The ground state energy of a classical gas |
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Authors: | Joseph G. Conlon |
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Affiliation: | 1. Institut für Theoretische Physik, Universit?t Wien, Boltzmanngasse 5, A-1090, Wien, Austria
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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 $$H_N (alpha ) = alpha sumlimits_{i = 1}^N {( - Delta _i )^{1/2} + } sumlimits_{i< j} {left| {x_i - x_j } right|^{ - 1} } - sumlimits_{i,j} {left| {x_i - R_j } right|^{ - 1} } + sumlimits_{i< j} {left| {R_i - R_j } right|^{ - 1} } $$ where Δ i is the Laplacian in the variablex i ∈?3 andR 1, ...,R N are fixed points in ?3. 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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