Differences
This shows you the differences between two versions of the page.
|
grand_canonical_expectation_value [2013/10/13 16:18] nikolaj |
grand_canonical_expectation_value [2014/03/21 11:11] |
||
|---|---|---|---|
| Line 1: | Line 1: | ||
| - | ===== Grand canonical expectation value === | ||
| - | ==== Definition ==== | ||
| - | | @#88DDEE: $ w $ ... grand canonical weight | | ||
| - | | @#FFBB00: $\langle A\rangle:=\sum_{N=0}^\infty w_N\cdot \langle A_N\rangle_N$ | | ||
| - | |||
| - | The functional $\langle \cdot\rangle_N$ denotes the expectation in the canonical ensamble of particle number $N$. So the grand canonical expectation value $\langle \cdot\rangle$ takes sequences of observables to a real. | ||
| - | |||
| - | ==== Discussion ==== | ||
| - | We adopt the names of observables in canonical ensamble for the grand canonical ensamble. For example, if the internal energy in the canonical ensamble is defined as $U=\langle H\rangle$, then the grand canonical expectation value of the energy is denoted by $U$ as well and if formed from the sequence of all the $N$-particle Hamiltonians $H_N$. | ||
| - | ==== Parents ==== | ||
| - | === Requirements === | ||
| - | [[Grand canonical weight]] | ||
