Linear and Nonlinear Electron Transport in Solids by David C. Langreth (auth.), J. T. Devreese, V. E. van Doren
By David C. Langreth (auth.), J. T. Devreese, V. E. van Doren (eds.)
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2 ~' C. Lett. J. , Universitaire Installing Antwerpen,Wilrijk,Belgium I. INTRODUCTION In these lectures we shall sketch the philosophy behind nonequilibrium Statistical Physics and illustrate the procedure using an exactly soluble model. We shall concentrate on the question of direct conductivity and mean energy. The statistical properties of an independent thermodynamic system in equilibrium can be extracted from its density matrix, peq , which is fully determined by the system Hamiltonian H. It is assumed that we are considering a very large number of systems each described by the Hamiltonian H.
J. Math. , 1. 309 (19BO); 2, 373 (196']). , Physica 26, 274, (1960). 7. , Physica 32, 74, (1966). 8. , Pti"Ysica 74, 529 (1974). 9. P. R~ Quantum Mechanics and Path Integrals, McGraw-Hill pp. 63~64. (New York,1965l. , Ann. Physik 44, 196 (1914). , J. Phys. A6, 1479 (1973). C. , 30, 137 (:1957). , Tables of Integrals, Series and Products, Academic Press, p. 419 (London,1965l. ASPECTS OF LINEAR AND NONLINEAR ELECTRONIC CONDUCTION IN DISSIPATIVE MEDIA K. K. A. ABSTRACT We review a general approach to the calculation of electronic transport properties under steady-state but nonequilibrium conditions.
3c,d). Furthermore where x and for the (bare) charged particle energy we find <- 1 -+ 2m
2 + m 2 -+ 2 2S1 < X> - -+ -+ e E ( t l . 6c) As is well known the last term in equilibrium oscillator energy. 6cl in the more telling form : 53 CONDUCTIVITY VIA NONEOUILIBRIUM STATISTICAL PHYSICS •--+-+ '--;.. 6dl eq is the mean equilibrium oscillator energy. 6cl in the case of the free charge on which a constant electric field is applied from time t=o onwards. 7a,bl we have made use of ref. . s. 7al rises from zero to unity as t approaches infinity ; in fact it becomes 1 for t of the order of tr and then oscillates about this value with everdecreasing amplitude.