Abstract
Now that the properties of low temperature Bose gases at low density, ρ, can be examined experimentally it is appropriate to revisit some of the formulas deduced by many authors four to five decades ago. One of these is that the leading term in the energy/particle is 27πh 2 ρa/m, where a is the scattering length. Owing to the delicate and peculiar nature of bosonic correlations, four decades of research have failed to establish this plausible formula rigorously. The only known lower bound for the energy was found by Dyson in 1957, but it was 14 times too small. The correct bound is proved here.
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References
F.J. Dyson, Phys. Rev. 106, 20 (1957).
W. Ketterle and N. J. van Druten, in Advances in Atomic, Molecular and Optical Physics, edited by B. Bederson and H. Walther (Academic Press, New York, 1996), Vol. 37, p. 181VAN.
B. Baumgartner, J. Phys. A 30, L741 (1997).
J. Oliva, Phys. Rev. B 39, 4197 (1989).
F.J. Dyson, J. Math. Phys. (N.Y.) 8, 1538 (1967).
J. G. Conlon, E. H. Lieb, and H-T. Yau, Commun. Math. Phys. 116, 417 (1988).
N.N. Bogoliubov, J. Phys. (U.S.S.R.) 11, 23 (1947)
N.N. Bogoliubov and D.N. Zubarev, Sov. Phys. JETP 1, 83 (1955).
K. Huang and C.N. Yang, Phys. Rev. 105, 767–775 (1957)
T.D. Lee, K. Huang, and C.N. Yang, Phys. Rev. 106, 1135–1145 (1957)
K.A. Brueckner and K. Sawada, Phys. Rev. 106, 1117–1127 (1957)
K.A. Brueckner and K. Sawada, Phys. Rev. 106, 1128–1135 (1957)
S.T. Beliaev, Sov. Phys. JETP 7, 299–307 (1958)
T.T. Wu, Phys. Rev. 115, 1390 (1959)
N. Hugenholtz and D. Pines, Phys. Rev. 116, 489 (1959)
M. Girardeau and R. Arnowitt, Phys. Rev. 113, 755 (1959)
T.D. Lee and C.N. Yang, Phys. Rev. 117, 12 (1960).
E.H. Lieb, Phys. Rev. 130, 2518 (1963)
E.H. Lieb and A.Y. Sakakura, Phys. Rev. 133, A899 (1964)
E.H. Lieb and W. Liniger, Phys. Rev. 134, A312 (1964).
E.H. Lieb, Proc. Nat. Acad. Sci. U.S.A. 46, 1000 (1960).
E.H. Lieb, The Bose Fluid, in Lecture Notes in Theoretical Physics VIIC, edited by W.E. Brittin (University of Colorado Press, Boulder, Colorado, 1964), p. 175.
E.H. Lieb, T. Kennedy, and S. Shastry, J. Stat. Phys. 53, 1019(1988).
G. Temple, Proc. R. Soc. London A 119, 276 (1928).
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Lieb, E.H., Yngvason, J. (2001). Ground State Energy of the Low Density Bose Gas. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04360-8_44
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DOI: https://doi.org/10.1007/978-3-662-04360-8_44
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