- #1
Petar Mali
- 283
- 0
Canonical ensemble
equilibrium average value
\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta \hat{H}_0}...)
\hat{\rho}_0=Q^{-1}e^{-\beta \hat{H}_0}
Grand canonical ensemble
\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta (\hat{H}_0-\mu\hat{N})}...)
for example let's say
\hat{\mathcal{H}}_0=\hat{H}_0-\mu\hat{N}
Can I say that the equilibrium statistical operator
\hat{\rho}_0=Q^{-1}e^{-\beta (\hat{H}_0-\mu\hat{N})}=Q^{-1}e^{-\beta \hat{\mathcal{H}}_0 }
equilibrium average value
\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta \hat{H}_0}...)
\hat{\rho}_0=Q^{-1}e^{-\beta \hat{H}_0}
Grand canonical ensemble
\left\langle...\right\rangle_0=Q^{-1}Tr(e^{-\beta (\hat{H}_0-\mu\hat{N})}...)
for example let's say
\hat{\mathcal{H}}_0=\hat{H}_0-\mu\hat{N}
Can I say that the equilibrium statistical operator
\hat{\rho}_0=Q^{-1}e^{-\beta (\hat{H}_0-\mu\hat{N})}=Q^{-1}e^{-\beta \hat{\mathcal{H}}_0 }
