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Short-time Loschmidt gap in dynamical systems with critical chaos
Carl T West1, Tomaz Prosen, Tsampikos Kottos
1Department of Physics, Wesleyan University, Middletown, Connecticut 06459, USA.
Summary
The Loschmidt echo in critical chaotic systems reveals distinct classical and quantum behaviors. Quantum echoes are insensitive to potential singularity, unlike classical echoes, due to diffraction effects.
Area of Science:
- Physics
- Quantum Mechanics
- Dynamical Systems
Background:
- The Loschmidt echo (F(t)) measures the sensitivity of quantum systems to perturbations.
- Critical chaos describes dynamical systems exhibiting complex, unpredictable behavior near a critical point.
- Understanding the interplay between classical and quantum dynamics in chaotic systems is crucial.
Purpose of the Study:
- To investigate the Loschmidt echo in dynamical systems with critical chaos.
- To analyze the behavior of the classical and quantum echo gaps in a prototype model.
- To identify the underlying mechanisms causing discrepancies between classical and quantum dynamics.
Main Methods:
- Utilizing a kicked rotor model with a singular potential.
- Analyzing the scaling laws of the classical echo gap (F_g) with respect to potential singularity (alpha) and initial phase-space density spread (eta).
- Comparing classical results with quantum echo gap scaling and random matrix theory models.
Main Results:
- The classical echo gap (F_g) exhibits scaling dependent on the potential singularity order (alpha).
- The quantum echo gap is insensitive to alpha, following a different scaling law.
- A quantum-classical discrepancy was identified and attributed to strong diffraction effects.
Conclusions:
- Diffraction effects significantly influence quantum dynamics in critical chaotic systems.
- Random matrix theory effectively models the quantum echo behavior in these systems.
- The study highlights fundamental differences in how classical and quantum mechanics describe chaotic dynamics.
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