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classical_microcanonical_ensemble [2013/11/05 19:03] nikolaj |
classical_microcanonical_ensemble [2015/08/18 20:33] nikolaj |
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| ===== Classical microcanonical ensemble === | ===== Classical microcanonical ensemble === | ||
| - | ==== Definition ==== | + | ==== Set ==== |
| - | | @#88DDEE: $ \Delta \in \mathbb R_+ $ | | + | | @#55CCEE: context | @#55CCEE: $ \Delta \in \mathbb R_+ $ | |
| - | + | | @#FFBB00: definiendum | @#FFBB00: $ \langle \mathcal M, H,{\hat\rho}\rangle \in \mathrm{it} $ | | |
| - | | @#FFBB00: $ \langle \mathcal M, H,{\hat\rho}\rangle \in \mathrm{it} $ | | + | | @#55EE55: postulate | @#55EE55: $\langle \mathcal M, H,{\hat\rho}\rangle$ ... classical statistical ensemble | |
| - | + | | @#55EE55: postulate | @#55EE55: $\hat\rho: \mathbb R_+\to(\Gamma_{\mathcal M} \to\mathbb R_+) $ | | |
| - | | @#55EE55: $\langle \mathcal M, H,{\hat\rho}\rangle$ ... classical statistical ensemble | | + | | @#55EE55: postulate | @#55EE55: $\hat\rho(E;{\bf q},{\bf p}):=\begin{cases} 1 & \mathrm{if}\ E\le H({\bf q},{\bf p})\le E+\Delta \\\\ 0 & \mathrm{else} \end{cases}$ | |
| - | + | ||
| - | + | ||
| - | | @#55EE55: $\hat\rho: \mathbb R_+\to(\Gamma_{\mathcal M} \to\mathbb R_+) $ | | + | |
| - | | @#55EE55: $\hat\rho(E;{\bf q},{\bf p}):=\begin{cases} 1 & \mathrm{if}\ E\le H({\bf q},{\bf p})\le E+\Delta \\\\ 0 & \mathrm{else} \end{cases}$ | | + | |
| ==== Discussion ==== | ==== Discussion ==== | ||
