The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models

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dc.creatorOwusu, H. K.
dc.creatorWagh, K.
dc.creatorYuzbashyan, E. A.
dc.date2008-07-02
dc.date2009-01-14
dc.date.accessioned2026-07-07T12:28:39Z
dc.date.available2026-07-07T12:28:39Z
dc.descriptionWe investigate the connection between energy level crossings in integrable systems and their integrability, i.e. the existence of a set of non-trivial integrals of motion. In particular, we consider a general quantum Hamiltonian linear in the coupling u, H(u) = T + uV, and require that it has the maximum possible number of nontrivial commuting partners also linear in u. We demonstrate how this commutation requirement alone leads to: (1) an exact solution for the energy spectrum and (2) level crossings, which are always present in these Hamiltonians in violation of the Wigner-von Neumann non-crossing rule. Moreover, we construct these Hamiltonians explicitly by resolving the above commutation requirement and show their equivalence to a sector of Gaudin magnets (central spin Hamiltonians). In contrast, fewer than the maximum number of conservation laws does not guarantee level crossings.
dc.description33 pages, 10 figures, minor typos corrected, reference added, model generalized beyond real symmetric to Hermitian operators
dc.identifierhttps://arxiv.org/abs/0807.0259
dc.identifierhttp://arxiv.org/abs/0807.0259
dc.identifier2009 J. Phys. A: Math. Theor. 42 035206
dc.identifierdoi:10.1088/1751-8113/42/3/035206
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/215612
dc.subjectStatistical Mechanics
dc.titleThe Link between Integrability, Level Crossings, and Exact Solution in Quantum Models
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