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particle_number_expectation_value [2015/08/16 13:27] nikolaj |
particle_number_expectation_value [2015/08/16 13:28] nikolaj |
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| ==== Set ==== | ==== Set ==== | ||
| | @#55CCEE: context | @#55CCEE: $ w $ ... grand canonical weight | | | @#55CCEE: context | @#55CCEE: $ w $ ... grand canonical weight | | ||
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| | @#FFBB00: definiendum | @#FFBB00: $ \langle\hat N\rangle(\beta,\mu) := \sum_{N=0}^\infty w_N(\beta,\mu)\cdot N $ | | | @#FFBB00: definiendum | @#FFBB00: $ \langle\hat N\rangle(\beta,\mu) := \sum_{N=0}^\infty w_N(\beta,\mu)\cdot N $ | | ||
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| - | ==== Discussion ==== | + | === Discussion === |
| The notation "$\langle\hat N\rangle$" is chosen for the function because we can also introduce the sequence of observables $\hat N$ defined to give us the particle number of each canonical ensemble, i.e. $\hat N_N=N$, and then the above coincides with the proper [[grand canonical expectation value]] of $\hat N$. Notice that this $\hat N$ is sometimes denoted by $N$, which can get a little confusing. | The notation "$\langle\hat N\rangle$" is chosen for the function because we can also introduce the sequence of observables $\hat N$ defined to give us the particle number of each canonical ensemble, i.e. $\hat N_N=N$, and then the above coincides with the proper [[grand canonical expectation value]] of $\hat N$. Notice that this $\hat N$ is sometimes denoted by $N$, which can get a little confusing. | ||
