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Loschmidt echo and time reversal in complex systems.

Arseni Goussev1, Rodolfo A Jalabert2, Horacio M Pastawski3

  • 1Department of Mathematics and Information Sciences, Northumbria University, Newcastle Upon Tyne NE1 8ST, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|May 4, 2016
PubMed
Summary
This summary is machine-generated.

The Loschmidt echo quantifies the stability of quantum evolution under perturbations in complex systems. This phenomenon, observed in various physics fields, is crucial for understanding imperfect time-reversal procedures.

Keywords:
chaosclassicalquantumreversibilitysemiclassical

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Area of Science:

  • Physics
  • Quantum Mechanics
  • Complex Systems

Background:

  • Echoes are fundamental in acoustics, optics, condensed matter, cold atoms, and geophysics.
  • Echo phenomena underpin techniques like nuclear magnetic resonance and photon echo.
  • Complex systems (chaotic, disordered, many-body) exhibit unique echo effects.

Purpose of the Study:

  • To introduce and define the Loschmidt echo.
  • To quantify the revival in quantum systems under imperfect time-reversal.
  • To characterize quantum evolution stability against perturbations.

Main Methods:

  • Analysis of echo phenomena in complex quantum systems.
  • Application of imperfect time-reversal procedures.
  • Quantification of quantum evolution stability.

Main Results:

  • The Loschmidt echo serves as a measure of quantum system stability.
  • It quantifies the revival of a quantum state after perturbation.
  • The concept is applicable to diverse complex physical systems.

Conclusions:

  • The Loschmidt echo is a key concept for studying quantum system dynamics.
  • It provides insights into the effects of perturbations on quantum evolution.
  • Recent research has significantly advanced the understanding and application of the Loschmidt echo.