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Annals of Physics

Collective energies from momentum- and angular momentum-projected determinantal wavefunctions

Felix M. H. Villars, Nancy Schmeing-Rogerson

Published Apr 1, 1971• 48 citations
Publisher
DOI
10.1016/0003-4916(71)90021-2

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The recent report on the realization of a Bose-Einstein condensate of G-wave molecule made up of bound pairs of Cesium bosons is a surprise. These molecules are created at the G-wave resonance at 19.87G, where the severe three-body loss usually associated with these resonance are found to be reduced significantly when the density of the gas is reduced in a quasi 2D setting. The G-wave molecules produced through this resonance have non-zero angular momentum projections, resulting in the first BEC with a macroscopic intrinsic angular momentum. Here, we show that this intrinsic angular momentum will lead to many new quantum effects. They include a splitting of collective modes in the absence of vortices, an orientation dependent energy shift due to the moment of inertia of the molecules, and a contribution to angular momentum in non-uniform magnetic fields different from that of the Berry phase current. The intrinsic angular momentum also provides a way to probe the half vortices, excitations that are unique to molecular condensates of bosons. The wavefunction giving rise to the intrinsic angular momentum can also be mapped out from the noise correlation.

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Boundary conditions on wavefunctions for three bodies at singular configurations

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Singular configurations have long been out of consideration in the study of many-particle systems. In this paper we show that a group theoretical method can provide boundary conditions on wavefunctions at singular configurations of many particles. The consequences of this method are qualitatively stated as follows. (i) If the projection of angular momentum on an axis does not vanish, the particles will not be aligned on the axis, i.e. the wavefunction vanishes at collinear configurations along the axis. (ii) If the total angular momentum does not vanish, the simultaneous collision at a point will not take place, i.e. the wavefunction vanishes at the configuration of simultaneous collision. Furthermore, on the assumption of analyticity of the wavefunction at singular configurations, the behaviour of the wavefunction around the singular configurations shows that (a) the larger the projection of angular momentum on an axis becomes, the less the particles are likely to be aligned on the line, and that (b) the more the total angular momentum grows, the less likely the particles are to collide at a point. The proof is carried out for three-body systems by transforming the power series expansion of a wavefunction into a Fourier series expansion in terms of the angular momentum eigenfunctions, in both cases of collinear configurations and of the triple collision, without reference to the Hamiltonian operator. These results are described quantitatively in terms of the angular momentum quantum numbers in propositions 1 and 3 in the text.

Journal of Physics A Mathematical and General•Jan 6, 2004•1 citation

COLLECTIVE EXCITATIONS WITH THE NUMBER-PROJECTED WAVE FUNCTIONS.

Sadao Kusuno, S. Yoshida

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The recent report on the realization of a Bose-Einstein condensate of G-wave molecule made up of bound pairs of Cesium bosons is a surprise. These molecules are created at the G-wave resonance at 19.87G, where the severe three-body loss usually associated with these resonance are found to be reduced significantly when the density of the gas is reduced in a quasi 2D setting. The G-wave molecules produced through this resonance have non-zero angular momentum projections, resulting in the first BEC with a macroscopic intrinsic angular momentum. Here, we show that this intrinsic angular momentum will lead to many new quantum effects. They include a splitting of collective modes in the absence of vortices, an orientation dependent energy shift due to the moment of inertia of the molecules, and a contribution to angular momentum in non-uniform magnetic fields different from that of the Berry phase current. The intrinsic angular momentum also provides a way to probe the half vortices, excitations that are unique to molecular condensates of bosons. The wavefunction giving rise to the intrinsic angular momentum can also be mapped out from the noise correlation.
Singular configurations have long been out of consideration in the study of many-particle systems. In this paper we show that a group theoretical method can provide boundary conditions on wavefunctions at singular configurations of many particles. The consequences of this method are qualitatively stated as follows. (i) If the projection of angular momentum on an axis does not vanish, the particles will not be aligned on the axis, i.e. the wavefunction vanishes at collinear configurations along the axis. (ii) If the total angular momentum does not vanish, the simultaneous collision at a point will not take place, i.e. the wavefunction vanishes at the configuration of simultaneous collision. Furthermore, on the assumption of analyticity of the wavefunction at singular configurations, the behaviour of the wavefunction around the singular configurations shows that (a) the larger the projection of angular momentum on an axis becomes, the less the particles are likely to be aligned on the line, and that (b) the more the total angular momentum grows, the less likely the particles are to collide at a point. The proof is carried out for three-body systems by transforming the power series expansion of a wavefunction into a Fourier series expansion in terms of the angular momentum eigenfunctions, in both cases of collinear configurations and of the triple collision, without reference to the Hamiltonian operator. These results are described quantitatively in terms of the angular momentum quantum numbers in propositions 1 and 3 in the text.