Related papers: Random Matrices and Chaos in Nuclear Physics
Symmetry techniques based on group theory play a prominent role in the analysis of nuclear phenomena, and in particular in the understanding of observed regular patterns in nuclear spectra and selection rules for electromagnetic…
The nuclear shell model is a benchmark for the description of the structure of atomic nuclei. The magic numbers associated with closed shells have long been assumed to be valid across the whole nuclear chart. Investigations in recent years…
Random matrix theory is a well-developed area of probability theory that has numerous connections with other areas of mathematics and its applications. Much of the literature in this area is concerned with matrices that possess many exact…
We use semiconductors as an example to show that quantum chaos manifests itself in the energy spectrum of crystals. We analyze the {\it ab initio} band structure of silicon and the tight-binding spectrum of the alloy $Al_xGa_{1-x}As$, and…
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…
This is a comprehensive review of the random-matrix approach to the theory of phase-coherent conduction in mesocopic systems. The theory is applied to a variety of physical phenomena in quantum dots and disordered wires, including universal…
We study the interplay between ordered and chaotic dynamics at the critical point of a generic first-order quantum phase transition in the interacting boson model of nuclei. Classical and quantum analyses reveal a distinct behavior of the…
We study a quantum particle propagating through a ``quantum mechanically chaotic'' background, described by parametric random matrices with only short range spatial correlations. The particle is found to exhibit turbulent-like diffusion…
Various applications of quantum algebraic techniques in nuclear structure physics, such as the su$_q$(2) rotator model and its extensions, the use of deformed bosons in the description of pairing correlations, and the construction of…
The chaotic properties of simple two-dimensional rotation-translation models are explored and simulated. The models are given in difference equation forms, while the corresponding differential equations systems are studied and the resulting…
Understanding the far-from-equilibrium dynamics of dissipative quantum systems, where dissipation and decoherence coexist with unitary dynamics, is an enormous challenge with immense rewards. Often, the only realistic approach is to forgo a…
Manifestation of dynamical instability and Hamiltonian chaos in the fundamental near-resonant matter-radiation interaction has been found analitically and in a Monte Carlo simulation in the behavior of atoms moving in a rigid optical…
We discuss the phenomenon of universal fluctuations in mesoscopic systems and nuclei. For this purpose we use Random Matrix Theory (RMT). The statistical $S$-matrix is used to obtain the physical observables in the case of Quantum Dots,…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
Nuclear many-body theory is based on the tenet that nuclear systems can be accurately described as collections of point-like particles. This picture, while providing a remarkably accurate explanation of a wealth of measured properties of…
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
The properties of the pairing interaction in the shell model framework are considered with the aid of the exact numerical solution utilizing the quasispin symmetry. We emphasize the features which are out of reach for the usual approximate…
A widely accepted definition of ``quantum chaos'' is ``the behavior of a quantum system whose \emph{classical} \emph{limit is chaotic}''. The dynamics of quantum-chaotic systems is nevertheless very different from that of their classical…
Phase-coupled oscillators serve as paradigmatic models of networks of weakly interacting oscillatory units in physics and biology. The order parameter which quantifies synchronization was so far found to be chaotic only in systems with…
The catastrophe theory is applied to a nuclear cluster model and an effective model for QCD at low energy. The study of quantum phase transitions in the cluster model was considered in an earlier publication, but restricted to spherical…