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particle_number_expectation_value [2015/08/16 13:27]
nikolaj
particle_number_expectation_value [2015/08/16 13:28] (current)
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.
  
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