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Published on: September 23, 2025
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A semiclassical reversibility paradox in simple chaotic systems.
1Max Planck Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187 Dresden, Germany Department of Physics and Astronomy, Washington State University, Pullman, WA 99164-2814, USA tomsovic@wsu.edu.
Summary
Semiclassical methods accurately approximate quantum dynamics using classical inputs, even for chaotic systems. This resolves the paradox of predicting stable quantum mechanics from unstable classical mechanics.
Area of Science:
- Quantum mechanics
- Classical mechanics
- Chaos theory
Background:
- Semiclassical methods offer accurate approximations in the short-wavelength limit of quantum dynamics.
- These approximations rely solely on classical dynamical input.
- Chaotic systems exhibit a short Ehrenfest time scale beyond which quantum and classical dynamics diverge.
Purpose of the Study:
- To resolve the paradox between the stability of quantum dynamics and the instability of classical dynamics.
- To explain how accurate semiclassical approximations of reversible quantum dynamics can be derived from irreversible classical dynamics.
Main Methods:
- Utilizing semiclassical methods for quantum dynamics approximations.
- Analyzing the behavior of chaotic systems and their Ehrenfest time scale.
- Investigating the properties of overlap integrals and their resistance to saddle point approximation.
Main Results:
- Semiclassical approximations remain valid far beyond the Ehrenfest time in chaotic systems.
- The inherent one-way structural stability of chaotic systems is crucial.
- The overlap integral's resistance to saddle point approximation is a key factor.
Conclusions:
- The apparent paradox is resolved by the unique properties of chaotic systems.
- Accurate semiclassical approximations bridge the gap between quantum reversibility and classical irreversibility.
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