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Valentin Boettcher 2021-10-22 17:59:50 +02:00
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@ -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 - see my notes. just calculate the time derivative of the bath energy
expectation expectation
- [[file:python/billohops/test_billohops.org][my first experiments]] yield bogus numerics... - [[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 *** TODO TeX notes
- done with nonlinear - done with nonlinear
*** TODO verify that second hops state vanishes *** 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]] - it works see [[file:python/richard_hops/energy_flow.org][Energy Flow]]
- interestingly with this model: only one aux state - interestingly with this model: only one aux state
*** TODO Test Nonlinear hops *** TODO Test Nonlinear hops
- see [[file:python/richard_hops/energy_flow_nonlinear.org][here]]
*** TODO Generalize to two Baths *** TODO Generalize to two Baths
*** TODO Generalize to Nonzero Temp *** TODO Generalize to Nonzero Temp
- in cite:RichardDiss the noise hamiltonian method is described - in cite:RichardDiss the noise hamiltonian method is described
- b.c. only on system -> calculation should go through :) - 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 *** TODO Analytic Verification
- cummings - cummings
- and pseudo-mode - 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 ** Rivas Vortrag
** Matrix Eigenvals ** Matrix Eigenvals
- see cite:Pan1999May - see cite:Pan1999May