calculation should go through :)
+- not that easy, see [[file:calca/heat_flow/nonlinear_hops.xoj][notes]]
+- includes time derivative of stoch proc
+- idea: sample time derivative and integrate
+- not as bad as thought: no exponential form needed -> process smooth
 *** TODO Analytic Verification
 - cummings
 - and pseudo-mode
+*** TODO figure out why means involving the stoch. process are so bad
+- maybe y is wrong -> no
+- then: not differentiable + too noisy
+- other term is integral and continous, converges faster?
+*** TODO VORTRAG
 ** Rivas Vortrag
 ** Matrix Eigenvals
 - see cite:Pan1999May