Related papers: Semiclassical matrix elements for a chaotic propag…
Matrix configurations coming from matrix models comprise many important aspects of modern physics. They represent special quantum spaces and are thus strongly related to noncommutative geometry. In order to establish a semiclassical limit…
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…
We use a continuous-time path integral to obtain the semiclassical propagator for minimal-spread spin coherent states. We pay particular attention to the ``extra phase'' discovered by Solari and Kochetov, and show that this correction is…
We have studied two complementary decoherence measures purity and fidelity for a generic diffusive noise in two different chaotic systems (the baker and the cat maps). For both quantities, we have found classical structures in quantum…
We consider quantum decay and photofragmentation processes in open chaotic systems in the semiclassical limit. We devise a semiclassical approach which allows us to consistently calculate quantum corrections to the classical decay to high…
We investigate the spectral statistics of chaotic quasi one dimensional systems such as long wires. To do so we represent the spectral correlation function $R(\epsilon)$ through derivatives of a generating function and semiclassically…
The fixed energy scattering matrix is defined on a perturbed stratified medium, and for a class of perturbations, its main part is shown to be a Fourier integral operator on the sphere at infinity. This is facilitated by developing a…
We construct Arnol'd cat map lattice field theories in phase space and configuration space. In phase space we impose that the evolution operator of the linearly coupled maps be an element of the symplectic group, in direct generalization of…
We introduce the notion of multi-dimensional chaos that applies to processes described by erratic functions of several dynamical variables. We employ this concept in the interpretation of classical and quantum scattering off a pinball…
The statistical properties of the quantum chaotic spectra have been studied, so far, only up to the second order correlation effects. The numerical as well as the analytical evidence that random matrix theory can successfully model the…
We calculate within a semiclassical approximation the autocorrelation function of cross sections. The starting point is the semiclassical expression for the diagonal matrix elements of an operator. For general operators with a smooth…
In this article we extend previous semiclassical studies by including more general perturbative potentials of the harmonic oscillator in arbitrary spatial dimensions. Our starting point is a radial harmonic potential with an arbitrary even…
The quantum ratchet effect in fully chaotic systems is approached by studying, for the first time, \emph{statistical} properties of the ratchet current over well-defined sets of initial states. Natural initial states in a semiclassical…
We use random matrix theory to explore late-time chaos in supersymmetric quantum mechanical systems. Motivated by the recent study of supersymmetric SYK models and their random matrix classification, we consider the Wishart-Laguerre unitary…
We study the relationship of the spectral form factor with quantum as well as classical probabilities to return. Defining a quantum return probability in phase space as a trace over the propagator of the Wigner function allows us to…
We study the stability of classical structures in chaotic systems when a dissipative quantum evolution takes place. We consider a paradigmatic model, the quantum baker map in contact with a heat bath at finite temperature. We analyze the…
This work represents a first systematic attempt to create a common ground for semi-classical and time-frequency analysis. These two different areas combined together provide interesting outcomes in terms of Schr\"odinger type equations.…
We present a semiclassical theory for the scattering matrix ${\cal S}$ of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multi-bounce expansion, we show how the Liouville conservation…
We study the quantum probability to survive in an open chaotic system in the framework of the van Vleck-Gutzwiller propagator and present the first such calculation that accounts for quantum interference effects. Specifically we calculate…
Characteristic functions contain complete information about all the moments of a classical distribution and the same holds for the Fourier transform of the Wigner function: a quantum characteristic function, or the chord function. However,…