1997/03/21 by Christopher Jarzynski, C. Jarzynski
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Protein Structure and Dynamics #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy #chao-dyn #cond-mat.stat-mech #nlin.CD #quant-ph
paper · pdf · doi:10.1103/physreve.56.2254
published as Phys Rev E 56, 2254 (1997) · 8 pages, no figures
arxiv created 1997/03/21 · openalex publication_date 1997/08/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that, by applying a principle of information theory, one obtains Berry’s conjecture regarding the high-lying quantal energy eigenstates of classically chaotic systems. Typeset using REVTEX 1 In many problems of physical interest, it is necessary to abandon a search for the exact solution, and to turn instead to a statistical approach. This involves mentally replacing the answer which we seek, with an ensemble of possibilities, then adopting the attitude that each member of the ensemble is an equally likely candidate for the true solution. The choice of ensemble then becomes centrally important, and here information theory provides a reliable guiding principle. The principle instructs us to choose the least biased ensemble (the one which minimizes information content), subject to some relevant constraints. A well-known illustration arises in classical statistical mechanics: the least biased distribution in phase space, subject to a fixed normalization and average energy, is the canonical ensemble of Gibbs [1]. Another example appears in random matrix theory: by minimizing the information content of an ensemble of matrices, subject to various simple constraints, one obtains the standard random matrix ensembles [2]. The purpose of this paper is to point out that Berry’s conjecture [3] regarding the energy eigenstates of chaotic systems, also emerges naturally from this principle of least bias. Berry’s conjecture makes two assertions regarding the high-lying energy eigenstates ψE of quantal systems whose classical counterparts are chaotic and ergodic1: (1) Such eigenstates appear to be random Gaussian functions ψ(x) on configuration space, (2) with two-point correlations given by ψ ∗ ( x − s ψ x +