Abstract
The recent experimental success in creating Bose-Einstein condensates of alkali atoms, honored by the Nobel prize awards in 2001 [1,5], led to renewed interest in the mathematical description of interacting Bose gases.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
E.A. Cornell and C.E. Wieman, Bose-Einstein condensation in a dilute gas, the first 70 years and some recent experiments, in: Les Prix Nobel 2001 (The Nobel Foundation, Stockholm, 2002), pp. 87–108. Reprinted in: Rev. Mod. Phys. 74, 875–893 (2002); Chem. Phys. Chem. 3, 476–493 (2002).
F. Dalfovo, S. Giorgini, L.P. Pitaevskii, and S. Stringari, Theory of Bose- Einstein condensation in trapped gases, Rev. Mod. Phys. 71, 463–512 (1999).
F.J. Dyson, Ground-State Energy of a Hard-Sphere Gas, Phys. Rev. 106, 20–26 (1957).
E.P. Gross, Structure of a Quantized Vortex in Boson Systems, Nuovo Cimento 20, 454–466 (1961). Hydrodynamics of a superfluid condensate, J. Math. Phys. 4, 195–207 (1963).
W. Ketterle, When atoms behave as waves: Bose-Einstein condensation and the atom laser, in: Les Prix Nobel 2001 (The Nobel Foundation, Stockholm, 2002), pp. 118–154. Reprinted in: Rev. Mod. Phys. 74, 1131–1151 (2002); Chem. Phys. Chem. 3, 736–753 (2002).
W. Lenz, Die Wellenfunktion und Geschwindigkeitsverteilung des entarteten Gases, Z. Phys. 56, 778–789 (1929).
E.H. Lieb, Simplified Approach to the Ground State Energy of an Imperfect Bose Gas, Phys. Rev. 130, 2518–2528 (1963).
E.H. Lieb and W. Liniger, Exact Analysis of an Interacting Bose Gas. I. The General Solution and the Ground State, Phys.Rev. 130, 1605–1616 (1963). E.H. Lieb, Exact Analysis of an Interacting Bose Gas. II. The Excitation Spectrum, Phys. Rev. 130, 1616–1624 (1963).
E.H. Lieb and M. Loss, Analysis, 2nd ed., Amer. Math. Soc., Providence (2001).
E.H. Lieb and R. Seiringer, Proof of Bose-Einstein Condensation for Dilute Trapped Gases, Phys. Rev. Lett. 88, 170409-1–4 (2002).
E.H. Lieb, R. Seiringer, J.P. Solovej, and J. Yngvason, The Ground State of the Bose Gas, in: Current Developments in Mathematics, 2001, 131–178, International Press, Cambridge (2002). See also arXiv:math-/0405004
E.H. Lieb, R. Seiringer, and J. Yngvason, Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional, Phys. Rev. A 61, 043602-1–13 (2000).
E.H. Lieb, R. Seiringer, and J. Yngvason, A Rigorous Derivation of the Gross- Pitaevskii Energy Functional for a Two-Dimensional Bose Gas, Commun. Math. Phys. 224, 17–31 (2001).
E.H. Lieb, R. Seiringer, and J. Yngvason, Superfluidity in Dilute Trapped Bose Gases, Phys. Rev. B 66, 134529-1–6 (2002).
E.H. Lieb, R. Seiringer, and J. Yngvason, Poincaré Inequalities in Punctured Domains, Ann. Math. 158, 1067–1080 (2003).
E.H. Lieb, R. Seiringer, and J. Yngvason, One-Dimensional Bosons in Three-Dimensional Traps, Phys. Rev. Lett. 91, 150401-1–4 (2003). One-Dimensional Behavior of Dilute, Trapped Bose Gases, Commun. Math. Phys. 244, 347–393 (2004).
E.H. Lieb and J. Yngvason, Ground State Energy of the Low Density Bose Gas, Phys. Rev. Lett. 80, 2504–2507 (1998).
E.H. Lieb and J. Yngvason, The Ground State Energy of a Dilute Two- Dimensional Bose Gas, J. Stat. Phys. 103, 509–526 (2001).
O. Penrose and L. Onsager, Bose-Einstein Condensation and Liquid Helium, Phys. Rev. 104, 576–584 (1956).
L.P. Pitaevskii, Vortex lines in an imperfect Bose gas, Sov. Phys. JETP 13, 451–454 (1961).
M. Reed and B. Simon, Methods of Modern Mathematical Physics IV. Analysis of Operators, Academic Press (1978).
R. Seiringer, Gross-Pitaevskii Theory of the Rotating Bose Gas, Commun. Math. Phys. 229, 491–509 (2002).
R. Seiringer, Ground state asymptotics of a dilute, rotating gas, J. Phys. A: Math. Gen. 36, 9755–9778 (2003).
B. Simon, Trace ideals and their application, Cambridge University Press (1979).
G. Temple, The theory of Rayleigh's principle as applied to continuous systems, Proc. Roy. Soc. London A 119, 276–293 (1928).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer
About this chapter
Cite this chapter
Seiringer, R. (2006). Dilute, Trapped Bose Gases and Bose-Einstein Condensation. In: Dereziński, J., Siedentop, H. (eds) Large Coulomb Systems. Lecture Notes in Physics, vol 695. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-32579-4_6
Download citation
DOI: https://doi.org/10.1007/3-540-32579-4_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-32578-9
Online ISBN: 978-3-540-32579-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)