The Mathematics of the Bose Gas and its Condensation

By Elliott H. Lieb, Robert Seiringer, J. P. Solovej, J. Yngvason. 2005

582 citations recorded by the source corpus.

The Dilute Bose Gas in 3D.- The Dilute Bose Gas in 2D.- Generalized Poincare Inequalities.- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases.- Gross-Pitaevskii Equation for Trapped Bosons.- Bose-Einstein Condensation and Superfluidity for Dilute Trapped Gases.- One-Dimensional Behavior of Dilute Bose Gases in Traps.- Two-Dimensional Behavior in Disc-Shaped Traps.- The Charged Bose Gas, the One- and Two-Component Cases.- Bose-Einstein Quantum Phase Transition in an Optical Lattice Model.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/b04a434ac33320d017adb91edb924519ca095f45

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In Atomic and Molecular Physics, and Optics

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Citations in the corpus

The Excitation Spectrum for Weakly Interacting Bosons in a Trap (2012, background): “From the point of view of mathematical physics, starting with the basic underlying many-body Schrödinger equation, it remains a big challenge to understand many features of cold quantum gases [8,9].”
The quintic NLS as the mean field limit of a boson gas with three-body interactions (2008, background): “The mathematical study of systems of interacting Bose gases is a central research area in mathematical physics which has in recent years experienced remarkable progress.”
Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases (2005, result): “As in our previous work [15, 12, 17, 23, 14 ] on dilute, trapped Bose gases we start with the Hamiltonian for N bosons”
Bogoliubov Spectrum of Interacting Bose Gases (2012, methodology): “The operator UN is a mathematical tool which implements what is called a c-number substitution [41, 40].”
Normalized solution to the Schrödinger equation with potential and general nonlinear term: Mass super-critical case (2021, background): “We point out that there are situations in the Bose-Einstein condensate theory that requires the chemical potentials are positive, see [13, 20].”
Dark solitons in atomic Bose–Einstein condensates: from theory to experiments (2010, background): “The above results (as well as the ones in [81]) were proved for stationary solutions of the GP equation and, in particular, for the ground-state solution.”
Second-Order Corrections to Mean Field Evolution of Weakly Interacting Bosons. I. (2009, background): “Introduction Experimental advances in the Bose-Einstein condensation (BEC) of dilute atomic gases [1, 3] have stimulated interesting questions on the quantum theory of many-body systems.”
Derivation of Hartree's theory for generic mean-field Bose systems (2013, background): “Recently, the experimental realization of Bose-Einstein condensates has motivated the study of a more subtle, so called Gross-Pitaevskii, limit [43, 41].”
The Excitation Spectrum for Weakly Interacting Bosons (2010, background): “The Bogoliubov approximation [1, 11] predicts that E0(N) is close to 12Nv̂(0) + E , where E = −(1) 2 ∑”
Quantitative Derivation of the Gross‐Pitaevskii Equation (2012, background): “)| ≤ C |x|2 +1 . (57) Proof. Standard arguments show that 0 ≤ f(x) ≤ 1 holds for every x∈ R3 (f(x) ≤ 1 follows from V ≥ 0, because of the monotonic dependence of f on the potential; see Appendix C in [19]). This implies that 0 ≤ w(x) ≤ 1 for all x∈ R3. From the zero energy scattering equation, we ha”
Mathematical Models and Numerical Methods for Bose-Einstein Condensation (2012, methodology): “For a BEC of ultracold dilute gas withN identical bosons confined in an external trap, only binary interaction is important, then the many-body Hamiltonian for it can be written as [56, 58]”