Related papers: Semiclassical calculation of time delay statistics…
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…
We theoretically and experimentally establish a connection between linearly chirped pulse propagation properties and the complex generalization of Wigner-Smith time delay for both transmitted and reflected pulses in linear and dispersive…
The fundamental correspondence between quantum chaotic single-particle systems and random matrix theory is well-understood via periodic orbit theory. In contrast, we show that many-body systems with explicit subsystem structure possess…
Time-symmetric quantum mechanics can be described in the usual Weyl--Wigner--Moyal formalism (WWM) by using the properties of the Wigner distribution, and its generalization, the cross-Wigner distribution. The use of the latter makes clear…
We consider quantum systems with a chaotic classical limit that are perturbed by a point-like scatterer. The spectral form factor K(tau) for these systems is evaluated semiclassically in terms of periodic and diffractive orbits. It is shown…
The statistics of S-matrix fluctuations are numerically investigated on a model for irregular quantum scattering in which a classical chaotic diffusion takes place within the interaction region. Agreement with various random-matrix…
The main purpose of these lectures is to discuss briefly recent methods of calculation of statistical properties of quantum eigenvalues for chaotic systems based on semi-classical trace formulas. Under the assumption that periodic orbit…
The intuitive classical space-time picture breaks down in quantum gravity, which makes a comparison and the development of semiclassical techniques quite complicated. Using ingredients of the group averaging method to solve constraints one…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
We present a step by step introduction to the notion of time-delay in classical and quantum mechanics, with the aim of clarifying its foundation at a conceptual level. In doing so, we motivate the introduction of the concepts of "fuzzy" and…
While plenty of results have been obtained for single-particle quantum systems with chaotic dynamics through a semiclassical theory, much less is known about quantum chaos in the many-body setting. We contribute to recent efforts to make a…
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…
Starting from the Schr\"odinger-equation of a composite system, we derive unified dynamics of a classical harmonic system coupled to an arbitrary quantized system. The classical subsystem is described by random phase-space coordinates…
We describe a semiclassical method to calculate universal transport properties of chaotic cavities. While the energy-averaged conductance turns out governed by pairs of entrance-to-exit trajectories, the conductance variance, shot noise and…
We investigate the behavior of weak localization, conductance fluctuations, and shot noise of a chaotic scatterer in the semiclassical limit. Time resolved numerical results, obtained by truncating the time-evolution of a kicked quantum map…
We construct a class of systems for which quantum dynamics can be expanded around a mean field approximation with essentially classical content. The modulus of the quantum overlap of mean field states naturally introduces a classical…
We consider the time discretization based on Lie-Trotter splitting, for the nonlinear Schrodinger equation, in the semi-classical limit, with initial data under the form of WKB states. We show that both the exact and the numerical solutions…
We present a comprehensive semiclassical investigation of the three-dimensional Sinai billiard, addressing a few outstanding problems in "quantum chaos". We were mainly concerned with the accuracy of the semiclassical trace formula in two…
We introduce a complex generalization of Wigner time delay $\tau$ for sub-unitary scattering systems. Theoretical expressions for complex time delay as a function of excitation energy, uniform and non-uniform loss, and coupling, are given.…
This is the first of two subsequent publications where the probability distribution of delay-times in scattering of wave packets is discussed. The probability distribution is expressed in terms of the on-shell scattering matrix, the…