Solving the quantum nonlinear Schrödinger equation with δ-type impurity

Caudrelier, Vincent; Mintchev, Mihail; Ragoucy, É.

doi:10.1063/1.1842353

Cited by 32 publications

(52 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…More recently, a new framework was introduced to handle reflecting and transmitting impurities in integrable systems [19] and was shown to be more general [20]. It was successfully applied to the NLS model with impurity [21,22] providing the first non-trivial integrable system with impurity.…”

Section: Introductionmentioning

confidence: 99%

Exact Results for the One-Dimensional Many-Body Problem With Contact Interaction: Including a Tunable Impurity

Caudrelier

Crampé

2007

Rev. Math. Phys.

Self Cite

View full text Add to dashboard Cite

The one-dimensional problem of N particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establish for different boundary conditions in the presence of the impurity. These impurity Bethe equations contain as special cases well-known Bethe equations for systems on the half-line. We briefly study them on their own through the toy-examples of one and two particles. It turns out that the impurity can be tuned to lift degeneracies in the energies and can create bound states when it is sufficiently attractive. The example of an impurity sitting at the center of a box and breaking parity invariance shows that such an impurity can be used to confine asymmetrically a stationary state. This could have interesting applications in condensed matter physics.

show abstract

Section: Introductionmentioning

confidence: 99%

Exact Results for the One-Dimensional Many-Body Problem With Contact Interaction: Including a Tunable Impurity

Caudrelier

Crampé

2007

Rev. Math. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…The topic of defects, or impurities, in integrable systems has quite a rich literature, especially for quantum aspects [1,2,3,4,6,7,8,9], even if quite a lot remains to be done. Strangely enough, the problem of integrable defects in classical field theories had received less attention.…”

Section: Introductionmentioning

confidence: 99%

On a Systematic Approach to Defects in Classical Integrable Field Theories

Caudrelier

2008

Int. J. Geom. Methods Mod. Phys.

Self Cite

101

View full text Add to dashboard Cite

We present an inverse scattering approach to defects in classical integrable field theories. Integrability is proved systematically by constructing the generating function of the infinite set of modified integrals of motion. The contribution of the defect to all orders is explicitely identified in terms of a defect matrix. The underlying geometric picture is that those defects correspond to Bäcklund transformations localized at a given point. A classification of defect matrices as well as the corresponding defect conditions is performed. The method is applied to a collection of well-known integrable models and previous results are recovered (and extended) directly as special cases. Finally, a brief discussion of the classical r-matrix approach in this context shows the relation to inhomogeneous lattice models and the need to resort to lattice regularizations of integrable field theories with defects.

show abstract

“…For this reason RT algebras represent a natural and universal tool for studying QFT with defects [16,17,23,24] and it is not at all surprising that they appear also in the process of bosonization with impurities. The derivation of the correlation functions of {ϕ , ϕ} in the Fock representation [13] of the RT algebra (2.11-2.13) is straightforward.…”

Section: General Settingmentioning

confidence: 99%

“…The associated reflection and transmission matrices 16) satisfy hermitian analyticity 17) and unitarity…”

Section: General Settingmentioning

confidence: 99%

Bosonization and Vertex Algebras with Defects

Mintchev

Sorba²

2006

Ann. Henri Poincaré

Self Cite

View full text Add to dashboard Cite

The method of bosonization is extended to the case when a dissipationless point-like defect is present in space-time. Introducing the chiral components of a massless scalar field, interacting with the defect in two dimensions, we construct the associated vertex operators. The main features of the corresponding vertex algebra are established. As an application of this framework we solve the massless Thirring model with defect. We also construct the vertex representation of the sl(2) Kac-Moody algebra, describing the complex interplay between the left and right sectors due to the interaction with the defect. The Sugawara form of the energy-momentum tensor is also explored.

show abstract

Solving the quantum nonlinear Schrödinger equation with δ-type impurity

Cited by 32 publications

References 35 publications

Exact Results for the One-Dimensional Many-Body Problem With Contact Interaction: Including a Tunable Impurity

Exact Results for the One-Dimensional Many-Body Problem With Contact Interaction: Including a Tunable Impurity

On a Systematic Approach to Defects in Classical Integrable Field Theories

Bosonization and Vertex Algebras with Defects

Contact Info

Product

Resources

About