Jon Links et al 2003 J. Phys. A: Math. Gen. 36 R63 doi:10.1088/0305-4470/36/19/201
Jon Links, Huan-Qiang Zhou, Ross H McKenzie and Mark D Gould
Show affiliationsIn this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose–Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose–Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic–molecular Bose–Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics. Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions. In applying all the above models to physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.
17B80 Applications to integrable systems
81R12 Relations with integrable systems (See also 17Bxx, 37J35)
Quantum gases, liquids and solids
Issue 19 (16 May 2003)
Received 6 January 2003
Published 29 April 2003
Jon Links et al 2003 J. Phys. A: Math. Gen. 36 R63
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