Testing Boltzmann's ergodic hypothesis with electron gas models

Lee, M Howard

doi:10.1088/0305-4470/39/17/s52

Cited by 9 publications

(9 citation statements)

References 34 publications

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“…Conclusion -In this work we revisited the problem of the validity of the EH and that of the MC, and we obtained an agreement between our previous result [1] and recent results using the recurrence relations method [4]. However, for anomalous diffusion our condition can be less restrictive than that of Lee.…”

supporting

confidence: 73%

“…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 [2][3][4]. Lee shows that ergodicity is violated in the dynamics of the electron gas [4].…”

mentioning

confidence: 78%

“…With the development of the recurrence relations method by Lee [2], it became possible to obtain general solutions for the Heisenberg equations of motion. In this way it is possible to verify the validity of the EH [3,4].We have avoided this problem using the asymptotic limit of the correlation function, which allows us to verify the EH without a full solution of the dynamical equations of motion. For that, we just need the memory, which is our starting point.…”

mentioning

confidence: 99%

“…Since diffusion is a main phenomenon in physics we use that as our starting point. The method used by Lee [2][3][4] is quite general and applies to any response function. In this context, the equivalence between this and our results strengthens both.…”

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confidence: 99%

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Mixing, ergodicity and slow relaxation phenomena

Costa

Vainstein

Lapas

et al. 2006

Physica A: Statistical Mechanics and its Applications

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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.Comment: 6 pages, 1 figure. Corrected last citation. Proceedings of LAWNP0

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supporting

confidence: 73%

mentioning

confidence: 78%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Mixing, ergodicity and slow relaxation phenomena

Costa

Vainstein

Lapas

et al. 2006

Physica A: Statistical Mechanics and its Applications

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“…It is possible to speak about these systems in terms of ergodic (or quasi-ergodic) behavior, however, with a certain reservation (for a recent analysis of the ergodic behavior of many-body systems see Refs. [247][248][249][250][251][252][253][254][255][256] ). It may be of use to remind a few useful properties of the relaxation function.…”

Section: Linear Response Theorymentioning

confidence: 99%

Electronic Transport in Metallic Systems and Generalized Kinetic Equations

Kuzemsky

2011

Int. J. Mod. Phys. B

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This paper reviews some selected approaches to the description of transport properties, mainly electroconductivity, in crystalline and disordered metallic systems. A detailed qualitative theoretical formulation of the electron transport processes in metallic systems within a model approach is given. Generalized kinetic equations which were derived by the method of the nonequilibrium statistical operator are used. Tight-binding picture and modified tightbinding approximation (MTBA) were used for describing the electron subsystem and the electron-lattice interaction correspondingly. The low-and high-temperature behavior of the resistivity was discussed in detail. The main objects of discussion are nonmagnetic (or paramagnetic) transition metals and their disordered alloys. The choice of topics and the emphasis on concepts and model approach makes it a good method for a better understanding of the electrical conductivity of the transition metals and their disordered binary substitutional alloys, but the formalism developed can be applied (with suitable modification), in principle, to other systems. The approach we used and the results obtained complements the existent theories of the electrical conductivity in metallic systems. The present study extends the standard theoretical format and calculation procedures in the theories of electron transport in solids.Keywords: Transport phenomena in solids; electrical conductivity in metals and alloys; transition metals and their disordered alloys; tight-binding and modified tight-binding approximation; method of the nonequilibrium statistical operator; generalized kinetic equations.

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