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A class of exactly solvable many-particle models

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Conclusions

We have found a class of exactly solvable many-particle two-component quantum models with arbitrary form of the two-body interaction for which it is possible to construct exact eigenstates corresponding to a condensate of noninteracting composite particles. The fulfillment of the necessary symmetry conditions between the components means effectively that there are no many-particle correlations in the state with condensate. This can be regarded as the reason why an exact solution is possible. In the case of physical realizations, for which the required properties cannot be satisfied with complete accuracy, our treatment may be helpful as a good initial approximation.

Examples of such systems are quasitwo-dimensional electron-hole (and multicomponent electron) systems in a strong magnetic field, when as a result of the action of the field and size quantization the particles have no kinetic energy. There could also be other physical realizations, including discrete models.

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Authors
  1. A. B. Dzyubenko
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  2. Yu. E. Lozovik
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Scientific-Research Center for Technological Lasers, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 86, No. 1, pp. 98–110, January, 1991.

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Dzyubenko, A.B., Lozovik, Y.E. A class of exactly solvable many-particle models. Theor Math Phys 86, 67–76 (1991). https://doi.org/10.1007/BF01018498

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