| 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 |
| 1568 |
|
\Delta U = - \sum\limits_{\alpha = 1}^N {g_\alpha x_\alpha x} |
| 1569 |
|
\] |
| 1570 |
|
where $g_\alpha$ are the coupling constants between the bath |
| 1571 |
< |
coordinates ($x_ \apha$) and the system coordinate ($x$). |
| 1571 |
> |
coordinates ($x_ \alpha$) and the system coordinate ($x$). |
| 1572 |
|
Introducing |
| 1573 |
|
\[ |
| 1574 |
|
W(x) = U(x) - \sum\limits_{\alpha = 1}^N {\frac{{g_\alpha ^2 |
