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 TMF, 1973, Volume 14, Number 2, Pages 211–219 (Mi tmf3379)

On the existence and continuity of the pressure in quantum statistical mechanics

L. A. Pastur

Abstract: It is shown that in the case of all three statistics (Maxwell–Boltzmann; Bose–Einstein, and Fermi–Dirac) the pressure in the canonical ensemble is a continuous function that satisfies a Lipschitz condition provided the pair interaction potential $\Phi(r)$ for $r\eqslantgtr a$ ($a\eqslantgtr0$ is the hardcore radius) is a twice continuously differentiable function. Apart from the usual conditions needed to ensure the existence of the thermodynamic limit, this function satisfies for some $\varepsilon>0$ the further inequality
$$\tilde U_N(x_1,x_2,…,x_N)=\sum_{i<j}\tilde{\Phi}(|x_i-x_j|)\eqslantgtr-\tilde BN,\quad\tilde B\eqslantgtr0,$$
where $\tilde{\Phi}(r)=\Phi(r)+\varepsilon(2r\Phi'(r)-r^2\Phi"(r)).$ Some sufficient conditions to be imposed on $\Phi(r)$ for this inequality to hold are given.

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English version:
Theoretical and Mathematical Physics, 1973, 14:2, 157–163

Citation: L. A. Pastur, “On the existence and continuity of the pressure in quantum statistical mechanics”, TMF, 14:2 (1973), 211–219; Theoret. and Math. Phys., 14:2 (1973), 157–163

Citation in format AMSBIB
\Bibitem{Pas73} \by L.~A.~Pastur \paper On the existence and continuity of the pressure in quantum statistical mechanics \jour TMF \yr 1973 \vol 14 \issue 2 \pages 211--219 \mathnet{http://mi.mathnet.ru/tmf3379} \transl \jour Theoret. and Math. Phys. \yr 1973 \vol 14 \issue 2 \pages 157--163 \crossref{https://doi.org/10.1007/BF01036354}