By Professor Dr. Hermann Grabert (auth.)

ISBN-10: 3540116354

ISBN-13: 9783540116356

ISBN-10: 354039446X

ISBN-13: 9783540394464

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Additional resources for Projection Operator Techniques in Nonequilibrium Statistical Mechanics

Sample text

Correlation is a natural generalization to nonequilibrium states of KUBO's canonical correlation function [101,102]. c. 10). c. state p ( t ) . 8) projecting out the macroscoplc 4 Unless otherwise stated variables of the system are always assumed to be represented by s e l f - a d j o i n t operators. c. correlation function is a real quantity. Of course, the generalization to non-Hermitian operators is s t r a i g h t forward. -1 is the inverse of the matrix Xij and not the inverse of a 5 I n our.

This includes applications to c r i t i c a l systems [49-52], metastable and unstable systems [127-134], and systems in nonequilibrium steady states [46,55,83,135-138], to mention only a t i n y portion of recent work based on Fokker-Planck or closely related methods. 1 Relevant P r o b a b i l i t y Density We confine ourselves to classical s t a t i s t i c a l mechanics. The macroscopic state of the system w i l l be described by a set of macroscopic variables A = (A 1, . . Ai . . ) which represent coordinates in the state space Z.

Correlation function is a real quantity. Of course, the generalization to non-Hermitian operators is s t r a i g h t forward. -1 is the inverse of the matrix Xij and not the inverse of a 5 I n our. • p a r t l c u l a r matrlx ~lement, 32 variables may be w r i t t e n + ~ . 2 [27] -1 ( e i L t x , a A j ( t ) ) . 17), i . e . 3) of the relevant p r o b a b i l i t y density. We w r i t e the Hamiltonian in the form H = [H- ! ~i(t)Ai] + ! 3). 8). Next we wish to transform the expression for the disorganized d r i f t .

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Projection Operator Techniques in Nonequilibrium Statistical Mechanics by Professor Dr. Hermann Grabert (auth.)


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