Exactly Solvable BCS-BEC crossover Hamiltonians
Abstract
We demonstrate a novel approach that allows the determination of very general classes of exactly solvable Hamiltonians via Bethe ansatz methods. This approach combines aspects of both the co-ordinate Bethe ansatz and algebraic Bethe ansatz. The eigenfunctions are formulated as factorisable operators acting on a suitable reference state. Yet, we require no prior knowledge of transfer matrices or conserved operators. By taking a variational form for the Hamiltonian and eigenstates we obtain general exact solvability conditions. The procedure is conducted in the framework of Hamiltonians describing the crossover between the low-temperature phenomena of superconductivity, in the Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC).
Cite
@article{arxiv.1303.1611,
title = {Exactly Solvable BCS-BEC crossover Hamiltonians},
author = {Andrew Birrell and Phillip S. Isaac and Jon Links},
journal= {arXiv preprint arXiv:1303.1611},
year = {2013}
}
Comments
6 Pages, To appear in Proceedings of The XXIXth International Colloquium on Group-Theoretical Methods in Physics at Chern Institute of Mathematics