|
This article is cited in 11 scientific papers (total in 11 papers)
Polynomial Conservation Laws in Quantum Systems
V. V. Kozlov, D. V. Treschev M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Abstract:
We consider systems with a finite number of degrees of freedom and potential energy that is a finite sum of exponentials with purely imaginary or real exponents. Such systems include the generalized Toda chains and systems with a toric configuration space. We consider the problem of describing all the quantum conservation laws, i.e. the differential operators that are polynomial in the derivatives and commute with the Hamiltonian operator. We prove that in the case where the potential energy spectrum is invariant under reflection with respect to the origin, such nontrivial operators exist only if the system under consideration decomposes into a direct sum of decoupled subsystems. In the general case (without the spectrum symmetry assumption), we prove that the existence of a complete set of independent conservation laws implies the complete integrability of the corresponding classical system.
Keywords:
Hamiltonian operator, polynomial differential operator, system with exponential interaction, potential spectrum.
Received: 15.12.2003 Revised: 02.02.2004
Citation:
V. V. Kozlov, D. V. Treschev, “Polynomial Conservation Laws in Quantum Systems”, TMF, 140:3 (2004), 460–479; Theoret. and Math. Phys., 140:3 (2004), 1283–1298
Linking options:
https://www.mathnet.ru/eng/tmf103https://doi.org/10.4213/tmf103 https://www.mathnet.ru/eng/tmf/v140/i3/p460
|
Statistics & downloads: |
Abstract page: | 706 | Full-text PDF : | 272 | References: | 95 | First page: | 6 |
|