Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only | center dot | (V) over cap epsilon l(1)(Z(3)). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy.
Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential / Benedikter, Niels; Porta, Marcello; Schlein, Benjamin; Seiringer, Robert. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 247:4(2023), pp. 1-57. [10.1007/s00205-023-01893-6]
Correlation Energy of a Weakly Interacting Fermi Gas with Large Interaction Potential
Porta, Marcello;
2023-01-01
Abstract
Recently the leading order of the correlation energy of a Fermi gas in a coupled mean-field and semiclassical scaling regime has been derived, under the assumption of an interaction potential with a small norm and with compact support in Fourier space. We generalize this result to large interaction potentials, requiring only | center dot | (V) over cap epsilon l(1)(Z(3)). Our proof is based on approximate, collective bosonization in three dimensions. Significant improvements compared to recent work include stronger bounds on non-bosonizable terms and more efficient control on the bosonization of the kinetic energy.File | Dimensione | Formato | |
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