arXiv subjects

Anastasia Doikou

Publications and source records attributed to Anastasia Doikou.

At least 55 records · Page 3Linked to original sources

arXiv2015

Scattering matrices in the sl(3) twisted Yangian

A quantum spin chain with non-conventional boundary conditions is studied. The distinct nature of these boundary conditions arises from the conversion of a soliton to an anti-soliton after being reflected to the boundary, hence the appellation soliton non-preserving boundary conditions. We focus on the simplest non-trivial case of this class of models based on the twisted Yangian quadratic algebra. Our computations are performed through the Bethe ansatz equations in the thermodynamic limit. We formulate a suitable quantization condition describing the scattering process and proceed with explicitly determining the bulk and boundary scattering amplitudes. The energy and quantum numbers of the low lying excitations are also derived.

hep-th↗

arXiv2015

Lax pair formulation in the simultaneous presence of boundaries and defects

Inspired by recent results on the effect of integrable boundary conditions on the bulk behavior of an integrable system, and in particular on the behavior of an existing defect we systematically formulate the Lax pairs in the simultaneous presence of integrable boundaries and defects. The respective sewing conditions as well as the relevant equations of motion on the defect point are accordingly extracted. We consider a specific prototype i.e. the vector non-linear Schrödinger (NLS) model to exemplify our construction. This model displays a highly non-trivial behavior and allows the existence of two distinct types of boundary conditions based on the reflection algebra or the twisted Yangian.

hep-th↗

arXiv2014

Classical impurities associated to high rank algebras

Classical integrable impurities associated to high rank (gl_N) algebras are investigated. A particular prototype i.e. the vector non-linear Schrödinger (NLS) model is chosen as an example. A systematic construction of local integrals of motion as well as the time components of the corresponding Lax pairs is presented based on the underlying classical algebra. Suitable gluing conditions compatible with integrability are also extracted. The defect contribution is also examined in the case where non-trivial integrable conditions are implemented. It turns out that the integrable boundaries may drastically alter the bulk behavior, and in particular the defect contribution.

hep-th↗

arXiv2014

A note on gl_N type-I integrable defects

Type-I quantum defects are considered in the context of the gl_N spin chain. The type-I defects are associated to the generalized harmonic oscillator algebra, and the chosen defect matrix is the one of the vector non-linear Schrodinger (NLS) model. The transmission matrices relevant to this particular type of defects are computed via the Bethe ansatz methodology.

math-ph↗

arXiv2013

Type-I integrable quantum impurities in the Heisenberg model

Type-I quantum impurities are investigated in the context of the integrable Heisenberg model. This type of defects is associated to the (q)-harmonic oscillator algebra. The transmission matrices associated to this particular type of defects are computed via the Bethe ansatz methodology for the XXX model, as well as for the critical and non-critical XXZ spin chain. In the attractive regime of the critical XXZ spin chain the transmission amplitudes for the breathers are also identified.

math-ph↗

arXiv2013

Transmission matrices in gl(N) & U_q(gl(N)) quantum spin chains

The gl(N) and U_q(gl(N)) quantum spin chains in the presence of integrable spin impurities are considered. Within the Bethe ansatz formulation, we derive the associated transmission amplitudes, and the corresponding transmission matrices -representations of the underlying quadratic algebra- that physically describe the interaction between the various particle-like excitations displayed by these models and the spin impurity.

hep-th↗

arXiv2013

On boundary super algebras

We examine the symmetry breaking of super algebras due to the presence of appropriate integrable boundary conditions. We investigate the boundary breaking symmetry associated to both reflection algebras and twisted super Yangians. We extract the generators of the resulting boundary symmetry as well as we provide explicit expressions of the associated Casimir operators.

math-ph↗

arXiv2013

New reflection matrices for the U_q(gl(m|n)) case

We examine super symmetric representations of the B-type Hecke algebra. We exploit such representations to obtain new non-diagonal solutions of the reflection equation associated to the super algebra U_q(gl(m|n)). The boundary super algebra is briefly discussed and it is shown to be central to the super symmetric realization of the B-type Hecke algebra

math-ph↗

arXiv2013

Transmission amplitudes from Bethe ansatz equations

We consider the Heisenberg spin chain in the presence of integrable spin defects. Using the Bethe ansatz methodology, we extract the associated transmission amplitudes, that describe the interaction between the particle-like excitations displayed by the models and the spin impurity. In the attractive regime of the XXZ model, we also derive the breather's transmission amplitude. We compare our findings with earlier relevant results in the context of the sine-Gordon model.

math-ph↗

arXiv2013

The sine-Gordon model in the presence of defects

The sine-Gordon model in the presence of dynamical integrable defects is investigated. This is an application of the algebraic formulation introduced for integrable defects in earlier works. The quantities in involution as well as the associated Lax pairs are explicitly extracted. Integrability i also shown using certain sewing constraints, which emerge as suitable continuity conditions.

hep-th↗

arXiv2012

Sigma models in the presence of dynamical point-like defects

Point-like Liouville integrable dynamical defects are introduced in the context of the Landau-Lifshitz and Principal Chiral (Faddeev-Reshetikhin) models. Based primarily on the underlying quadratic algebra we identify the first local integrals of motion, the associated Lax pairs as well as the relevant sewing conditions around the defect point. The involution of the integrals of motion is shown taking into account the sewing conditions.

hep-th↗

arXiv2012

The sine-Gordon model with integrable defects revisited

Application of our algebraic approach to Liouville integrable defects is proposed for the sine-Gordon model. Integrability of the model is ensured by the underlying classical r-matrix algebra. The first local integrals of motion are identified together with the corresponding Lax pairs. Continuity conditions imposed on the time components of the entailed Lax pairs give rise to the sewing conditions on the defect point consistent with Liouville integrability.

hep-th↗

arXiv2012

Solutions of the Generic Non-Compact Weyl Equation

In this paper, solutions of the generic non-compact Weyl equation are obtained. In particular, by identifying a suitable similarity transformation and introducing a non-trivial change of variables we are able to implement azimuthal dependence on the solutions of the diagonal non-compact Weyl equation. We also discuss some open questions related to the construction of infinite BPS monopole configurations.

hep-th↗

arXiv2012

Selected Topics in Classical Integrability

Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition description is presented. The classical r-matrix approach for discrete and continuum classical integrable models is introduced. Using this framework the associated classical integrals of motion and the corresponding Lax pair are extracted based on algebraic considerations. Our attention is restricted to classical discrete and continuum integrable systems with periodic boundary conditions. Typical examples of discrete (Toda chain, discrete NLS model) and continuum integrable models (NLS, sine-Gordon models and affine Toda field theories) are also discussed.

math-ph↗

arXiv2012

Liouville integrable defects: the non-linear Schrodinger paradigm

A systematic approach to Liouville integrable defects is proposed, based on an underlying Poisson algebraic structure. The non-linear Schrodinger model in the presence of a single particle-like defect is investigated through this algebraic approach. Local integrals of motions are constructed as well as the time components of the corresponding Lax pairs. Continuity conditions imposed upon the time components of the Lax pair to all orders give rise to sewing conditions, which turn out to be compatible with the hierarchy of charges in involution. Coincidence of our results with the continuum limit of the discrete expressions obtained in earlier works further confirms our approach.

hep-th↗

arXiv2011

BPS Monopoles and Open Spin Chains

We construct SU(n+1) BPS spherically symmetric monopoles with minimal symmetry breaking by solving the full Weyl equation. In this context, we explore and discuss the existence of open spin chain-like part within the Weyl equation. For instance, in the SU(3) case the relevant spin chain is the 2-site spin 1/2 XXX chain with open boundary conditions. We exploit the existence of such a spin chain part in order to solve the full Weyl equation.

hep-th↗

arXiv2011

Generalized Landau-Lifshitz models on the interval

We study the classical generalized gl(n) Landau-Lifshitz (L-L) model with special boundary conditions that preserve integrability. We explicitly derive the first non-trivial local integral of motion, which corresponds to the boundary Hamiltonian for the sl(2) L-L model. Novel expressions of the modified Lax pairs associated to the integrals of motion are also extracted. The relevant equations of motion with the corresponding boundary conditions are determined. Dynamical integrable boundary conditions are also examined within this spirit. Then the generalized isotropic and anisotropic gl(n) Landau-Lifshitz models are considered, and novel expressions of the boundary Hamiltonians and the relevant equations of motion and boundary conditions are derived.

hep-th↗

arXiv2011

Defects in the discrete non-linear Schrodinger model

The discrete non-linear Schrodinger (NLS) model in the presence of an integrable defect is examined. The problem is viewed from a purely algebraic point of view, starting from the fundamental algebraic relations that rule the model. The first charges in involution are explicitly constructed, as well as the corresponding Lax pairs. These lead to sets of difference equations, which include particular terms corresponding to the impurity point. A first glimpse regarding the corresponding continuum limit is also provided.

hep-th↗