A Study of Quantum ManyBody Systems With Nearest And NexttoNearest Neighbour LongRange Interactions
Abstract
The scattering and bound states of the manybody systems, related to the shortrange Dyson model, are studied. First, we show that the scattering states can be realized as coherent states and the scattering Hamiltonian can be connected to a free system. Unlike the closely related CalogeroMoser model, only a part of the partial waves acquire energy independent phase shifts, after scattering. The cause of the same is traced to the reduction in the degeneracies. The bound state Hamiltonian for the fullline problem is also studied and the relationship of its Hilbert space with that of the decoupled oscillators elucidated. Finally, we analyze the related models on circle and construct a part of the excitation spectrum through symmetry arguments.
 Publication:

arXiv eprints
 Pub Date:
 July 2000
 arXiv:
 arXiv:condmat/0007005
 Bibcode:
 2000cond.mat..7005E
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 28 pages