arXiv:0712.2495 · Advances in Theoretical and Mathematical Physics

On the Quantum Instability of Attractive Bose Systems

George Edwin Cragg, Arthur K. Kerman

Published Jan 1, 2010• 0 citations

Abstract

We explore the zero-temperature behavior of an assembly of bosons interacting through a zero-range, attractive potential.Because the twobody interaction admits a bound state, the many-body model is best described by a Hamiltonian that includes the coupling between atomic and molecular components.Due to the positive scattering length, the low-density collection is expected to remain stable against collapse despite the attraction between particles.Although a variational many-body analysis indicates a collapsing solution with only a molecular component to its condensate at low density, the expected atomic condensate solution can be obtained if the chemical potential is allowed to be complex valued.In addition to revealing two discrete eigenfrequencies associated with the molecular case, an expansion in small oscillations quantifies the imaginary part of the chemical potential as proportional to a coherent decay rate of the atomic condensate into a continuum of collective phonon excitations about the collapsing lower state.

DOI: 10.4310/atmp.2010.v14.n1.a2

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arXiv:0712.2495 · Advances in Theoretical and Mathematical Physics

On the Quantum Instability of Attractive Bose Systems

George Edwin Cragg, Arthur K. Kerman

Published Jan 1, 2010• 0 citations

arXiv HTML PDF

Abstract

DOI: 10.4310/atmp.2010.v14.n1.a2

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N

-body density operator, we discuss the thermodynamic properties at low temperature and the relative stability of the system towards the formation of an atomic Bose-Einstein condensate. We also derive an approximate Gross-Pitaevskii equation for the molecular condensate leading to the prediction of a Bogoliubov spectrum.

g

. For small

|g|

, the bosons form a stable Bose-Einstein condensate with the energy per particle uniformly bounded from below. For large

|g|

, the energy per particle is no longer uniformly bounded from below, signaling the collapse of the condensate.

N

of atoms is not too big. The transition between the two classes of solutions as a function of

N

can be either sharp or smooth according to the ratio between the range of the attractive interaction and the length of the trap. A tight trap leads to a smooth transition. In addition to the energy and the shape of the cloud we study also the dynamics of the system. In particular, we study the frequencies of collective oscillation of the Bose condensate as a function of the number of atoms both in the local and in the non local case. Moreover, we consider the dynamics of the cloud when the external trap is switched off.