Level repulsion near integrability: a random matrix analogy
- 7 November 1990
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 23 (21), 4903-4909
- https://doi.org/10.1088/0305-4470/23/21/029
Abstract
Using the analogy between the statistics of the levels of quantum Hamiltonians and the eigenvalues of random matrices the authors use (an appropriate choice of) the latter in order to study the transition region near integrability. They show that the nearest-neighbour spacing distribution is linear for small spacings while the inverse of its slope is proportional to the amplitude of the (integrability-destroying) perturbation.Keywords
This publication has 24 references indexed in Scilit:
- Spectral fluctuations of classically chaotic quantum systemsPublished by Springer Nature ,2008
- Chaotic motion and random matrix theoriesPublished by Springer Nature ,2005
- Algorithmic complexity of the eigenvalue sequence of a nonintegrable Hamiltonian systemPhysical Review Letters, 1989
- Extreme level repulsion for chaotic quantum HamiltoniansPhysics Letters A, 1989
- Quantum mechanics of classically non-integrable systemsPhysics Reports, 1988
- Connection between long-range correlations in quantum spectra and classical periodic orbitsPhysical Review Letters, 1987
- Quantum spectra of classically chaotic systems without time reversal invariancePhysics Letters A, 1985
- Quantizing a classically ergodic system: Sinai's billiard and the KKR methodAnnals of Physics, 1981
- Regular and irregular spectraJournal of Physics B: Atomic and Molecular Physics, 1973
- A Brownian-Motion Model for the Eigenvalues of a Random MatrixJournal of Mathematical Physics, 1962