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Physics Letters A

The role of spin in the development of coherent structures in many-body systems

J.M. Dixon, Jack A. Tuszyński

Published May 1, 1991• 11 citations
Publisher
DOI
10.1016/0375-9601(91)90574-r

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No author provided

Spin components have been explicitly included in an accurate analytical approach for the study of coherent structures in many-body systems. Equations of motion for annihilators and creators are transformed into non-linear equations of motion for a spin-dependent quantum field. It is demonstrated, using commutation relations for the quantum field operators, that spin-up, psi+, and spin-down, psi-, fields may be decoupled. The equation of motion for psi+ is shown to have a form identical to the equation of motion for psi+ which, in turn, is equivalent to that for a field with no specific spin component. The latter equations have the same form for both bosons and fermions.

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A stable spin-structure found in a 3-body system with spin-3 cold atoms and its role in N-body condensates

Y M Liu, Y. Z. He, Bao Cheng-guang

We have found a stable spin-structure of N [Formula: see text] 3 system in which three spin-3 atoms are trapped and coupled to total spin S [Formula: see text] 3. We have proved that a pair of this structure is nearly an exact solution for N [Formula: see text] 6 systems in a very broad district in the parameter-space. Comparing with the well-known singlet pairs, this pair is a more promising candidate to serve as a building block for large N systems with spin-3 atoms. This is because the spin-structure of the latter can be modified depending on the interactions to reduce the energy while the singlet pairs can not. In fact, we have proved that, for a specific set of strengths (a point in the parameter-space) the product state based on this pair is an exact solution of the N-body Hamiltonian. Thus, in the neighborhood of this point, the product state will appear as an approximate solution. However, how broad this neighborhood would be remains to be clarified.

Scientific Reports•Jan 19, 2021•2 citations
The authors combine two developments in the areas of mathematical physics and many body systems. The first is the introduction of systems of q-bosons in connection with the study of quantum groups. The second is the formulation of nonlinear dynamics for interacting many-particle systems. They demonstrate the role of quantum groups via the introduction of interacting q-bosons. A number of interesting properties emerge which involve dissipative nonlinear dynamics, bifurcation effects and transitions between localized and extended states.
Spin components have been explicitly included in an accurate analytical approach for the study of coherent structures in many-body systems. Equations of motion for annihilators and creators are transformed into non-linear equations of motion for a spin-dependent quantum field. It is demonstrated, using commutation relations for the quantum field operators, that spin-up, psi+, and spin-down, psi-, fields may be decoupled. The equation of motion for psi+ is shown to have a form identical to the equation of motion for psi+ which, in turn, is equivalent to that for a field with no specific spin component. The latter equations have the same form for both bosons and fermions.
We have found a stable spin-structure of N [Formula: see text] 3 system in which three spin-3 atoms are trapped and coupled to total spin S [Formula: see text] 3. We have proved that a pair of this structure is nearly an exact solution for N [Formula: see text] 6 systems in a very broad district in the parameter-space. Comparing with the well-known singlet pairs, this pair is a more promising candidate to serve as a building block for large N systems with spin-3 atoms. This is because the spin-structure of the latter can be modified depending on the interactions to reduce the energy while the singlet pairs can not. In fact, we have proved that, for a specific set of strengths (a point in the parameter-space) the product state based on this pair is an exact solution of the N-body Hamiltonian. Thus, in the neighborhood of this point, the product state will appear as an approximate solution. However, how broad this neighborhood would be remains to be clarified.