Exact pair correlation of the one-dimensional quantum gas with 1/r2 repulsion derived from the sympletic Dyson ensemble

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.

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.

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.

Dynamic structure factor of the Calogero-Sutherland model

We evaluate the dynamic structure factor S(q, omega) of a one-dimensional quantum Hamiltonian with the inverse-square interaction (Calogero-Sutherland model). For a fixed small q, the structure factor differs from zero in a finite interval of frequencies of the width deltaomega proportional to q2/m. At the borders of this interval S(q, omega) exhibits power-law singularities with exponents depending on the interaction strength. The singularities are similar in origin to the well-known Fermi-edge singularity in the x-ray absorption spectra of metals.