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Open Quantum Systems Decoherence Quantum Simulation Quantum State Preparation Representation Entanglement Theory Quantum Correlations

The BC1 Elliptic model: algebraic forms, hidden algebra sl(2), polynomial eigenfunctions

arXiv
Authors: Alexander V. Turbiner

Year

2014

Paper ID

48190

Status

Preprint

Abstract Read

~2 min

Abstract Words

110

Citations

N/A

Abstract

The potential of the BC1 quantum elliptic model is a superposition of two Weierstrass functions with doubling of both periods (two coupling constants). The BC1 elliptic model degenerates to A1 elliptic model characterized by the Lamé Hamiltonian. It is shown that in the space of BC1 elliptic invariant, the potential becomes a rational function, while the flat space metric becomes a polynomial. The model possesses the hidden sl(2) algebra for arbitrary coupling constants: it is equivalent to sl(2)-quantum top in three different magnetic fields. It is shown that there exist three one-parametric families of coupling constants for which a finite number of polynomial eigenfunctions (up to a factor) occur.

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  • The potential of the BC1 quantum elliptic model is a superposition of two Weierstrass functions with doubling of both periods (two coupling constants).

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References & Citation Signals

[1] DOI https://doi.org/arXiv:1408.1610 [2] arXiv https://arxiv.org/abs/1408.1610 [3] Publisher https://arxiv.org/abs/1408.1610

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