5 research outputs found
Dyson's Brownian Motion and Universal Dynamics of Quantum Systems
We establish a correspondence between the evolution of the distribution of
eigenvalues of a matrix subject to a random Gaussian perturbing
matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we
prove the equivalence conjectured by Altshuler et al between the space-time
correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit
and a set of two-variable correlations for disordered quantum systems
calculated by them. Multiple variable correlation functions are, however, shown
to be inequivalent for the two cases.Comment: 10 pages, revte
Random-Matrix Theory of Parametric Correlations in the Spectra of Disordered Metals and Chaotic Billiards
We study the response to an external perturbation of the energy levels of a
disordered metallic particle, by means of the Brownian-motion model introduced
by Dyson in the theory of random matrices, and reproduce the results of a
recent microscopic theory of Altshuler, Simons, and Szafer. This establishes
the validity of Dyson's basic assumption, that parametric correlations in the
energy spectrum are dominated by level repulsion, and therefore solely
dependent on the symmetry of the hamiltonian. ***Submitted to Physica A.****Comment: 24 pages, REVTeX-3.0, INLO-PUB-931028
Inequivalent quantization of the rational Calogero model with a Coulomb type interaction
We consider the inequivalent quantizations of a -body rational Calogero
model with a Coulomb type interaction. It is shown that for certain range of
the coupling constants, this system admits a one-parameter family of
self-adjoint extensions. We analyze both the bound and scattering state sectors
and find novel solutions of this model. We also find the ladder operators for
this system, with which the previously known solutions can be constructed.Comment: 15 pages, 3 figures, revtex4, typos corrected, to appear in EPJ