Abstract
We continue the analysis of the one-dimensional gas of Bose particles interacting via a repulsive delta function potential by considering the excitation spectrum. Among other things we show that: (i) the elementary excitations are most naturally thought of as a double spectrum, not a single one; (ii) the velocity of sound derived from the macroscopic compressibility is shown to agree with the velocity of sound derived from microscopic considerations, i.e., from the phonon spectrum. We also introduce a distinction between elementary excitations and quasiparticles, on the basis of which we give some heuristic reasons for expecting the double spectrum to be a general feature, even in three dimensions, and not an exception.
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Reference
E. Lieb and W. Liniger, Phys. Rev. 130, 1605 (1963) (referred to here as I).
See I, Sec. IV.
See, for example, The Many Body Problem, edited by C. DeWitt ( John Wiley & Sons, Inc., New York, 1958 ), pp. 347–355.
R. P. Feynman, Phys. Rev. 91, 1291 (1953).
R. P. Feynman, Phys. Rev. 91, 1301 (1953).
R. P. Feynman, Phys. Rev. 94, 262 (1954).
See, for example, F. London, Superfluids (John Wiley & Sons, Inc., New York, 1954 ), Vol. II, p. 83.
M. Girardeau, J. Math. Phys. 1, 516 (1960).
V. M. Galitskii and A. B. Migdal, Soviet Phys.—JETP 7, 96 (1958).
A. Maradudin, P. Mazur, E. Montroll, and G. Weiss, Rev. Mod. Phys. 30, 175 (1958).
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Lieb, E.H. (2004). Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum. In: Nachtergaele, B., Solovej, J.P., Yngvason, J. (eds) Condensed Matter Physics and Exactly Soluble Models. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06390-3_37
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DOI: https://doi.org/10.1007/978-3-662-06390-3_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-06093-9
Online ISBN: 978-3-662-06390-3
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