相关论文: Semiclassical Trace Formulae and Eigenvalue Statis…

The semi-quantal dynamics is applied to investigate the influence of quantum fluctuations on problems in classical chaos through intermittency involving bifurcations. The results of the numerical calculations indicate that quantum effects…

Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…

To study electronic transport through chaotic quantum dots, there are two main theoretical approachs. One involves substituting the quantum system with a random scattering matrix and performing appropriate ensemble averaging. The other…

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 consider the characteristic polynomials of random unitary matrices $U$ drawn from various circular ensembles. In particular, the statistics of the coefficients of these polynomials are studied. The variances of these ``secular…

We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as…

We study multifractal properties of wave functions for a one-parameter family of quantum maps displaying the whole range of spectral statistics intermediate between integrable and chaotic statistics. We perform extensive numerical…

Both the topics of entanglement and particle statistics have aroused enormous research interest since the advent of quantum mechanics. Using two pairs of entangled particles we show that indistinguishability enforces a transfer of…

We study the level statistics of an interacting multi-qubit system, namely the kicked Ising spin chain, in the regime of quantum chaos. Long range quasi-energy level statistics show effects analogous to the ones observed in semi-classical…

We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their…

Periodic orbit quantization requires an analytic continuation of non-convergent semiclassical trace formulae. We propose two different methods for semiclassical quantization. The first method is based upon the harmonic inversion of…

We prove scalar and operator-valued Khintchine inequalities for mixtures of free and tensor-independent semicircle variables, interpolating between classical and free Khintchine-type inequalities. Specifically, we characterize the norm of…

In this thesis, we describe some recent results obtained in the analysis of two-dimensional quantum field theories by means of semiclassical techniques. These achievements represent a natural development of the non-perturbative studies…

We consider quantum walks on a finite graphs to which infinite tails are attached. We explore how the propagating and bound states depend on the structure of the finite graph. The S-matrix for such graphs is defined. Its unitarity is proved…

We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…

It was recently conjectured that 1/f noise is a fundamental characteristic of spectral fluctuations in chaotic quantum systems. This conjecture is based on the behavior of the power spectrum of the excitation energy fluctuations, which is…

We extend the application of the concept of structural invariance to bounded time independent systems. This concept, previously introduced by two of us to argue that the connection between random matrix theory and quantum systems with a…

We introduce a semiclassical quantization method which is based on a stroboscopic description of the classical and the quantum flows. We show that this approach emerges naturally when one is interested in extracting the energy spectrum…

Turbulence is a complex spatial and temporal structure created by the strong non-linear dynamics of fluid flows at high Reynolds numbers. Despite being an ubiquitous phenomenon that has been studied for centuries, a full understanding of…

States supported by chaotic open quantum systems fall into two categories: a majority showing instantaneous ballistic decay, and a set of quantum resonances of classically vanishing support in phase space. We present a theory describing…