Mesoscopic Fluctuations of the Loschmidt Echo

Abstract

We investigate the time-dependent variance of the fidelity with which an initial narrow wavepacket is reconstructed after its dynamics is time-reversed with a perturbed Hamiltonian. In the semiclassical regime of perturbation, we show that the variance first rises algebraically up to a critical time $t_c$, after which it decays. To leading order in the effective Planck's constant ${\hslash }_{\mathrm{eff}}$, this decay is given by the sum of a classical term $\simeq \exp [-2\lambda t]$, a quantum term $\simeq 2{\hslash }_{\mathrm{eff}}\exp [-\Gamma t]$ and a mixed term $\simeq 2\exp [-(\Gamma +\lambda )t]$. Compared to the behavior of the average fidelity, this allows for the extraction of the classical Lyapunov exponent $\lambda$ in a larger parameter range. Our results are confirmed by numerical simulations.

Final, extended version; to appear in Physical Review E

References in corpus (4)

• A random matrix formulation of fidelity decay
• Stability of Quantum Motion: Beyond Fermi-golden-rule and Lyapunov decay
• Anomalous power law of quantum reversibility for classically regular dynamics
• Loschmidt echo for a chaotic oscillator

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• Fidelity and quantum chaos in the mesoscopic device for the Josephson flux qubit
• Uniform Semiclassical Approach to Fidelity Decay: from Weak to Strong Perturbation
• Loschmidt echo for local perturbations: non-monotonous cross-over from the Fermi-golden-rule to the escape-rate regime
• Loschmidt echo decay from local boundary perturbations
• Loschmidt echo in quantum maps: the elusive nature of the Lyapunov regime
• Semiclassical propagation of coherent states using complex and real trajectories
• Long-time saturation of the Loschmidt echo in quantum chaotic billiards
• Fractal Fidelity as a signature of Quantum Chaos
• Quantum non-Markovian behavior at the chaos border