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Short-time decay of the Loschmidt echo.
1Departamento de Física, J. J. Giambiagi, FCEN, UBA, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina. wisniacki@df.uba.ar
Summary
The Loschmidt echo reveals quantum evolution sensitivity. In chaotic systems, its short-time decay is governed by the local density of states width, offering insights into quantum dynamics.
Area of Science:
- Quantum mechanics
- Statistical mechanics
- Chaos theory
Background:
- The Loschmidt echo quantifies the sensitivity of quantum evolutions to perturbations.
- Understanding its behavior in classically chaotic systems is crucial for quantum information science.
Purpose of the Study:
- To investigate the short-time decay of the Loschmidt echo in classically chaotic systems.
- To identify the key physical parameter governing this decay regime.
Main Methods:
- Application of perturbation theory to analyze the Loschmidt echo.
- Numerical simulations using a two-dimensional chaotic billiard system.
- Investigation of various perturbation types and initial conditions.
Main Results:
- The characteristic time of the short-time decay is determined by the inverse of the local density of states width.
- Sub-Planck structures in time evolution influence the decay dynamics.
- Numerical results validate the theoretical predictions.
Conclusions:
- The local density of states width provides a robust descriptor for the Loschmidt echo's short-time decay in chaotic systems.
- The study highlights the interplay between system chaos, perturbations, and quantum interference effects.