Normal form expansions and thermal decay rates of Bose-Einstein condensates with short- and long-range interaction
arXiv:1411.0458 · doi:10.1140/epjd/e2015-50883-3
Abstract
The thermally induced coherent collapse of Bose-Einstein condensates at finite temperature is the dominant decay mechanism near the critical scattering length in condensates with at least partially attractive interaction. The collapse dynamics out of the ground state is mediated by a transition state whose properties determine the corresponding decay rate or lifetime of the condensate. In this paper, we perform normal form expansions of the ground and the transition state of condensates with short-range scattering interaction as well as with anisotropic and long-range dipolar interaction in a variational framework. This method allows one to determine the local properties of these states, i.e. their mean-field energy, their normal modes, the coupling between different modes, and the structure of the reaction channel to any desired order. We discuss the physical interpretation of the transition state as a certain density distribution of the atomic cloud and the behavior of the single normal form contributions in dependence on the s-wave scattering length. Moreover, we investigate the convergence of the local normal form when using extended Gaussian variational approaches, and present the condensate's decay rate.
10 pages, 8 figures, accepted for publication in Eur. Phys. J. D
References in corpus (17)
- Bose-Einstein condensation of chromium
- Bose-Einstein Condensation of Erbium
- Stabilizing a purely dipolar quantum gas against collapse
- d-wave collapse and explosion of a dipolar Bose-Einstein condensate
- Radial and angular rotons in trapped dipolar gases
- Anisotropic solitons in dipolar Bose-Einstein Condensates
- Wigner's Dynamical Transition State Theory in Phase Space: Classical and Quantum
- Ground-state structure and stability of dipolar condensates in anisotropic traps
- Coherent collapse of a dipolar Bose-Einstein condensate for different trap geometries
- Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept
- Dynamics and stability of Bose-Einstein condensates with attractive 1/r interaction
- Relation between the eigenfrequencies of Bogoliubov excitations of Bose-Einstein condensates and the eigenvalues of the Jacobian in a time-dependent variational approach
- Symmetry-breaking thermally induced collapse of dipolar Bose-Einstein condensates
- Transition state theory for wave packet dynamics. II. Thermal decay of Bose-Einstein condensates with long-range interaction
- Transition state theory for wave packet dynamics. I. Thermal decay in metastable Schrödinger systems
- A variational approach to Bogoliubov excitations and dynamics of dipolar Bose-Einstein condensates
- Macroscopic quantum tunneling of Bose-Einstein condensates with long-range interaction