Related papers: Random Matrices and Chaos in Nuclear Physics
In many situations, the statistical properties of wave systems with chaotic classical limits are well-described by random matrix theory. However, applications of random matrix theory to scattering problems require introduction of system…
A brief review of the supersymmetry method and its application to mesoscopic physics and quantum chaos is given. Alghough a non-linear supermatrix $% \sigma $-model in this approach was derived from models with random potential, it is…
We provide compelling evidence for the presence of quantum chaos in the unitary part of Shor's factoring algorithm. In particular we analyze the spectrum of this part after proper desymmetrization and show that the fluctuations of the…
We review the random matrix theory describing elastic scattering through zero-dimensional ballistic cavities (having chaotic classical dynamics) and quasi-one dimensional disordered systems. In zero dimension, general symmetry…
This paper addresses the three following questions. (i) How the structures of group and of chain of groups enter nuclear, atomic and molecular spectroscopy? (ii) How these structures can be exploited, in a quantum- mechanical framework, in…
Scattering is an important phenomenon which is observed in systems ranging from the micro- to macroscale. In the context of nuclear reaction theory the Heidelberg approach was proposed and later demonstrated to be applicable to many chaotic…
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to…
The spectral problem for matrices with a block-hierarchical structure is often considered in context of the theory of complex systems. In the present article, a new class of matrices with a block-rectangular non-symmetric hierarchical…
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,…
Similarities between models of fragmenting nuclei and disordered systems in condensed matter suggest corresponding methods. Several theoretical models of fragmentation investigated in this fashion show marked differences, indicating…
To show the existence of precursor phenomena of the transition order$\ to$chaos in atomic nuclei a simple analysis has been made, based on a recent criterion proposed by Pavli\-chenkov. The basic idea is that nonlinear effects in rotational…
In this article, using the principles of Random Matrix Theory (RMT), we give a measure of quantum chaos by quantifying Spectral From Factor (SFF) appearing from the computation of two-point Out of Time Order Correlation function (OTOC)…
Classical random matrix ensembles were originally introduced in physics to approximate quantum many-particle nuclear interactions. However, there exists a plethora of quantum systems whose dynamics is explained in terms of few-particle…
The Projected Shell Model with zero-, two- and four-quasiparticle configurations is used to investigate the level statistics, i.e. chaoticity, of high spin spectroscopy. The model can describe many high spin phenomena and with the present…
The most general and versatile defining feature of quantum chaotic systems is that they possess an energy spectrum with correlations universally described by random matrix theory (RMT). This feature can be exhibited by systems with a well…
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…
In quantum chaos, the spectral statistics generally follows the predictions of Random Matrix Theory (RMT). A notable exception is given by scar states, that enhance probability density around unstable periodic orbits of the classical…
Quantum chaotic systems are conjectured to display a spectrum whose fine-grained features (gaps and correlations) are well described by Random Matrix Theory (RMT). We propose and develop a complementary version of this conjecture: quantum…
We study the conditions under which the nucleons inside a deformed nucleus can undergo chaotic motion. To do this we perform self-consistent calculations in semiclassical approximation utilizing a multipole-multipole interaction of the…
The onset of chaos and the mechanism of rotational damping are studied in an exactly soluble particle-rotor model. It is shown that the degree of chaoticity as inferred from the statistical measures is closely related to the onset of…