Berry's Conjecture and Information Theory Typeset Using Revt E X

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. 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