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Generalized local interactions in 1D: solutions of quantum many-body systems describing distinguishable particles
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
2005 (English)In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 22, 4957-4974 p.Article in journal (Refereed) Published
Abstract [en]

As is well known, there exists a four-parameter family of local interactions in 1D. We interpret these parameters as coupling constants of delta-type interactions which include different kinds of momentum-dependent terms, and determine all cases leading to many-body systems of distinguishable particles which are exactly solvable by the coordinate Bethe ansatz. We find two such families of systems, one with two independent coupling constants deforming the well-known delta-interaction model to non-identical particles, and the other with a particular one-parameter combination of the delta and (the so-called) delta-prime interaction. We also find that the model of non-identical particles gives rise to a somewhat unusual solution of the Yang-Baxter relations. For the other model we write down explicit formulae for all eigenfunctions.

Place, publisher, year, edition, pages
2005. Vol. 38, no 22, 4957-4974 p.
Keyword [en]
nonlinear schrodinger model, point interactions, one-dimension, bethe-ansatz, potentials, operators
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-7252DOI: 10.1088/0305-4470/38/22/018ISI: 000230980100019Scopus ID: 2-s2.0-19944394240OAI: oai:DiVA.org:kth-7252DiVA: diva2:12208
Note
QC 20101130Available from: 2007-05-31 Created: 2007-05-31 Last updated: 2017-12-14Bibliographically approved
In thesis
1. Exactly solved quantum many-body systems in one dimension
Open this publication in new window or tab >>Exactly solved quantum many-body systems in one dimension
2005 (English)Licentiate thesis, comprehensive summary (Other scientific)
Abstract [en]

This thesis is devoted to the study of various examples of exactly solved quantum many-body systems in one-dimension. It is divided into two parts: the first provides background and complementary results to the second, which consists of three scientific papers. The first paper concerns a particu- lar extension, corresponding to the root system CN, of the delta-interaction model. We prove by construction that its exact solution, even in the gen- eral case of distinguishable particles, can be obtained by the coordinate Bethe ansatz. We also elaborate on the physical interpretation of this model. It is well known that the delta-interaction is included in a four parameter family of local interactions. In the second paper we interpret these parameters as cou- pling constants of certain momentum dependent interactions and determine all cases leading to a many-body system of distinguishable particles which can be solved by the coordinate Bethe ansatz. In the third paper we consider the so-called rational Calogero-Sutherland model, describing an arbitrary number of particles on the real line, confined by a harmonic oscillator potential and interacting via a two-body interaction proportional to the inverse square of the inter-particle distance. We construct a novel solution algorithm for this model which enables us to obtain explicit formulas for its eigenfunctions. We also show that our algorithm applies, with minor changes, to all extensions of the rational Calogero-Sutherland model which correspond to a classical root system.

Place, publisher, year, edition, pages
Stockholm: KTH, 2005. vii, 40 p.
Series
Trita-FYS, ISSN 0280-316X ; 2005:57
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-564 (URN)91-7178-224-9 (ISBN)
Presentation
2005-12-14, seminarierum 112:028, AlbaNova hus 11, Roslagstullsbacken 11, Stockholm, 10:15
Opponent
Supervisors
Note
QC 20101130Available from: 2005-12-28 Created: 2005-12-28 Last updated: 2010-11-30Bibliographically approved

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