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Updated: Mar 21, 2026
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Published on: May 27, 2021
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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.
Summary
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.
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.
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