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Quantum Maps with Memory from Generalized Lindblad Equation.

Vasily E Tarasov1,2

  • 1Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991 Moscow, Russia.

Entropy (Basel, Switzerland)
|April 30, 2021
PubMed
Summary
This summary is machine-generated.

We developed an exactly solvable model for non-Markovian dynamics in open quantum systems, incorporating memory effects and environmental kicks. This approach uses fractional calculus to describe quantum systems with power-law fading memory.

Keywords:
Lindblad equationdiscrete map with memoryfractional derivativefractional differential equationfractional dynamicsfractional integralnon-Markovian quantum dynamicsopen quantum systempower-law memory

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Area of Science:

  • Quantum Physics
  • Non-Markovian Dynamics
  • Open Quantum Systems

Background:

  • Traditional models often assume Markovian dynamics, neglecting system memory.
  • Open quantum systems interacting with their environment exhibit complex behaviors, including memory effects.
  • Periodic environmental interactions (kicks) further complicate system dynamics.

Purpose of the Study:

  • To propose an exactly solvable model for non-Markovian dynamics in open quantum systems.
  • To incorporate power-law fading memory and periodic environmental kicks into quantum dynamics.
  • To generalize the Lindblad equation for systems with memory.

Main Methods:

  • Generalization of the Lindblad equation using fractional calculus (Caputo derivatives of non-integer orders).
  • Modeling power-law fading memory in open quantum systems.
  • Derivation of discrete-time quantum maps from generalized Lindblad equations without approximations.
  • Representation of periodic kicks using Dirac delta-functions.

Main Results:

  • An exactly solvable model for non-Markovian quantum dynamics with memory and kicks was developed.
  • Generalized Lindblad equations incorporating power-law memory were formulated.
  • Exact solutions for coordinate and momentum operators were obtained.
  • Discrete-time quantum maps (linear and nonlinear) were derived from the generalized equations.

Conclusions:

  • The proposed model accurately describes non-Markovian quantum dynamics in systems with memory and periodic kicks.
  • Fractional calculus provides a powerful tool for modeling quantum systems with memory effects.
  • The derived discrete-time quantum maps offer a precise and efficient way to study these complex systems.