arXiv subjects

B. D. Simons

Publications and source records attributed to B. D. Simons.

60 records · Page 4Linked to original sources

arXiv1996

Semiclassical Field Theory Approach to Quantum Chaos

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the form of a functional supermatrix nonlinear $σ$-model where the effective action involves the evolution operator of the classical dynamics. Low-lying degrees of freedom of the field theory are shown to reflect the irreversible classical dynamics describing relaxation of phase space distributions. The validity of this approach is investigated over a wide range of energy scales. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach accounts correctly for the short-time limit yielding results which agree with the diagonal approximation of periodic orbit theory.

cond-mat↗

arXiv1996

Quantum Chaos, Irreversible Classical Dynamics and Random Matrix Theory

The Bohigas--Giannoni--Schmit conjecture stating that the statistical spectral properties of systems which are chaotic in their classical limit coincide with random matrix theory is proved. For this purpose a new semiclassical field theory for individual chaotic systems is constructed in the framework of the non--linear $σ$-model. The low lying modes are shown to be associated with the Perron--Frobenius spectrum of the underlying irreversible classical dynamics. It is shown that the existence of a gap in the Perron-Frobenius spectrum results in a RMT behavior. Moreover, our formalism offers a way of calculating system specific corrections beyond RMT.

cond-mat↗

arXiv1995

Sensitivity of quantum chaotic wavefunction intensities to changes in external perturbations

We examine the sensitivity of wavefunction intensities in chaotic quantum systems to small changes in an arbitrary external perturbation. A universal scaling is proposed for all three Dyson ensembles and a novel theoretical approach is used to determine exact expressions for systems which violate T-invariance. Analytical results are compared with numerical simulations of tight-binding Anderson Hamiltonians.

cond-mat↗

arXiv1995

Spectral Correlation and Response functions in Quantum Dots

We derive a general relation between correlators of density of states fluctuations and density response functions. It applies equally to quantum chaotic systems of pure symmetry (unitary, orthogonal, and symplectic) as well as to the crossover region between the universality classes. This relation is much more robust than Wigner-Dyson statistics; its validity extends to disordered metals with finite conductance and even to the Anderson insulators with large localization length.

cond-mat↗

arXiv1994

Crossover Driven by Time-reversal Symmetry Breaking in Quantum Chaos

Parametric correlations of energy spectra of quantum chaotic systems are presented in the orthogonal-unitary and symplectic-unitary crossover region. The spectra are allowed to disperse as a function of two external perturbations: one of which preserves time-reversal symmetry, while the other violates it. Exact analytical expressions for the parametric two-point autocorrelation function of the density of states are derived in the crossover region by means of the supermatrix method. For the orthogonal-unitary crossover, the velocity distributions is determined and shown to deviate from Gaussian.

cond-mat↗

arXiv1993

Exact Dynamical Correlations of the 1/r^2 Model

We present exact results for the dynamical structure function, i.e.~the density-density correlations for the 1/r^2 system of interacting particles at three special values of the coupling constant. The results are interpreted in terms of exact excitations of the model which are available from Bethe's Ansatz, thereby throwing light on the quasi-particle content of the elementary excitations. We also obtain the first moment of the discrete version of the model, which provides a non-trivial check on its structure function. We show that the property of spectrum saturation is a common feature of both versions.

cond-mat↗