Emergence of Quantum Ergodicity in Rough Billiards

Budker Institute of Nuclear Physics, Novo-Nikolaevsk, Novosibirsk, Russia
Physical Review Letters (Impact Factor: 7.51). 02/1997; 79(10). DOI: 10.1103/PhysRevLett.79.1833
Source: arXiv


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

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    • "p 2 when x is inside, and H(x, p) = ∞ when x is outside. If (for pedagogical simplicity) we take the billiard to be nearly circular with radius L (e.g, a stadium with a short straight segment [7], or a circle with rough walls [8]), and the bouncing ball to have energy E = "
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    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.
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    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 · 7.51 Impact Factor
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    ABSTRACT: We calculate the energy level statistics in a two-dimensional disc with diffusive boundary scattering by the means of the recently proposed ballistic nonlinear sigma-model.
    Physical Review B 03/1998; 58(3). DOI:10.1103/PhysRevB.58.1122 · 3.74 Impact Factor
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