scholarly journals Time correlation functions of a one-dimensional infinite system

1978 ◽  
Vol 18 (3) ◽  
pp. 309-317 ◽  
Author(s):  
Toshio Niwa
Keyword(s):  
Correlation Functions ◽  
Infinite System ◽  
Time Correlation ◽  
Time Correlation Functions ◽  
One Dimensional

Theoretical Study of Time Correlation Functions in a Discrete Chaotic Process

1978 ◽  
Vol 33 (12) ◽  
pp. 1455-1460 ◽  
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.

The Nature of Chaos in a Simple Dynamical System

1979 ◽  
Vol 34 (11) ◽  
pp. 1283-1289 ◽  
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

Statistical Mechanics of Thermotransport of a Heavy Impurity in an Insulating Solid

1971 ◽  
Vol 26 (1) ◽  
pp. 10-17 ◽  
Author(s):  
A. R. Allnatt
Keyword(s):  
Heat Flux ◽  
Time Correlation ◽  
Three Dimensions ◽  
Time Correlation Functions ◽  
Single Vacancy ◽  
One Dimensional ◽  
Enthalpy Of Activation ◽  
Heavy Impurity ◽  
The One ◽  
Non Equilibrium

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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