Abstract
In this paper we study the ground state energy of a classical gas. Our interest centers mainly on Coulomb systems. We obtain some new lower bounds for the energy of a Coulomb gas. As a corollary of our results we can show that a fermionic system with relativistic kinetic energy and Coulomb interaction is stable. More precisely, letH N (α) be theN particle Hamiltonian
where Δ i is the Laplacian in the variablex i ∈ℝ3 andR 1, ...,R N are fixed points in ℝ3. We show that for sufficiently large α, independent ofN, the HamiltonianH N (α) is nonnegative on the space of square integrable functions ψ(x 1, ...,x N ), antisymmetric in the variablesx i , 1≦i≦N.
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Communicated by B. Simon
Research supported by grants from the Austrian National Science Foundation and University of Missouri research council
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Conlon, J.G. The ground state energy of a classical gas. Commun.Math. Phys. 94, 439–458 (1984). https://doi.org/10.1007/BF01403881
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DOI: https://doi.org/10.1007/BF01403881