arXiv:1201.1540

On Large Densities in Fermi Systems

V. A. Malyshev, Zamyatin, A. A.

Published Jan 7, 2012• 0 citations

arXiv HTML PDF

Abstract

The goal of this paper is to give some rigorous results, concerning high density behavior of Fermi systems.

DOI: 10.48550/arxiv.1201.1540

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arXiv:1201.1540

On Large Densities in Fermi Systems

V. A. Malyshev, Zamyatin, A. A.

Published Jan 7, 2012• 0 citations

arXiv HTML PDF

Abstract

The goal of this paper is to give some rigorous results, concerning high density behavior of Fermi systems.

DOI: 10.48550/arxiv.1201.1540

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Abstract We investigate the BCS critical temperature

T_c

T c in the high-density limit and derive an asymptotic formula, which strongly depends on the behavior of the interaction potential V on the Fermi-surface. Our results include a rigorous confirmation for the behavior of

T_c

T c at high densities proposed by Langmann et al. (Phys Rev Lett 122:157001, 2019) and identify precise conditions under which superconducting domes arise in BCS theory.

We give a rigorous derivation of the Hartree equation for the many-body dynamics of pseudo-relativistic Fermi systems at high density

\varrho \gg 1

, on arbitrarily large domains, at zero temperature. With respect to previous works, we show that the many-body evolution can be approximated by the Hartree dynamics locally, proving convergence of the expectation of observables that are supported in regions with fixed volume, independent of

\varrho

. The result applies to initial data describing fermionic systems at equilibrium confined in arbitrarily large domains, under the assumption that a suitable local Weyl-type estimate holds true. The proof relies on the approximation of the initial data through positive temperature quasi-free states, that satisfy strong local semiclassical bounds, which play a key role in controlling the growth of the local excitations of the quasi-free state along the many-body dynamics.