master-thesis/project.org

• Literature
  • Stochastic Processes
  • Open Systems
  • Stochastic Unravelings
  • NMQSD
  • HOPS
  • Numerik
• Important Basics
• Todo
  • Where is stochastic unraveling explained in more detail?
  • RESOLVED Ito formalism necessary?
  • RESOLVED the stochastic calculus…
  • understanding NMQSD
  • How are gaussian processes described by their autocorellation
  • Which mean is meant in the Bath Correlation Function?
  • What is the justification for substitutiong zt for a stochastic process?
  • Why in the first place? -> sampling -> but why processes
  • The langevin eq. for Q in cite:Strunz2001Habil is NO LANGEVIN equation?!
  • Mathematical nitpicks in cite:Strunz2001Habil
  • IN cite:Strunz2001Habil this is meant as integral over initial conditions?
  • ASK Quantum Fluctuation theorems?
  • Submit stocproc and … patches
• Tasks
  • Implement Basic HOPS
  • Find the Steady State
  • Quantify Heat Transfer
  • Relation between coerrelation time and hops depth

Literature

Stochastic Processes

• Introduction to stochastic processes-lecture notes
• Stochastic processes for physicists: understanding noisy systems
• Probability and stochastic processes for physicists ||

Open Systems

• Open Quantum Systems by Rivas
• Fundamentals of quantum optics benjamin by Klauder

Stochastic Unravelings

• The quantum-state diffusion model applied to open systems one of the first applications
• Decoherent histories and quantum state diffusion

NMQSD

See also NMQSD.

• The non-markovian stochastic schr\ifmmodeo\else\"o\fidinger equation for open systems
• Non-Markovian Quantum State Diffusion
• Open system dynamics with non-markovian quantum trajectories

HOPS

See also HOPS.

• Hierarchy of stochastic pure states for open quantum system dynamics
• Exact open quantum system dynamics using the hierarchy of pure states (hops)
• Open quantum system response from the hierarchy of pure states

Numerik

See Numerics

• Numerical Recipes

Important Basics

• 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 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 Quantum Fluctuation theorems?

TODO Submit stocproc and … patches

Tasks

Implement Basic HOPS

CLOCK: [2021-10-08 Fri 08:51] CLOCK: [2021-10-07 Thu 13:38]–[2021-10-07 Thu 17:50] => 4:12

• see my stoch. proc experiments
• ill use richards package

Find the Steady State

Quantify Heat Transfer

• not as easy as in the cite:Kato2015Aug paper

Relation between coerrelation time and hops depth