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Related Experiment Videos

Multiple-time correlation functions for non-markovian interaction: beyond the quantum regression theorem.

Daniel Alonso1, Inés de Vega

  • 1Departamento de Física Fundamental y Experimental, Electrónica y Sistemas, Universidad de La Laguna, La Laguna 38203, Tenerife, Spain.

Physical Review Letters
|August 11, 2005
PubMed
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We derived a dynamical equation for the reduced propagator, crucial for calculating multiple-time correlation functions (MTCFs). The quantum regression theorem is generally not satisfied, even in the weak-coupling limit.

Area of Science:

  • Quantum mechanics
  • Statistical physics
  • Open quantum systems

Background:

  • Calculating multiple-time correlation functions (MTCFs) is essential for understanding open quantum systems.
  • The behavior of quantum systems interacting with their environment is complex, especially when the environment is not in a vacuum state initially.

Purpose of the Study:

  • Derive the dynamical equation for the reduced propagator.
  • Investigate the evolution of MTCFs under weak-coupling conditions.
  • Examine the validity of the quantum regression theorem in this context.

Main Methods:

  • Derivation of the dynamical equation for the reduced propagator.
  • Analysis of MTCF evolution in the weak-coupling limit.
  • Exact model solution and numerical integration for a system coupled to a thermal environment.

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Main Results:

  • The dynamical equation for the reduced propagator was successfully derived.
  • The quantum regression theorem was shown to be generally not satisfied.
  • Illustrative examples, including an exact model and numerical simulations, were presented.

Conclusions:

  • The derived reduced propagator provides a new tool for studying open quantum systems.
  • The breakdown of the quantum regression theorem highlights the complexities of quantum dynamics in non-vacuum environments.
  • The findings offer insights into the behavior of quantum systems interacting with thermal environments.