Article

Emergence of Quantum Ergodicity in Rough Billiards

Budker Institute of Nuclear Physics, Novo-Nikolaevsk, Novosibirsk, Russia
Physical Review Letters (Impact Factor: 7.73). 02/1997; 79(10). DOI: 10.1103/PhysRevLett.79.1833
Source: arXiv

ABSTRACT By analytical mapping of the eigenvalue problem in rough billiards on to a band random matrix model a new regime of Wigner ergodicity is found. There the eigenstates are extended over the whole energy surface but have a strongly peaked structure. The results of numerical simulations and implications for level statistics are also discussed. Comment: revtex, 4 pages, 4 figures

0 Followers
 · 
41 Views
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: In a recent paper [Nature 412, 712 (2001)], Zurek has argued that (1) time evolution typically causes chaotic quantum systems to generate structure that varies on the scale of phase-space volume elements of size $(\hbar^2/A)^d$, where A is a classical action characteristic of the state and d is the number of degrees of freedom, and that (2) this structure implies that a small change in a phase-space coordinate X by an amount $\delta X \sim \hbar X/A$ generically results in an orthogonal state. While we agree with (1), we argue that (2) is not correct if the number of degrees of freedom is small. Our arguments are based on the Berry-Voros ansatz for the structure of energy eigenstates in chaotic systems. We find, however, that (2) becomes valid if the number of degrees of freedom is large. This implies that many-body environments may be crucial for the phenomenon of quantum decoherence.
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: We review the development of random-matrix theory (RMT) during the last fifteen years. We emphasize both the theoretical aspects, and the application of the theory to a number of fields. These comprise chaotic and disordered systems, the localization problem, many-body quantum systems, the Calogero-Sutherland model, chiral symmetry breaking in QCD, and quantum gravity in two dimensions. The review is preceded by a brief historical survey of the developments of RMT and of localization theory since their inception. We emphasize the concepts common to the above-mentioned fields as well as the great diversity of RMT. In view of the universality of RMT, we suggest that the current development signals the emergence of a new "statistical mechanics": Stochasticity and general symmetry requirements lead to universal laws not based on dynamical principles.
    Physics Reports 01/1998; 299:189-425. DOI:10.1016/S0370-1573(97)00088-4 · 22.91 Impact Factor
  • Source
    [Show abstract] [Hide abstract]
    ABSTRACT: Statistical properties of energy levels and eigenfunctions in a ballistic system with diffusive surface scattering are investigated. The two-level correlation function, the level number variance, the correlation function of wavefunction intensities, and the inverse participation ratio are calculated. Comment: 4 pages REVTEX, two figures included as eps files
    Physical Review Letters 02/1998; 80(19). DOI:10.1103/PhysRevLett.80.4161 · 7.73 Impact Factor

Preview

Download
1 Download
Available from