ar X iv : c on d - m at / 9 60 51 19 v 1 2 0 M ay 1 99 6 Dynamics of Collapse of a Confined Bose Gas
نویسنده
چکیده
Rigorous results on the nonlinear dynamics of a dilute Bose gas with a negative scattering length in an harmonic magnetic trap are presented and sufficient conditions for the collapse of the system are formulated. By using the virial theorem for the Gross-Pitaevskii equation in an external field we analyze the temporal evolution of the mean square radius I = r 2 | ψ | 2 dV of the gas cloud. In the 2D case this quantity undergoes harmonic oscillations with frequency 2ω 0. It implies that for a negative value of the energy of the system, the gas cloud will collapse after a finite time interval. For positive energy the cloud collapses if the initial conditions correspond to a large enough amplitude of oscillations. Stable oscillations with a small amplitude are possible. In the 3D case the system also collapses after a finite time for a state with negative energy. A stringent condition for the collapse is also derived.
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