Semiclassical field theory approach to quantum chaos |
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| Institution: | 1. Department of Physics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA;2. NEC Research Institute, 4 Independence Way, Princeton, NJ 08540, USA;3. Cavendish Laboratory, Madingley Road, Cambridge, CB3 0HE, UK;1. Department of Applied Chemistry and Institute of Molecular Science, National Chiao Tung University, Hsinchu, 30010, Taiwan;2. Center for Emergent Functional Matter Science, National Chiao Tung University, Hsinchu, 30010, Taiwan;3. Institute of Atomic and Molecular Sciences, Academia Sinica, Taipei, 10617, Taiwan;1. B. Verkin Institute for Low Temperature Physics and Engineering, National Academy of Sciences of Ukraine, 47, Lenin Ave., Kharkov 61103, Ukraine;2. Department of Chemistry and Biochemistry, University of Arizona, Tucson, AZ 85721, USA;1. King’s College London, Department of Mathematics, London WC2R 2LS, United Kingdom;2. CNRS-Laboratoire de Physique Théorique de l’École Normale Supérieure, 24 rue Lhomond, 75231 Paris, France;3. LPTMS, CNRS, Univ. Paris-Sud, Université Paris-Saclay, 91405 Orsay, France |
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| Abstract: | We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the form of a functional supermatrix non-linear σ-model where the effective action involves the evolution operator of the classical dynamics. Low-lying degrees of freedom of the field theory are shown to reflect the irreversible classical dynamics describing relaxation of phase space distributions. The validity of this approach is investigated over a wide range of energy scales. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach accounts correctly for the short-time limit yielding results which agree with the diagonal approximation of periodic orbit theory. |
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