Universal spectral correlations in interacting chaotic few-body quantum systems.

The emergence of random matrix spectral correlations in interacting quantum systems is a defining feature of quantum chaos. We study such correlations in terms of the spectral form factor and its moments in interacting chaotic few- and many-body systems, modeled by suitable random-matrix ensembles. We obtain the spectral form factor exactly for large Hilbert space dimension.

Characterizing quantum chaoticity of kicked spin chains.

Quantum many-body systems are commonly considered as quantum chaotic if their spectral statistics, such as the level spacing distribution, agree with those of random matrix theory (RMT). Using the example of the kicked Ising chain we demonstrate that even if both level spacing distribution and eigenvector statistics agree well with random matrix predictions, the entanglement entropy deviates from the expected RMT behavior, i.e.

Fast bit flipping based on stability transition of coupled spins.

A bipartite spin system is proposed for which a fast transfer from one defined state into another exists. For sufficient coupling between the spins, this implements a bit-flipping mechanism, which is much faster than that induced by tunneling. The states correspond in the semiclassical limit to equilibrium points with a stability transition from elliptic-elliptic stability to complex instability for increased coupling.

Quantum coherence controls the nature of equilibration and thermalization in coupled chaotic systems.

A bipartite system whose subsystems are fully quantum chaotic and coupled by a perturbative interaction with a tunable strength is a paradigmatic model for investigating how isolated quantum systems relax toward an equilibrium. It is found that quantum coherence of the initial product states in the energy eigenbasis of the subsystems-quantified by the off-diagonal elements of the subsystem density matrices-can be viewed as a resource for equilibration and thermalization as manifested by the entanglement generated. Results are given for four distinct perturbation strength regimes, the ultraweak, weak, intermediate, and strong regimes.

Entanglement in coupled kicked tops with chaotic dynamics.

The entanglement of eigenstates in two coupled, classically chaotic kicked tops is studied in dependence of their interaction strength. The transition from the noninteracting and unentangled system toward full random matrix behavior is governed by a universal scaling parameter. Using suitable random matrix transition ensembles we express this transition parameter as a function of the subsystem sizes and the coupling strength for both unitary and orthogonal symmetry classes.