Time correlation functions for the one-dimensional Lorentz gas

AbstractA kinetic equation is derived for the singlet distribution function for a heavy impurity in a lattice of lighter atoms in a temperature gradient. In the one dimensional case the equation can be solved to find formal expressions for the jump probability and hence the heat of transport, q*. for a single vacancy jump of the impurity, q* is the sum of the enthalpy of activation, a term involving only averaging in an equilibrium ensemble, and two non-equilibrium terms involving time correlation functions. The most important non-equilibrium term concerns the correlation between the force on the impurity and a microscopic heat flux. A plausible extension to three dimensions is suggested and the relation to earlier isothermal and non-isothermal theories is indicated

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Theoretical Study of Time Correlation Functions in a Discrete Chaotic Process

Zeitschrift für Naturforschung A ◽

10.1515/zna-1978-1207 ◽

1978 ◽

Vol 33 (12) ◽

pp. 1455-1460 ◽

Cited By ~ 3

Author(s):

Hirokazu Fujisaka ◽

Tomoji Yamada

Keyword(s):

Correlation Function ◽

Correlation Functions ◽

Characteristic Time ◽

Theoretical Study ◽

Time Correlation ◽

Time Correlation Function ◽

Point Of View ◽

Time Correlation Functions ◽

Chaotic Motions ◽

One Dimensional

Abstract One-dimensional discrete chaotic processes are studied from a statistical-dynamical point of view. A set of equations which describe the behavior of the time correlation functions is derived with the aid of Mori’s projector formalism. A condition under which a process is Markoffian is obtained, and an approximate method is developed for a non-Markoffian process. As an illustration, a time correlation function for a simple system is calculated and the comparison with results of computer simulations is made. The relation between the instability of a trajectory and the characteristic time of chaotic motions is also discussed.

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The Nature of Chaos in a Simple Dynamical System

Zeitschrift für Naturforschung A ◽

10.1515/zna-1979-1105 ◽

1979 ◽

Vol 34 (11) ◽

pp. 1283-1289 ◽

Cited By ~ 1

Author(s):

Akira Shibata ◽

Toshihiro Mayuyama ◽

Masahiro Mizutani ◽

Nobuhiko Saitô

Keyword(s):

Dynamical System ◽

Distribution Function ◽

Probability Distribution ◽

Correlation Functions ◽

Probability Distribution Function ◽

Time Correlation ◽

Time Correlation Functions ◽

One Dimensional ◽

Initial Distributions ◽

Simple Dynamical System

A simple one-dimensional transformation xn = axn-1 + 2 - a (0 ≦ xn-1 ≦ 1 - 1 / a ) , xn = a( 1 - xn-1) (1 - 1 a ≦ xn-1 ≦ 1) (1 ≦ a ≦ 2) is investigated by introducing the probability distribution function Wn(x). Wn ( x ) converges when n → oo for a > V 2 , but oscillates for 1 < a ≦ V2. The final distribution of Wn(x) does not depend on the initial distributions for a > V2, but does for 1 < a ≦V2 Time-correlation functions are also calculated

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