Level Dynamics and Universality of Spectral Fluctuations

Foundations of Physics 31 (4):613-622 (2001)
  Copy   BIBTEX

Abstract

The spectral fluctuations of quantum (or wave) systems with a chaotic classical (or ray) limit are mostly universal and faithful to random-matrix theory. Taking up ideas of Pechukas and Yukawa we show that equilibrium statistical mechanics for the fictitious gas of particles associated with the parametric motion of levels yields spectral fluctuations of the random-matrix type. Previously known clues to that goal are an appropriate equilibrium ensemble and a certain ergodicity of level dynamics. We here complete the reasoning by establishing a power law for the ħ dependence of the mean parametric separation of avoided level crossings. Due to that law universal spectral fluctuations emerge as average behavior of a family of quantum dynamics drawn from a control parameter interval which becomes vanishingly small in the classical limit; the family thus corresponds to a single classical system. We also argue that classically integrable dynamics cannot produce universal spectral fluctuations since their level dynamics resembles a nearly ideal Pechukas–Yukawa gas

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 76,101

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

A semiclassical interpretation of wave mechanics.Nathan Rosen - 1984 - Foundations of Physics 14 (7):579-605.
Fluctuations in the dynamics of single quantum systems.Anton Amann & Harald Atmanspacher - 1998 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 29 (2):151-182.
Self-turbulence in the motion of a free particle.G. Sivashinsky - 1978 - Foundations of Physics 8 (9-10):735-744.
The Arrow of Time and the Action of the Mind at the Molecular Level.Jean E. Burns - 2006 - In Daniel P. Sheehan (ed.), Frontiers of Time. American Inst. Of Physics.
Local fluctuations and local observers in equilibrium statistical mechanics.Itamar Pitowsky - 2001 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 32 (4):595-607.
Quantum graphic dynamics.Stanley P. Gudder - 1988 - Foundations of Physics 18 (7):751-776.

Analytics

Added to PP
2013-11-22

Downloads
82 (#150,229)

6 months
1 (#447,139)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Marek Kus
Polish Academy of Sciences

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references