A collisional approach to the calculation of time correlation functions. Transport coefficients of gases

1975 ◽  
Vol 13 (4) ◽  
pp. 283-300 ◽  
Author(s):  
John E. Reissner ◽  
William A. Steele
Keyword(s):  
Correlation Functions ◽  
Transport Coefficients ◽  
Time Correlation ◽  
Time Correlation Functions

Time Correlation Functions

2006 ◽  
Author(s):  
Abraham Nitzan
Keyword(s):  
Correlation Functions ◽  
Thermal Environment ◽  
Structural Information ◽  
Transport Coefficients ◽  
Kinetic Equations ◽  
Relevant Information ◽  
Time Correlation ◽  
Time Correlation Functions ◽  
Dynamical Information

In the previous chapter we have seen how spatial correlation functions express useful structural information about our system. This chapter focuses on time correlation functions that, as will be seen, convey important dynamical information. Time correlation functions will repeatedly appear in our future discussions of reduced descriptions of physical systems. A typical task is to derive dynamical equations for the time evolution of an interesting subsystem, in which only relevant information about the surrounding thermal environment (bath) is included. We will see that dynamic aspects of this relevant information usually enter via time correlation functions involving bath variables. Another type of reduction aims to derive equations for the evolution of macroscopic variables by averaging out microscopic information. This leads to kinetic equations that involve rates and transport coefficients, which are also expressed as time correlation functions of microscopic variables. Such functions are therefore instrumental in all discussions that relate macroscopic dynamics to microscopic equations of motion. It is important to keep in mind that dynamical properties are not exclusively relevant only to nonequilibrium system. One may naively think that dynamics is unimportant at equilibrium because in this state there is no evolution on the average. Indeed in such systems all times are equivalent, in analogy to the fact that in spatially homogeneous systems all positions are equivalent. On the other hand, just as in the previous chapter we analyzed equilibrium structures by examining correlations between particles located at different spatial points, also here we can gain dynamical information by looking at the correlations between events that occur at different temporal points. Time correlation functions are our main tools for conveying this information in stationary systems. These are systems at thermodynamic equilibrium or at steady state with steady fluxes present.

Computer simulation of time correlation functions and matter transport coefficients for a model order–disorder alloy

1998 ◽  
Vol 76 (11) ◽  
pp. 1548-1553
Author(s):  
Ziqiang Qin ◽  
Alan R Allnatt ◽  
E Loftus Allnatt
Keyword(s):  
Correlation Function ◽  
Transition Temperature ◽  
Correlation Functions ◽  
Theoretical Calculations ◽  
Transport Coefficients ◽  
Time Correlation ◽  
Time Correlation Function ◽  
Time Correlation Functions ◽  
Matter Transport ◽  
Phenomenological Coefficients

The time correlation functions associated with the Onsager phenomenological coefficients for isothermal matter transport have been calculated by Monte Carlo simulation for a binary system (A,B) at the equiatomic composition according to the Kikuchi-Sato model of an order-disorder alloy with vacancy transport mechanism. The diagonal (AA) time correlation functions are positive, decay monotonically to zero, and exhibit a long time tail where they vary as t-n where t is time; the exponent n varies weakly with temperature at high temperatures and more rapidly as the temperature is lowered through the order-disorder transition temperature. In the region of short-range order the off-diagonal (AB) time correlation function is negative but otherwise shows similar behaviour to the diagonal one, although as the transition temperature is approached n varies more rapidly. At the transition temperature and below, the off-diagonal time correlation function increases from an initial negative value to a maximum where it is positive and then, at later times, decreases to zero. The implications of these observations for approximate theoretical calculations of the phenomenological coefficients are briefly indicated.Key words: diffusion, non-equilibrium phenomena, statistical mechanics, transport properties.

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