Das ideale einatomige Gas ist dadurch gekennzeichnet, daß ∊i durch die kinetische Energie der Teilchen gegeben ist und keine Wechselwirkungsenergie zwischen den Teilchen auftritt. Vom letzten Abschnitt her kennen wir für Bose-, Fermi-und Maxwell-Boltzmann Gas die Beziehungen (16.1) $$ {{PV} \over {kT}} = -{\Omega \over {kT}} = \ln Z = \left\{ \matrix{ -\sum\limits_i {\ln (1 -\sigma {e^{ -{{{ \in _i}} \over {kT}}}}) \ldots BE} \hfill \cr \sum\limits_i {\ln (1 + \sigma {e^{ -{{{ \in _i}} \over {kT}}}}) \ldots BE} \hfill \cr \sum\limits_i {\sigma {e^{ -{{{ \in _i}} \over {kT}}}}) \ldots MB} \hfill \cr} \right\} $$ (16.2) $$ N = -\left( {{{\partial \Omega } \over {\partial \mu }}} \right)\left\{ \matrix{ \sum\limits_i {{1 \over {{\sigma ^{ -1}}{e^{{ \in _i}/kT}} -1}} \ldots BE} \hfill \cr \sum\limits_i {{1 \over {{\sigma ^{ -1}}{e^{{ \in _i}/kT}} + 1}} \ldots FD} \hfill \cr \hfill \cr \sum\limits_i {{1 \over {{\sigma ^{ -1}}{e^{{ \in _i}/kT}}}} \ldots MB} \hfill \cr \hfill \cr} \right\} $$ (16.3) $\sigma : = {e^{{\mu \over {kT}}}}$ (16.4) ${ \in _i} = {{p_i^2} \over {2m}}.$ Das ideale einatomige Gas ist dadurch gekennzeichnet, daß ∊i durch die kinetische Energie der Teilchen gegeben ist und keine Wechselwirkungsenergie zwischen den Teilchen auftritt. Vom letzten Abschnitt her kennen wir für Bose-, Fermi-und Maxwell-Boltzmann Gas die Beziehungen (16.1) $$ {{PV} \over {kT}} = -{\Omega \over {kT}} = \ln Z = \left\{ \matrix{ -\sum\limits_i {\ln (1 -\sigma {e^{ -{{{ \in _i}} \over {kT}}}}) \ldots BE} \hfill \cr \sum\limits_i {\ln (1 + \sigma {e^{ -{{{ \in _i}} \over {kT}}}}) \ldots BE} \hfill \cr \sum\limits_i {\sigma {e^{ -{{{ \in _i}} \over {kT}}}}) \ldots MB} \hfill \cr} \right\} $$ (16.2) $$ N = -\left( {{{\partial \Omega } \over {\partial \mu }}} \right)\left\{ \matrix{ \sum\limits_i {{1 \over {{\sigma ^{ -1}}{e^{{ \in _i}/kT}} -1}} \ldots BE} \hfill \cr \sum\limits_i {{1 \over {{\sigma ^{ -1}}{e^{{ \in _i}/kT}} + 1}} \ldots FD} \hfill \cr \hfill \cr \sum\limits_i {{1 \over {{\sigma ^{ -1}}{e^{{ \in _i}/kT}}}} \ldots MB} \hfill \cr \hfill \cr} \right\} $$ (16.3) $$ \sigma : = {e^{{\mu \over {kT}}}} $$ (16.4) $$ { \in _i} = {{p_i^2} \over {2m}}. $$

Vieweg+Teubner eBooksJan 1, 19881 citation

The universal sound velocity formula for the strongly interacting unitary Fermi gas

Ke Liu, Jisheng Chen

Due to the scale invariance, the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas. For example, the virial theorem between pressure and energy density of the ideal gas P = 2 E /3 V is still satisfied by the unitary Fermi gas. This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation. For comparison, the sound velocities for the ideal Boltzmann, Bose and Fermi gas are also given. Quite interestingly, the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.Due to the scale invariance, the thermodynamic laws of strongly interacting limit unitary Fermi gas can be similar to those of non-interacting ideal gas. For example, the virial theorem between pressure and energy density of the ideal gas P = 2 E /3 V is still satisfied by the unitary Fermi gas. This paper analyses the sound velocity of unitary Fermi gases with the quasi-linear approximation. For comparison, the sound velocities for the ideal Boltzmann, Bose and Fermi gas are also given. Quite interestingly, the sound velocity formula for the ideal non-interacting gas is found to be satisfied by the unitary Fermi gas in different temperature regions.

Chinese Physics BFeb 1, 20115 citations

\sigma : = {e^{{\mu \over {kT}}}}

(16.4)

{ \in _i} = {{p_i^2} \over {2m}}.