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 TMF, 1991, Volume 86, Number 1, Pages 98–110 (Mi tmf5425)

A class of exactly solvable many-particle models

A. B. Dzyubenko, Yu. E. Lozovik

Abstract: A class of many-particle quantum models with arbitrary space dimension and arbitrary particle statistics for which it is possible to construct a number of exact eigenstates is found. In the models, the following assumptions are made: 1) the presence of two (or $2m$) components with “symmetric” matrix elements of the two-body interactions (equality up to the sign of all the interaction potentials and equality up to a phase factor of the wave functions of particles of two species; otherwise the two-body interactions are arbitrary), 2) degeneracy of the (total) spectrum of the free particles. The exact states correspond to a condensate of noninteracting composite particles (“excitons”) that are not precisely bosons and to excitations over the condensate. The possibility of exact solution rests on the symmetry with respect to continuous rotations in the isospin space, this corresponding to Bogolyubov transformations with momentum-independent parameters $u$$v$. The class includes, in particular, two-dimensional electron-hole systems in a strong magnetic field.

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English version:
Theoretical and Mathematical Physics, 1991, 86:1, 67–76

Bibliographic databases:

Citation: A. B. Dzyubenko, Yu. E. Lozovik, “A class of exactly solvable many-particle models”, TMF, 86:1 (1991), 98–110; Theoret. and Math. Phys., 86:1 (1991), 67–76

Citation in format AMSBIB
\Bibitem{DzyLoz91} \by A.~B.~Dzyubenko, Yu.~E.~Lozovik \paper A~class of exactly solvable many-particle models \jour TMF \yr 1991 \vol 86 \issue 1 \pages 98--110 \mathnet{http://mi.mathnet.ru/tmf5425} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=1106828} \zmath{https://zbmath.org/?q=an:0989.82502} \transl \jour Theoret. and Math. Phys. \yr 1991 \vol 86 \issue 1 \pages 67--76 \crossref{https://doi.org/10.1007/BF01018498} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1991GC79000008}