| 1110 |
|
particle $j$ in the system |
| 1111 |
|
\[ |
| 1112 |
|
g(r) = \frac{V}{{N^2 }}\left\langle {\sum\limits_i {\sum\limits_{j |
| 1113 |
< |
\ne i} {\delta (r - r_{ij} )} } } \right\rangle = \fract{\rho |
| 1113 |
> |
\ne i} {\delta (r - r_{ij} )} } } \right\rangle = \frac{\rho |
| 1114 |
|
(r)}{\rho}. |
| 1115 |
|
\] |
| 1116 |
|
Note that the delta function can be replaced by a histogram in |
| 1117 |
< |
computer simulation. Figure |
| 1118 |
< |
\ref{introFigure:pairDistributionFunction} shows a typical pair |
| 1119 |
< |
distribution function for the liquid argon system. The occurrence of |
| 1120 |
< |
several peaks in the plot of $g(r)$ suggests that it is more likely |
| 1121 |
< |
to find particles at certain radial values than at others. This is a |
| 1122 |
< |
result of the attractive interaction at such distances. Because of |
| 1123 |
< |
the strong repulsive forces at short distance, the probability of |
| 1124 |
< |
locating particles at distances less than about 3.7{\AA} from each |
| 1125 |
< |
other is essentially zero. |
| 1117 |
> |
computer simulation. Peaks in $g(r)$ represent solvent shells, and |
| 1118 |
> |
the height of these peaks gradually decreases to 1 as the liquid of |
| 1119 |
> |
large distance approaches the bulk density. |
| 1120 |
|
|
| 1127 |
– |
%\begin{figure} |
| 1128 |
– |
%\centering |
| 1129 |
– |
%\includegraphics[width=\linewidth]{pdf.eps} |
| 1130 |
– |
%\caption[Pair distribution function for the liquid argon |
| 1131 |
– |
%]{Pair distribution function for the liquid argon} |
| 1132 |
– |
%\label{introFigure:pairDistributionFunction} |
| 1133 |
– |
%\end{figure} |
| 1121 |
|
|
| 1122 |
|
\subsubsection{\label{introSection:timeDependentProperties}\textbf{Time-dependent |
| 1123 |
|
Properties}} |
| 1555 |
|
\Delta U = - \sum\limits_{\alpha = 1}^N {g_\alpha x_\alpha x} |
| 1556 |
|
\] |
| 1557 |
|
where $g_\alpha$ are the coupling constants between the bath |
| 1558 |
< |
coordinates ($x_ \apha$) and the system coordinate ($x$). |
| 1558 |
> |
coordinates ($x_ \alpha$) and the system coordinate ($x$). |
| 1559 |
|
Introducing |
| 1560 |
|
\[ |
| 1561 |
|
W(x) = U(x) - \sum\limits_{\alpha = 1}^N {\frac{{g_\alpha ^2 |
