Thermalization in the two-body random ensemble

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Using the ergodicity principle for the expectation values of several types of observables, we investigate the thermalization process in isolated fermionic systems. These are described by the two-body random ensemble, which is a paradigmatic model to study quantum chaos and especially the dynamical transition from integrability to chaos. By means of exact diagonalizations we analyze the relevance of the eigenstate thermalization hypothesis as well as the influence of other factors, such as the energy and structure of the initial state, or the dimension of the Hilbert space. We also obtain analytical expressions linking the degree of thermalization for a given observable with the so-called number of principal components for transition strengths originating at a given energy, with the dimensions of the whole Hilbert space and microcanonical energy shell, and with the correlations generated by the observable. As the strength of the residual interaction is increased, an order-to-chaos transition takes place, and we show that the onset of Wigner spectral fluctuations, which is the standard signature of chaos, is not sufficient to guarantee thermalization in finite systems. When all the signatures of chaos are fulfilled, including the quasicomplete delocalization of eigenfunctions, the eigenstate thermalization hypothesis is the mechanism responsible for the thermalization of certain types of observables, such as (linear combinations of) occupancies and strength function operators. Our results also suggest that fully chaotic systems will thermalize relative to most observables in the thermodynamic limit.
© IOP Publishing. The authors A. R. and J. R. are thankful to L. Muñoz and J. M. G. Gómez for their collaboration and enlightening discussions. V. K. B. K. and M. V. thank Navinder Singh for useful discussions. This work is supported in part by Spanish Government grants for the research projects FIS2006-12783-C03-02, FIS2009-11621-C02-01, CSPD-2007-00042-Ingenio2010, and by the Universidad Complutense de Madrid grant UCM-910059. One of us, A. R., is supported by the spanish program JAE-Doc.
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