تقرير
The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models
| العنوان: | The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models |
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| المؤلفون: | Owusu, H. K., Wagh, K., Yuzbashyan, E. A. |
| المصدر: | 2009 J. Phys. A: Math. Theor. 42 035206 |
| سنة النشر: | 2008 |
| المجموعة: | Condensed Matter |
| مصطلحات موضوعية: | Condensed Matter - Statistical Mechanics |
| الوصف: | 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. Comment: 33 pages, 10 figures, minor typos corrected, reference added, model generalized beyond real symmetric to Hermitian operators |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1088/1751-8113/42/3/035206 |
| URL الوصول: | http://arxiv.org/abs/0807.0259 |
| رقم الأكسشن: | edsarx.0807.0259 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1088/1751-8113/42/3/035206 |
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