We propose a mechanical (Hamiltonian) interpretation of the so-called spectrality property introduced by Sklyanin and Kuznetsov in the context of Backlund transformations (BTs) for finite-dimensional integrable systems. This property turns out to be deeply connected with the Hamilton-Jacobi separation of variables and can lead to the explicit integration of the corresponding model using the BTs. We show that once such a construction is given, we can interpret the Baxter Q-operator defining the quantum BTs as the Green's function or the propagator of the time-dependent Schrodinger equation for an interpolating Hamiltonian.
Ragnisco O, & Zullo F (2012). Quantum backlund transformations: Some ideas and examples. THEORETICAL AND MATHEMATICAL PHYSICS, 172(2), 1160-1171 [10.1007/s11232-012-0104-8].
Titolo: | Quantum backlund transformations: Some ideas and examples | |
Autori: | ||
Data di pubblicazione: | 2012 | |
Rivista: | ||
Citazione: | Ragnisco O, & Zullo F (2012). Quantum backlund transformations: Some ideas and examples. THEORETICAL AND MATHEMATICAL PHYSICS, 172(2), 1160-1171 [10.1007/s11232-012-0104-8]. | |
Abstract: | We propose a mechanical (Hamiltonian) interpretation of the so-called spectrality property introduced by Sklyanin and Kuznetsov in the context of Backlund transformations (BTs) for finite-dimensional integrable systems. This property turns out to be deeply connected with the Hamilton-Jacobi separation of variables and can lead to the explicit integration of the corresponding model using the BTs. We show that once such a construction is given, we can interpret the Baxter Q-operator defining the quantum BTs as the Green's function or the propagator of the time-dependent Schrodinger equation for an interpolating Hamiltonian. | |
Handle: | http://hdl.handle.net/11590/134628 | |
Appare nelle tipologie: | 1.1 Articolo in rivista |