Quantum corrections to fidelity decay in chaotic systems

Parametric number covariance in quantum chaotic spectra

We study spectral parametric correlations in quantum chaotic systems and introduce the number covariance as a measure of such correlations. We derive analytic results for the classical random matrix ensembles using the binary correlation method and obtain compact expressions for the covariance. We illustrate the universality of this measure by presenting the spectral analysis of the quantum kicked rotors for the time-reversal invariant and time-reversal noninvariant cases. A local version of the parametric number variance introduced earlier is also investigated.

Scattering approach to fidelity decay in closed systems and parametric level correlations

Based on an exact analytical approach to describe scattering fidelity experiments [Köber et al., Phys. Rev. E 82, 036207 (2010)], we obtain an expression for the fidelity amplitude decay of quantum chaotic or diffusive systems under arbitrary Hermitian perturbations. This allows us to rederive previous separately obtained results in a simpler and unified manner, as is shown explicitly for the case of a global perturbation. The general expression is also used to derive a so far unpublished exact analytical formula for the case of a moving S-wave scatterer. In the second part of the paper, we extend a relation between fidelity decay and parametric level correlations from the universal case of global perturbations to an arbitrary combination of global and local perturbations. Thereby, the relation becomes a versatile tool for the analysis of unknown perturbations.

Semiclassical approach to the quantum Loschmidt echo in deep quantum regions: from validity to breakdown

Semiclassical results are usually expected to be valid in the semiclassical regime. An interesting question is, in models in which appropriate effective Planck constants can be introduced, to what extent will a semiclassical prediction stay valid when the effective Planck constant is increased? In this paper, we numerically study this problem, focusing on semiclassical predictions for the decay of the quantum Loschmidt echo in deep quantum regions. Our numerical simulations, carried out in the chaotic regime in the sawtooth model and in the kicked rotator model and also in the critical region of a one-dimensional Ising chain in transverse field, show that the semiclassical predictions may work even in deep quantum regions, particularly for perturbation strength in the so-called Fermi-Golden-Rule regime.

Lyapunov decoherence rate in classically chaotic systems

We provide a path integral treatment of the decoherence process induced by a heat bath on a single particle whose dynamics is classically chaotic and show that the decoherence rate is given by the Lyapunov exponent. The loss of coherence is charaterized by the purity, which is calculated semiclassically within diagonal approximation, when the particle initial state is a single Gaussian wave packet. The calculation is performed for weak dissipation and in the high-temperature limit. This situation allows us to simplify the heat bath description to a single random potential. Although the dissipative term is neglected in such approach, the fluctuating one can be treated phenomenologically to fit with the above regime. Our results are therefore valid for times shorter than the inverse of the dissipation rate.

Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents

We study fidelity decay in classically chaotic microwave billiards for a local, pistonlike boundary perturbation. We experimentally verify a predicted nonmonotonic crossover from the Fermi golden rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation. In particular, we observe pronounced oscillations of the decay rate as a function of the piston position which quantitatively agree with corresponding theoretical results based on a refined semiclassical approach for local boundary perturbations.