Mixing,ergodicity and slow relaxation phenomena |
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| Affiliation: | 1. Centro Atómico Bariloche and Instituto Balseiro, San Carlos de Bariloche, 8400 Río Negro, Argentina;2. Centro Atómico Bariloche and Instituto Balseiro, San Carlos de Bariloche, 8400 Río Negro, Argentina;1. Steklov Mathematical Institute of RAS, Russia;2. National University of Science and Technology MISIS, Russia;1. Department of Mathematics, University of Colorado at Boulder, Boulder, CO 80309, USA;2. Department of Mathematics, Yale University, New Haven, CT 06520, USA;3. Jockey Club Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong, China;4. Computing & Mathematical Sciences, California Institute of Technology, Pasadena, CA 91125, USA |
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| Abstract: | ![]()
Investigations on diffusion in systems with memory [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] have established a hierarchical connection between mixing, ergodicity, and the fluctuation–dissipation theorem (FDT). This hierarchy means that ergodicity is a necessary condition for the validity of the FDT, and mixing is a necessary condition for ergodicity. In this work, we compare those results with recent investigations using the Lee recurrence relations method [M.H. Lee, Phys. Rev. B 26 (1982) 2547; M.H. Lee, Phys. Rev. Lett. 87 (2001) 250601; M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. Lee shows that ergodicity is violated in the dynamics of the electron gas [M.H. Lee, J. Phys. A: Math. Gen. 39 (2006) 4651]. This reinforces both works and implies that the results of [I.V.L. Costa, R. Morgado, M.V.B.T. Lima, F.A. Oliveira, Europhys. Lett. 63 (2003) 173] are more general than the framework in which they were obtained. Some applications to slow relaxation phenomena are discussed. |
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