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• W2977890777 abstract "In contrast with the three-dimensional result, the Beth-Uhlenbeck (BU) formula in one dimension contains an extra $ensuremath{-}1/2$ term. The origin of this $ensuremath{-}1/2$ term is explained using a spectral density approach. To be explicit, a $ensuremath{delta}$-function potential is used to show that the correction term arises from a pole of the density of states at zero energy. The spectral density method shows that this term is actually an artifact of the non-normalizability of the scattering states and an infrared cutoff regularization scheme has to be used to get the correct result in one dimension. The formal derivation of the BU formula would miss this term since it ignores the effects of the boundary terms. While the result is shown for the $ensuremath{delta}$-function potential, the method and result are valid for more general potentials. Additionally, the one-dimensional Levinson theorem can be extracted from the spectral density method using the asymptotic form of general potentials. The importance of the result lies in the fact that all these correction terms in one dimension have a universal source: a pole at zero energy. Similar calculations using quantum field-theoretical approaches (without explicit infrared cutoff regularization schemes) also show the same subtleties with the correction term originating from the zero energy scattering states (Appendix A)." @default.
• W2977890777 created "2019-10-10" @default.
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• W2977890777 date "2019-12-09" @default.
• W2977890777 modified "2023-10-18" @default.
• W2977890777 title "Spectral density, Levinson's theorem, and the extra term in the second virial coefficient for the one-dimensional <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML><mml:mi>δ</mml:mi></mml:math> -function potential" @default.
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• W2977890777 doi "https://doi.org/10.1103/physreva.100.062110" @default.
• W2977890777 hasPublicationYear "2019" @default.
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