Spectral correlation and response functions in quantum dots

Parametric correlations versus fidelity decay: the symmetry breaking case

We provide formulas for fidelity decay and parametric energy correlations for random matrix ensembles where time-reversal invariance of the original Hamiltonian is broken by the perturbation. Like in the case of a symmetry conserving perturbation a simple relation between both quantities exists. Fidelity freeze is observed for systems with even and odd spin.

Universal and Nonuniversal Dynamical Conductivity in Small Metallic Grains: An Ambivalent Role of T-Invariance at Finite Frequency

The idea of random matrix theory is applicable not only to the level statistics but also to various physical observables. Taking the dynamical conductivity in isolated quantum dots with diffusive dynamics, we investigate analytically intertwining effects of the time-reversal invariance, level repulsion and quantum interference. We clarify an ambivalent role of the time-reversal invariance at finite frequency by a new invariant analysis respecting the symmetry of the effective field theory. A subtlety of the operator insertion, and the fast-slow mode separation within the effective field description is pointed out.

Differential identities for parametric correlation functions in disordered systems

We derive a family of differential identities for parametric correlation functions in disordered systems by casting them as first- or second-order Ward identities of an associated matrix model. We show that this approach allows for a systematic classification of such identities, and provides a template for deriving higher-order results. We also reestablish and generalize some identities of this type which had been derived previously using a different method.

Surprising relations between parametric level correlations and fidelity decay

Relations among fidelity, cross-form-factor (i.e., parametric level correlations), and level velocity correlations are found both by deriving a Ward identity in a two-matrix model and by comparing exact results, using supersymmetry techniques, in the framework of random matrix theory. A power law decay near Heisenberg time, as a function of the relevant parameter, is shown to be at the root of revivals recently discovered for fidelity decay. For cross-form-factors the revivals are illustrated by a numerical study of a multiply kicked Ising spin chain.