Related papers: Universal Parametric Correlations of Eigenfunction…
In a previous Letter [Phys. Rev. Lett. 77, 4158 (1996)], a new correlation measure was introduced that sensitively probes phase space localization properties of eigenstates. It is based on a system's response to varying an external…
It is shown that the Husimi representations of chaotic eigenstates are strongly correlated along classical trajectories. These correlations extend across the whole system size and, unlike the corresponding eigenfunction correlations in…
Electronic transport through chaotic quantum dots exhibits universal, system independent, properties, consistent with random matrix theory. The quantum transport can also be rooted, via the semiclassical approximation, in sums over the…
Chaotic systems exhibit rich quantum dynamical behaviors ranging from dynamical localization to normal diffusion to ballistic motion. Dynamical localization and normal diffusion simulate electron motion in an impure crystal with a vanishing…
The complicated interactions in presence of disorder lead to a correlated randomization of states. The Hamiltonian as a result behaves like a multi-parametric random matrix with correlated elements. We show that the eigenvalue correlations…
We consider scenarios where the dynamics of a quantum system are partially determined by prior local measurements of some interacting environmental degrees of freedom. The resulting effective system dynamics are described by a disordered…
Quantum-chaotic systems exhibit several universal properties, ranging from level repulsion in the energy spectrum to wavefunction delocalization. On the other hand, if wavefunctions are localized, the levels exhibit no level repulsion and…
While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…
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…
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 in interacting chaotic few- and many-body systems,…
In quantum/wave systems with chaotic classical analogs, wavefunctions evolve in highly complex, yet deterministic ways. A slight perturbation of the system, though, will cause the evolution to diverge from its original behavior increasingly…
The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…
We investigate the spectral properties of chaotic quantum graphs. We demonstrate that the `energy'--average over the spectrum of individual graphs can be traded for the functional average over a supersymmetric non--linear $\sigma$--model…
Having spectral correlations that, over small enough energy scales, are described by random matrix theory is regarded as the most general defining feature of quantum chaotic systems as it applies in the many-body setting and away from any…
Quantum counterparts of certain simple classical systems can exhibit chaotic behaviour through the statistics of their energy levels and the irregular spectra of chaotic systems are modelled by eigenvalues of infinite random matrices. We…
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for…
A general stability analysis is presented for the determination of the transition from incoherent to coherent behavior in an ensemble of globally coupled, heterogeneous, continuous-time dynamical systems. The formalism allows for the…
Collective behavior is studied in globally coupled maps with distributed nonlinearity. It is shown that the heterogeneity enhances regularity in the collective dynamics. Low-dimensional quasiperiodic motion is often found for the…
The supersymmetry method has proven to be a very powerful tool of study of the statistical properties of energy levels and eigenfunctions in disordered and chaotic systems. The aim of these lectures is to present a tutorial introduction to…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…