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

Abstract

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 The general expression is also used to derive a so far unpublished exact analytical formula for the case of a moving S-wave scatterer.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.

Microwave experiments in the realm of fidelity

“…This result is valid for finite λt where λ → 0 and t → ∞. An exact result was obtained showing first a linear decay and then approaching (4.4) [59].…”

Parametric number covariance in quantum chaotic spectra

“…In these studies, analytic results for the density-density correlation function [7,8,17] are of fundamental importance, and they have been obtained using the supersymmetric nonlinear σ-model for disordered systems. Recent studies of the parametric spectral cross-form factor and the fidelity [20][21][22] reemphasized the importance of parametric correlations. In addition to the above references we also mention Ref.…”