hiro/master-thesis-tex
1
0
Fork 0
mirror of https://github.com/vale981/master-thesis-tex synced 2025-03-05 09:31:39 -05:00
Code Issues Projects Releases Packages Wiki Activity Actions

grammer fixes

Browse source
This commit is contained in:
Valentin Boettcher 2022-09-12 14:12:56 +02:00
parent 5e98fe4c7b
commit 04e2203402
2 changed files with 25 additions and 23 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

12
flake.lock generated
View file

@ -2,11 +2,11 @@
"nodes": { "nodes": {
"flake-utils": { "flake-utils": {
"locked": { "locked": {
"lastModified": 1653893745, "lastModified": 1659877975,
"narHash": "sha256-0jntwV3Z8//YwuOjzhV2sgJJPt+HY6KhU7VZUL0fKZQ=", "narHash": "sha256-zllb8aq3YO3h8B/U0/J1WBgAL8EX5yWf5pMj3G0NAmc=",
"owner": "numtide", "owner": "numtide",
"repo": "flake-utils", "repo": "flake-utils",
"rev": "1ed9fb1935d260de5fe1c2f7ee0ebaae17ed2fa1", "rev": "c0e246b9b83f637f4681389ecabcb2681b4f3af0",
"type": "github" "type": "github"
}, },
"original": { "original": {
@ -17,11 +17,11 @@
}, },
"nixpkgs": { "nixpkgs": {
"locked": { "locked": {
"lastModified": 1655567057, "lastModified": 1662911228,
"narHash": "sha256-Cc5hQSMsTzOHmZnYm8OSJ5RNUp22bd5NADWLHorULWQ=", "narHash": "sha256-oJOrB2lEeBLaO8g1DKG5PK9a1zyOWypkscrEfxxEj8A=",
"owner": "NixOS", "owner": "NixOS",
"repo": "nixpkgs", "repo": "nixpkgs",
"rev": "e0a42267f73ea52adc061a64650fddc59906fc99", "rev": "c97e777ff06fcb8d37dcdf5e21e9eff1f34f0e90",
"type": "github" "type": "github"
}, },
"original": { "original": {

36
src/num_results.tex
View file

@ -1310,6 +1310,22 @@ coupling strengths.
The interaction strength was chosen linearly spaced and the simulation The interaction strength was chosen linearly spaced and the simulation
results are presented in \cref{fig:delta_energy_overview}. results are presented in \cref{fig:delta_energy_overview}.
As the shape of the BCF is not altered between the simulations, the
bath energy flows look very similar as do the interaction
energies. The main difference between the simulations is the magnitude
of the interaction energy. With increased coupling strength there is
an increased interaction energy and an increased flow which leads to
faster energy loss in the system and faster energy gain of the
bath. The stronger the coupling, the more pronounced is the
non-monotonicity in time of the interaction energy, which is reflected
in a non-monotonicity in the bath energy expectation value.
The bath energy reaches a maximum and falls slightly for the strongest
coupling simulations. If the interaction is strong enough,
``backflow'' can occur despite finite bath correlation times. In
\cref{fig:markov_analysis_steady} the bath memory is long,
additionally to a strong coupling so that multiple oscillations can be
seen.
\begin{figure}[htp] \begin{figure}[htp]
\centering \centering
\includegraphics{figs/one_bath_syst/δ_energy_overview} \includegraphics{figs/one_bath_syst/δ_energy_overview}
@ -1318,20 +1334,6 @@ results are presented in \cref{fig:delta_energy_overview}.
strengths. The curves are converged out, and the error funnels are strengths. The curves are converged out, and the error funnels are
not visible.} not visible.}
\end{figure} \end{figure}
As the shape of the BCF is not altered between the simulations, the
bath energy flows look very similar as do the interaction
energies. The main difference is the magnitude of the interaction
energy. With increased coupling strength there is an increased
interaction energy and an increased flow which leads to faster energy
loss in the system and faster energy gain of the bath. The stronger
the coupling, the more pronounced as the non-monotonicity in time of
the interaction energy, which is reflected in a non-monotonicity in
the bath energy expectation value. The bath energy reaches a maximum
and falls slightly for the strongest coupling simulations. If the
interaction is strong enough, ``backflow'' can occur despite finite
bath correlation times. In \cref{fig:markov_analysis_steady} the bath
memory is long, additionally to a strong coupling so that multiple
oscillations can be seen.
Despite these differences for finite times, the approximate steady Despite these differences for finite times, the approximate steady
state\footnote{excluding the \(α(0)=0.4\) cases} interaction energies, state\footnote{excluding the \(α(0)=0.4\) cases} interaction energies,
@ -1380,9 +1382,9 @@ found in
Many central questions in thermodynamics are concerned with energy Many central questions in thermodynamics are concerned with energy
extraction from macroscopic systems. These questions can be framed in extraction from macroscopic systems. These questions can be framed in
operational terms that don't require a specific definition of heat and operational terms that don't require a specific definition of heat and
just relying on energy change in the total system or its just rely on the energy change in the total system or its
constituents. Energy quantities are now accessible to us in a rather constituents. These quantities are now accessible to us in a rather
general settings, making issues related energy extraction a prime general setting, making issues related energy extraction a prime
application for our method. application for our method.
Here, we will focus on the closely related problems. The first is Here, we will focus on the closely related problems. The first is