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General Non-Markovian Quantum Dynamics.

Vasily E Tarasov1,2

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

Entropy (Basel, Switzerland)
|August 27, 2021
PubMed
Summary
This summary is machine-generated.

This study introduces a novel non-Markovian quantum theory using fractional calculus to model open quantum systems. It provides exactly solvable models for quantum dynamics with time non-locality.

Keywords:
fractional calculusfractional dynamicsgeneral fractional calculusnon-Hamiltonian systemsnon-Markovian quantum dynamicsnonlocality in timeopen quantum systems

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Area of Science:

  • Quantum Physics
  • Theoretical Chemistry
  • Mathematical Physics

Background:

  • Markovian quantum dynamics assumes memoryless evolution, which is insufficient for many open quantum systems.
  • Non-Markovian effects, characterized by memory and non-local temporal correlations, are crucial for accurate quantum system descriptions.
  • Existing models often struggle to capture the full complexity of non-Markovian quantum dynamics.

Purpose of the Study:

  • To propose a general framework for constructing non-Markovian quantum theories.
  • To develop a method for describing open quantum systems with general non-locality in time.
  • To provide exactly solvable models for non-Markovian quantum dynamics.

Main Methods:

  • Utilizing general fractional calculus to formulate non-Markovian equations for quantum observables and states.
  • Representing time non-locality using operator kernels of the Sonin type.
  • Generalizing Lindblad equations to incorporate non-locality and employing integro-differential equations with fractional derivatives and integrals.
  • Applying operational calculus for solving fractional differential equations.

Main Results:

  • A wide class of exactly solvable models for non-Markovian quantum dynamics has been established.
  • The proposed approach successfully describes open quantum systems with general forms of time non-locality.
  • Properties such as bi-positivity, complete positivity, and generalized dissipativity in non-Markovian dynamics are analyzed.
  • Exact solutions for quantum oscillator and two-level quantum systems with time non-locality are derived.

Conclusions:

  • The proposed general fractional calculus approach offers a powerful tool for constructing and analyzing non-Markovian quantum theories.
  • This framework allows for a more accurate description of open quantum systems exhibiting memory effects and temporal correlations.
  • The developed exactly solvable models provide valuable insights into the behavior of complex quantum systems.