Advanced

Gauge fields, point interactions and few-body problems in one dimension

Albeverio, Sergio; Fei, SM and Kurasov, Pavel LU (2004) In Reports on Mathematical Physics 53(3). p.363-370
Abstract
Point interactions for the second derivative operator in one dimension are studied. Every operator from this family is described by the boundary conditions which include a 2 x 2 real matrix with the unit determinant and a phase. The role of the phase parameter leading to unitarily equivalent operators is discussed in the present paper. In particular, it is shown that the phase parameter is not redundant (contrary to previous studios) if nonstationary problems are concerned. It is proven that the phase parameter can be interpreted as the amplitude of a singular gauge field. Considering the few-body problem we extend the range of parameters for which the exact solution can be found using the Bethe Ansatz.
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
point interactions, boundary conditions, system, few-body, Schrodinger operator
in
Reports on Mathematical Physics
volume
53
issue
3
pages
363 - 370
publisher
Elsevier
external identifiers
  • wos:000222006500004
  • scopus:4444358943
ISSN
0034-4877
language
English
LU publication?
yes
id
64f2df54-2770-4276-8ba2-b9b5425558b0 (old id 274989)
date added to LUP
2007-09-03 10:43:35
date last changed
2017-01-01 04:26:09
@article{64f2df54-2770-4276-8ba2-b9b5425558b0,
  abstract     = {Point interactions for the second derivative operator in one dimension are studied. Every operator from this family is described by the boundary conditions which include a 2 x 2 real matrix with the unit determinant and a phase. The role of the phase parameter leading to unitarily equivalent operators is discussed in the present paper. In particular, it is shown that the phase parameter is not redundant (contrary to previous studios) if nonstationary problems are concerned. It is proven that the phase parameter can be interpreted as the amplitude of a singular gauge field. Considering the few-body problem we extend the range of parameters for which the exact solution can be found using the Bethe Ansatz.},
  author       = {Albeverio, Sergio and Fei, SM and Kurasov, Pavel},
  issn         = {0034-4877},
  keyword      = {point interactions,boundary conditions,system,few-body,Schrodinger operator},
  language     = {eng},
  number       = {3},
  pages        = {363--370},
  publisher    = {Elsevier},
  series       = {Reports on Mathematical Physics},
  title        = {Gauge fields, point interactions and few-body problems in one dimension},
  volume       = {53},
  year         = {2004},
}