Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases

By Elliott H. Lieb, Robert Seiringer. 2005

218 citations recorded by the source corpus.

We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/a4ab01f720c5d8b8f7fb6124fd37ba141c03373e

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In Atomic and Molecular Physics, and Optics

Citations in the corpus

Mathematical Models and Numerical Methods for Bose-Einstein Condensation (2012, background): “At temperatures T much smaller than the critical temperature Tc [150], a two-component BEC with an internal atomic Josephson junction (or an external driving field) can be well described by the coupled Gross-Pitaevskii equations (CGPEs) [19,131,134,185,195],”
The Stability of Matter in Quantum Mechanics (2009, background): “In fact, the bosonic symmetry requirement is essential for understanding vortex formation in dilute Bose gases subject to homogeneous magnetic fields [162, 126].”
Rapidly rotating atomic gases (2008, background): “ the mean-ﬁeld interaction gn¯ to remain ﬁnite (for example, to stay in the 2D LLL regime), one should take gN → const. With this set of scalings, the GrossPitaevskii theory has been shown to be exact[73]: the groundstate is a pure condensate in this thermodynamic limit. We have shown explicit examp”
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].”