Low-dimensional bose liquids: beyond the gross-pitaevskii approximation

The Gross-Pitaevskii approximation is a long-wavelength theory widely used to describe a variety of properties of dilute Bose condensates, in particular trapped alkali gases. We point out that for short-ranged repulsive interactions this theory fails in dimensions d相似文献   

Gross-Pitaevskii Theory of the Rotating Bose Gas

 We study the Gross-Pitaevskii functional for a rotating two-dimensional Bose gas in a trap. We prove that there is a breaking of the rotational symmetry in the ground state; more precisely, for any value of the angular velocity and for large enough values of the interaction strength, the ground state of the functional is not an eigenfunction of the angular momentum. This has interesting consequences on the Bose gas with spin; in particular, the ground state energy depends non-trivially on the number of spin components, and the different components do not have the same wave function. For the special case of a harmonic trap potential, we give explicit upper and lower bounds on the critical coupling constant for symmetry breaking. Received: 1 December 2001 / Accepted: 19 April 2002 Published online: 6 August 2002     

Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases

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.     

Comment on the NMR lineshape in low-dimensional paramagnets

It will be demonstrated that the model used by some workers to describe the NMR lineshape in low-dimensional magnetic systems is of academic interest only. Furthermore, we will show that this model was not treated properly. The NMR lineshape in low-dimensional systems has a normal single-peaked structure.     

Crystalline boson phases in harmonic traps: beyond the Gross-Pitaevskii mean field

Strongly-interacting bosons in two-dimensional harmonic traps are described through breaking of rotational symmetry at the Hartree-Fock level and subsequent symmetry restoration via projection techniques, thus incorporating correlations beyond the Gross-Pitaevskii (GP) solution. The bosons localize and form polygonal-ringlike crystalline patterns, both for a repulsive contact potential and a Coulomb interaction, as revealed via conditional-probability-distribution analysis. For neutral bosons, the total energy of the crystalline phase saturates in contrast to the GP solution, and its spatial extent becomes smaller than that of the GP condensate. For charged bosons, the total energy and dimensions approach the values of classical pointlike charges in their equilibrium configuration.