2008/07/31 by H. K. Owusu, H K Owusu, K. Wagh +3 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Commutation #Connection (principal bundle) #Coupling (piping) #Equivalence (formal languages) #Exact solutions in general relativity #Hamiltonian (control theory) #Integrable system #Quantum #Quantum chaos and dynamical systems #Quantum many-body systems #cond-mat.stat-mech
paper · pdf · doi:10.1088/1751-8113/42/3/035206
published as 2009 J. Phys. A: Math. Theor. 42 035206 · 33 pages, 10 figures, minor typos corrected, reference added, model generalized beyond real symmetric to Hermitian operators
openalex publication_date 2008/12/09 · arxiv created 2009/01/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We 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.