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Valentin Boettcher 2021-11-05 11:30:05 +01:00
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@ -29,30 +29,7 @@ See [[id:f8d8a28b-7ae3-425a-921e-8f472b166866][Numerics]]
- [[id:eb435d2d-2625-4219-ae18-224eba0fa8a4][Coherent States]]
* Todo
** DONE Where is stochastic unraveling explained in more detail?
- maybe in sources 1-7 in the cite:Diosi1997
1. cite:Diosi1995Jan
- wait for hab...
** RESOLVED Ito formalism necessary?
** RESOLVED the stochastic calculus...
** DONE understanding NMQSD
** DONE How are gaussian processes described by their autocorellation
** DONE Which mean is meant in the [[id:85fc22ad-ad87-4f6e-a395-00c6fb33f263][Bath Correlation Function]]?
- ok mean in initial state
** DONE What is the justification for substitutiong zt for a stochastic process?
- actually we do not really substitute -> the sample trajectories /are/ a stoch. process
** DONE Why in the first place? -> sampling -> but why processes
** DONE The langevin eq. for Q in cite:Strunz2001Habil is NO LANGEVIN equation?!
- well sort of. the solution is correct
** DONE Mathematical nitpicks in cite:Strunz2001Habil
** DONE IN cite:Strunz2001Habil this is meant as integral over initial conditions?
** ASK [[id:c55b6bac-87e3-4b23-a238-c9135e3c1371][Quantum Fluctuation theorems?]]
** DONE Submit stocproc and ... patches
** ASK Only β dependence in Rivas H from definition, or also through time development?
** ASK Nonlinear woes!
- derivative of D operator?
- Heisenberg Method can't work. At least it's no linear operator
- ahh [[file:calca/nmqsd_doodles/nonlin_heisenberg.xoj][see the end of my notes]]
** RESEARCH [[id:c55b6bac-87e3-4b23-a238-c9135e3c1371][Quantum Fluctuation theorems?]]
* Tasks
** DONE Implement Basic HOPS
:LOGBOOK:
@ -76,14 +53,8 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] => 4:12
*** DONE TeX notes
- done with nonlinear
*** TODO verify that second hops state vanishes
*** DONE Try to get Richards old HOPS working
- code downloaded from [[https://cloudstore.zih.tu-dresden.de/index.php/s/9sdcn3FGGbDMDoj][here]]
- it works see [[file:python/richard_hops/energy_flow.org][Energy Flow]]
- interestingly with this model: only one aux state
*** DONE Test Nonlinear hops
- see [[file:python/richard_hops/energy_flow_nonlinear.org][here]]
*** TODO Generalize to two Baths
- bath-bath correlations
*** NEXT Adapt New HOPS
- [[id:64c775a3-860e-479d-8b08-904dc210991d][Strong coupling thermodynamics of open quantum systems]]
*** TODO Generalize to Nonzero Temp
- in cite:RichardDiss the noise hamiltonian method is described
- b.c. only on system -> calculation should go through :)
@ -93,6 +64,15 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] => 4:12
- not as bad as thought: no exponential form needed -> process smooth
- [[file:calca/heat_flow/nonzero_t_no_time_derivative.xoj][one can get around the time derivative]]
- i have implemented finite temperature [[file:python/richard_hops/energy_flow_thermal.org][here]]
**** TODO Think about transform
*** DONE Try to get Richards old HOPS working
- code downloaded from [[https://cloudstore.zih.tu-dresden.de/index.php/s/9sdcn3FGGbDMDoj][here]]
- it works see [[file:python/richard_hops/energy_flow.org][Energy Flow]]
- interestingly with this model: only one aux state
*** DONE Test Nonlinear hops
- see [[file:python/richard_hops/energy_flow_nonlinear.org][here]]
*** TODO Generalize to two Baths
- bath-bath correlations
*** TODO Analytic Verification
- cummings
- and pseudo-mode
@ -115,9 +95,20 @@ CLOCK: [2021-10-07 Thu 13:38]--[2021-10-07 Thu 17:50] => 4:12
- Initial time: \(E_{\text {int }}(0):=\operatorname{Tr}\left[\rho_{\mathrm{S}}(0) H_{\mathrm{S}}\right] \quad\left(H_{\mathrm{S}}^{\circledast}(0, \beta)=H_{\mathrm{S}}\right)\)
*** TODO Compare with Rivas Method
*** DONE Find Rivas Paper
*** TODO Make proper library
*** TODO Adapt New HOPS
- [[id:64c775a3-860e-479d-8b08-904dc210991d][Strong coupling thermodynamics of open quantum systems]]
*** NEXT Make proper library
*** TODO Three Bath Fridge
**** Mail from Konstantin
here is the paper I had in mind when we talked about the three-bath fridge.
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.108.070604
I don't know if this scenario has been considered in a strong coupling framework.
This fridge is working continuously. Maybe for HOPS a stroke-based model could be better to avoid long propagation to the steady state. Just as an example, here is an Otto-Fridge with strong coupling (I have not thou thoroughly read this paper)
https://link.springer.com/article/10.1140%2Fepjs%2Fs11734-021-00094-0
** Find the Steady State
** Matrix Eigenvals
- see cite:Pan1999May