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 grand_canonical_expectation_value [2013/10/13 16:22]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 $H_N$. - - We also extend function of classical canonical observables to such sequences. I.e. if $A$ has $A_N$, then $f(A)$ has entries $f(A_N)$. - ==== Parents ==== - === Requirements === - [[Grand canonical weight]] 