Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interactions. I. General concept

Variational methods with coupled Gaussian functions for Bose-Einstein condensates with long-range interaction

Transition state theory for wave packet dynamics: II. Thermal decay of Bose–Einstein condensates with long-range interaction

We apply transition state theory to coupled Gaussian wave packets and calculate thermal decay rates of Bose–Einstein condensates with additional long-range interaction. The ground state of such a condensate is metastable if the contact interaction is attractive and a sufficient thermal excitation may lead to its collapse. The use of transition state theory is made possible by describing the con...

Nonlinear Dynamics of Bose-Einstein Condensates with Long-Range Interactions

The motto of this paper is: Let's face Bose-Einstein condensation through nonUnear dynamics. We do this by choosing variational forms of the condensate wave functions (of given symmetry classes), which convert the Bose-Einstein condensates via the time-dependent GrossPitaevskii equation into Hamiltonian systems that can be studied using the methods of nonUnear dynamics. We consider in particula...

Anisotropic Bose-Einstein Condensates and Completely Integrable Dynamical Systems

A Gaussian ansatz for the wave function of two-dimensional harmonically trapped anisotropic Bose-Einstein condensates is shown to lead, via a variational procedure, to a coupled system of two second-order, nonlinear ordinary differential equations. This dynamical system is shown to be in the general class of Ermakov systems. Complete integrability of the resulting Ermakov system is proven. Usin...

Variational calculations on multilayer stacks of dipolar Bose-Einstein condensates

We investigate a multilayer stack of dipolar Bose-Einstein condensates in terms of a simple Gaussian variational ansatz and demonstrate that this arrangement is characterized by the existence of several stationary states. Using a Hamiltonian picture we show that in an excited stack there is a coupled motion of the individual condensates by which they exchange energy. We find that for high excit...