Quantum fidelity decay in quasi-integrable systems

Area of Science:

• Quantum mechanics
• Statistical physics
• Chaos theory

Background:

• Understanding quantum fidelity decay is crucial for quantum information processing and quantum chaos.
• Quasi-integrable systems offer a unique regime to study the transition between regular and chaotic dynamics.
• The relationship between classical and quantum dynamics in these systems remains an active area of research.

Purpose of the Study:

• To investigate the influence of initial coherent state location on quantum fidelity decay in quasi-integrable systems.
• To differentiate fidelity decay behaviors based on the nature of perturbations (frequency vs. shape changes).
• To explore the impact of perturbation strength on fidelity decay dynamics.

Main Methods:

• Numerical simulations of quasi-integrable systems.
• Analysis of quantum fidelity decay rates.
• Comparison with classical fidelity behavior.
• Examination of the energy spectrum of initial states.

Main Results:

• Quantum fidelity decay is strongly dependent on the initial state's position in classical phase space.
• Gaussian decay is observed when perturbations alter orbit frequencies; power-law decay occurs when orbit shapes are changed.
• Decay rates are sensitive to initial state location for both decay behaviors.
• Stronger perturbations can unexpectedly lead to higher fidelity than weaker ones for the same perturbation type.

Conclusions:

• The location of the initial coherent state is a critical factor governing quantum fidelity decay in quasi-integrable systems.
• Distinct perturbation types induce characteristic fidelity decay patterns (Gaussian vs. power-law).
• The interplay between perturbation strength and initial state properties can lead to non-intuitive fidelity outcomes.