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Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown
Pinquan Qin1, Qian Wang, Wen-Ge Wang
1Department of Modern Physics, University of Science and Technology of China, Hefei 230026, China.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 2, 2013
Summary
Semiclassical predictions for quantum Loschmidt echo decay remain valid even in deep quantum regimes. This holds true particularly when perturbation strength aligns with the Fermi-Golden-Rule, challenging traditional semiclassical validity assumptions.
Area of Science:
- Quantum mechanics
- Statistical physics
- Computational physics
Background:
- Semiclassical approximations are typically confined to the semiclassical regime.
- The validity of these approximations beyond this regime, especially with increased effective Planck constants, is an open question.
Purpose of the Study:
- To investigate the extent to which semiclassical predictions remain accurate in deep quantum regimes.
- To explore the behavior of the quantum Loschmidt echo decay under varying effective Planck constants.
Main Methods:
- Numerical simulations were employed to study the quantum Loschmidt echo decay.
- The study focused on chaotic systems (sawtooth and kicked rotator models) and a critical system (1D Ising chain in a transverse field).
Main Results:
- Semiclassical predictions demonstrated surprising accuracy even in deep quantum regions.
- The validity was particularly pronounced for perturbation strengths within the Fermi-Golden-Rule regime.
Conclusions:
- Semiclassical methods can offer reliable insights into quantum phenomena beyond their expected domain of validity.
- The Fermi-Golden-Rule regime appears crucial for extending the applicability of semiclassical approximations in quantum systems.
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