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Semiclassical evaluation of quantum fidelity.
1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
Summary
We developed a tractable semiclassical method to calculate quantum fidelity decay in chaotic systems. This new approach provides accurate results and allows direct testing of analytical theories.
Area of Science:
- Quantum mechanics
- Classical chaos
- Computational physics
Background:
- Evaluating quantum fidelity decay (Loschmidt echo) in classically chaotic systems is computationally challenging.
- Previous methods were considered intractable for such systems.
Purpose of the Study:
- To present a numerically feasible semiclassical (SC) method for evaluating quantum fidelity decay.
- To demonstrate the tractability and accuracy of this SC method.
Main Methods:
- Developed a uniform semiclassical (SC) expression.
- Applied Monte Carlo evaluation techniques.
- Analyzed the standard map in Fermi-golden-rule and Lyapunov regimes.
Main Results:
- The uniform SC expression is tractable and yields remarkably accurate numerical results.
- The method remains accurate even with a vast number of semiclassical contributions (10^70).
- The SC expression explicitly includes components of analytical theories, enabling direct testing of approximations.
Conclusions:
- The presented SC method offers a feasible and accurate way to study quantum fidelity decay in chaotic systems.
- This approach facilitates direct validation of theoretical approximations in quantum dynamics.
- The classical perturbation approximation's validity is extended, simplifying the 'diagonal approximation'.