Abstract
We study the asymptotics of the difference of the ground-state energies of two non-interacting N-particle Fermi gases in a finite volume of length L in the thermodynamic limit up to order 1/L. We are particularly interested in subdominant terms proportional to 1/L, called finite-size energy. In the nineties (Affleck, Nuc. Phys. B 58, 35–41 1997; Zagoskin and Affleck, J. Phys. A 30, 5743–5765 1997) claimed that the finite-size energy is related to the decay exponent occurring in Anderson’s orthogonality. We prove that the finite-size energy depends on the details of the thermodynamic limit and is therefore non-universal. Typically, it includes an additional linear term in the scattering phase shift.
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Work supported by SFB/TR 12 of the German Research Council (DFG)
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Gebert, M. Finite-size Energy of Non-interacting Fermi Gases. Math Phys Anal Geom 18, 27 (2015). https://doi.org/10.1007/s11040-015-9198-1
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DOI: https://doi.org/10.1007/s11040-015-9198-1