Thomas H. Seligman

Dynamics of Loschmidt echoes and fidelity decay

Fidelity serves as a benchmark for the reliability in quantum information processes, and has recently attracted much interest as a measure of the susceptibility of dynamics to perturbations. A rich variety of regimes for fidelity decay have emerged. The purpose of the present review is to describe these regimes, to give the theory that supports them, and to show some important applications and experiments. While we mention several approaches we use time correlation functions as a backbone for the discussion. Vaniceks uniform approach to semiclassics and random matrix theory provides important alternatives or complementary aspects. Other methods will be mentioned as we go along. Recent experiments in micro-wave cavities and in elastodynamic systems as well as suggestions for experiments in quantum optics shall be discussed.

TRANSITION FROM LOCALIZED TO EXTENDED EIGENSTATES IN THE ENSEMBLE OF POWER-LAW RANDOM BANDED MATRICES

We study statistical properties of the ensemble of large

Identifying States of a Financial Market

N\times N

Canonical Transformations and the Radial Oscillator and Coulomb Problems

random matrices whose entries

Information theory and statistical nuclear reactions. I. General theory and applications to few-channel problems☆

H_{ij}

Fourier's law for quasi-one-dimensional chaotic quantum systems

decrease in a power-law fashion

First experimental realization of the Dirac oscillator.

H_{ij}\sim|i-j|^{-\alpha}

Canonical transformations to action and angle variables and their representations in quantum mechanics

. Mapping the problem onto a nonlinear

Spectral fluctuation properties of Hamiltonian systems: the transition region between order and chaos

\sigma-

Dynamics of a Dirac oscillator coupled to an external field: a new class of solvable problems

model with non-local interaction, we find a transition from localized to extended states at