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Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems

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Abstract

We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them in the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension are identified with traces of quantum monodromy matrices for specific integrable systems with nonperiodic boundary conditions. Applications to the Azbel-Hofstadter problem are outlined.

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Authors and Affiliations

  1. Institute of Chemical Physics, Kosygina st. 4, 117334, Moscow, Russia

    A. V. Zabrodin

  2. ITEP, 117259, Moscow, Russia

    A. V. Zabrodin

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  1. A. V. Zabrodin
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 1, pp. 8–24, July, 1995.

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Zabrodin, A.V. Quantum transfer matrices for discrete and continuous quasi-exactly solvable problems. Theor Math Phys 104, 762–776 (1995). https://doi.org/10.1007/BF02066651

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