This review gives a pedagogical introduction to the eigenstate thermalization hypothesis
(ETH), its basis, and its implications to statistical mechanics and thermodynamics. In the first …

The article reviews recent developments in the theory of fluctuations and correlations of
energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various …

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Quantum Chaos Stöckmann, Hans-Jürgen Abstract Preface; 1. Introduction; 2. Billiard …

We calculate the 2-point spectral correlation function for classically chaotic systems in the
semiclassical limit using Gutzwiller's trace formula. The off-diagonal contributions from pairs …

In the last decade, there has been an increasing interest in the analysis of energy level
spectra and wave functions of nuclei, particles, atoms and other quantum many-body …

We prove that any deterministic matrix is approximately the identity in the eigenbasis of a
large random Wigner matrix with very high probability and with an optimal error inversely …

AMS :: Bulletin of the American Mathematical Society Skip to Main Content American
Mathematical Society American Mathematical Society MathSciNet Bookstore Publications …

Necessary conditions under which a classical description will give the correct quantum
relaxation behavior are analyzed. Assuming a nonequilibrium preparation, it is shown that …

We prove the Eigenstate Thermalisation Hypothesis for Wigner matrices uniformly in the
entire spectrum, in particular near the spectral edges, with a bound on the fluctuation that is …

We review recent progress in attaining a quantitative understanding of the scarring
phenomenon, the non-random behaviour of quantum wavefunctions near unstable periodic …