master-thesis/tex/talk/talk.org

• Introduction
  • General Model
  • Motivation
  • NMQSD
  • HOPS
• Bath Energy
  • Formulas and Generalizations
  • Interaction Energy
  • Demonstration one Bath
  • Demonstration two Baths
• Analytical Verification
  • Model
  • Solution
  • Comparison
  • Quick review of the two HO case
• HOPS Related, No Details
• Outlook

These are the planning and notes for the talk for "Wissenschaftliches Arbeiten".

There is a total time of 20 minutes to fill, which is going to be a pretty tough upper bound.

  (defun total-time ()
    (interactive)
    (let ((total 0))
      (message
       (number-to-string
        (apply
         #'+
         (org-map-entries
          #'(lambda ()
              (string-to-number
               (or (cdr (assoc "DURATION" (org-entry-properties))) "0")))))))))

• other seeds
• only analyt. sol
• no code comments :(: done, no we can :P
• convergence, only one/two
• other projects, less point but more pictures
• "norm based"
• outlook too much text

Introduction

DONE General Model   WAITING

• hamiltonian multiple baths
• (def. BCFs)

DONE Motivation

• weak coupling/equilibrium well settled
• strong coupling: no consensus (lots of citations)

• won't be settled in a masters thesis but ->

  • access to bath/interaction observables with exact dynamics would be helpful
• this where hopsflow will come in
• also: nice maintainable tooling would be good

DONE NMQSD

• nmqsd equation
• not much more

DONE HOPS

• hops for multiple baths
• with new normalization

Bath Energy

DONE Formulas and Generalizations

• short derivation
• explain hurdles
• explain nonzero

DONE Interaction Energy

• straight forward -> remove dot

Demonstration one Bath

• explain model
• show some plots of the single qubit

Demonstration two Baths

• explain model
• show some plots of the double qubit
• note that flow converges faster than system energy

Analytical Verification

Model

• for one HO
• give valentin credit

Solution

• give valentin credit
• general idea
• formula for laplace transform of exponential
• trick with mathematica

Comparison

• one bath case for zero and nonzero temperature

Quick review of the two HO case

• explain that generalization is straight forward
• problems with numerics (sensitive to bcf)
• show comparison

HOPS Related, No Details

• code and docs and tests and poetry
• auto norm
• new cutoff
• tree hops

Outlook

• concrete models

  • sweep
  • three baths
• steady state detection -> pseudo eigenstates?

• higher order moments of bath energy

  • may bring insight into role of aux states
  • better cutoff for multi bath (not as many cross terms)
• concrete importance sampling