Abstract
We report on some recent results regarding the dynamical behavior of a trapped Bose-Einstein condensate, in the limit of a large number of particles. These results were obtained in [4], a joint work with L. Erdős and H.-T. Yau.
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References
R. Adami, C. Bardos, F. Golse and A. Teta: Towards a rigorous derivation of the cubic nonlinear Schrödinger equation in dimension one. Asymptot. Anal. (2) 40 (2004), 93–108.
F.J. Dyson: Ground-state energy of a hard-sphere gas. Phys. Rev. (1) 106 (1957), 20–26.
A. Elgart, L. Erdős, B. Schlein, and H.-T. Yau: Gross-Pitaevskii equation as the mean field limit of weakly coupled bosons. Preprint math-ph/0410038. To appear in Arch. Rat. Mech. Anal.
L. Erdős, B. Schlein, and H.-T. Yau: Derivation of the Gross-Pitaevskii hierarchy for the dynamics of a Bose-Einstein condensate. Preprint math-ph/0410005.
L. Erdős and H.-T. Yau: Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Adv. Theor. Math. Phys. (6) 5 (2001), 1169–1205.
J. Ginibre and G. Velo: The classical field limit of scattering theory for non-relativistic many-boson systems. I and II. Commun. Math. Phys. 66 (1979), 37–76 and 68 (1979), 45–68.
E.P. Gross: Structure of a quantized vortex in boson systems. Nuovo Cimento 20 (1961), 454–466.
E.P. Gross: Hydrodynamics of a superfluid condensate. J. Math. Phys. 4 (1963), 195–207.
K. Hepp: The classical limit for quantum mechanical correlation functions. Commun. Math. Phys. 35 (1974), 265–277.
E.H. Lieb and R. Seiringer: Proof of Bose-Einstein Condensation for Dilute Trapped Gases. Phys. Rev. Lett. 88 (2002), 170409–1–4.
E.H. Lieb, R. Seiringer, J.P. Solovej, and J. Yngvason: The Quantum-Mechanical Many-Body Problem: Bose Gas. Preprint math-ph/0405004.
E.H. Lieb, R. Seiringer, J. Yngvason: Bosons in a Trap: A Rigorous Derivation of the Gross-Pitaevskii Energy Functional. Phys. Rev A 61 (2000), 043602.
E.H. Lieb and J. Yngvason: Ground State Energy of the low density Bose Gas. Phys. Rev. Lett. 80 (1998), 2504–2507.
L.P. Pitaevskii: Vortex lines in an imperfect Bose gas. Sov. Phys. JETP 13 (1961), 451–454.
H. Spohn: Kinetic Equations from Hamiltonian Dynamics. Rev. Mod. Phys. 52 no. 3 (1980), 569–615.
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Schlein, B. (2006). Derivation of the Gross-Pitaevskii Hierarchy. In: Asch, J., Joye, A. (eds) Mathematical Physics of Quantum Mechanics. Lecture Notes in Physics, vol 690. Springer, Berlin, Heidelberg . https://doi.org/10.1007/3-540-34273-7_20
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DOI: https://doi.org/10.1007/3-540-34273-7_20
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