We consider a system realized with one spinless quantum particle nd an array of N spins 1/2 in dimensions 1 and 3. We characterize all the Hamiltonians obtained as point perturbations of assigned free dynamics in terms of some generalized boundary conditions. For every boundary condition, we give the explicit formula for the resolvent of the corresponding Hamiltonian. We discuss the problem of locality and give two examples of spin-dependent point potentials that could be of interest as multi-component solvable models.
Spin dependent point potentials in one and three dimensions / Cacciapuoti, C.; Carlone, Raffaele; Figari, Rodolfo. - In: JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL. - ISSN 1751-8113. - STAMPA. - 40:(2007), pp. 249-261. [10.1088/1751-8113/40/2/004]
Spin dependent point potentials in one and three dimensions
CARLONE, RAFFAELE;FIGARI, RODOLFO
2007
Abstract
We consider a system realized with one spinless quantum particle nd an array of N spins 1/2 in dimensions 1 and 3. We characterize all the Hamiltonians obtained as point perturbations of assigned free dynamics in terms of some generalized boundary conditions. For every boundary condition, we give the explicit formula for the resolvent of the corresponding Hamiltonian. We discuss the problem of locality and give two examples of spin-dependent point potentials that could be of interest as multi-component solvable models.| File | Dimensione | Formato | |
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