- #1
Petar Mali
- 290
- 0
Canonical ensemble
equilibrium average value
[tex]\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta \hat{H}_0}...)[/tex]
[tex]\hat{\rho}_0=Q^{-1}e^{-\beta \hat{H}_0}[/tex]
Grand canonical ensemble
[tex]\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta (\hat{H}_0-\mu\hat{N})}...)[/tex]
for example let's say
[tex]\hat{\mathcal{H}}_0=\hat{H}_0-\mu\hat{N}[/tex]
Can I say that the equilibrium statistical operator
[tex]\hat{\rho}_0=Q^{-1}e^{-\beta (\hat{H}_0-\mu\hat{N})}=Q^{-1}e^{-\beta \hat{\mathcal{H}}_0 }[/tex]
equilibrium average value
[tex]\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta \hat{H}_0}...)[/tex]
[tex]\hat{\rho}_0=Q^{-1}e^{-\beta \hat{H}_0}[/tex]
Grand canonical ensemble
[tex]\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta (\hat{H}_0-\mu\hat{N})}...)[/tex]
for example let's say
[tex]\hat{\mathcal{H}}_0=\hat{H}_0-\mu\hat{N}[/tex]
Can I say that the equilibrium statistical operator
[tex]\hat{\rho}_0=Q^{-1}e^{-\beta (\hat{H}_0-\mu\hat{N})}=Q^{-1}e^{-\beta \hat{\mathcal{H}}_0 }[/tex]