66 citations · 1.3k across the 97 of their papers we have counts for
36 papers · 1 filter
Quantum Groups, Discrete Magnus Expansion, Pre-Lie and Tridendriform Algebras
Anastasia Doikou
We review the discrete evolution problem and the corresponding solution as a discrete Dyson series in order to rigorously derive a generalized discrete version of the Magnus expans…
Set theoretic Yang-Baxter equation, braces and Drinfeld twists
Anastasia Doikou
We consider involutive, non-degenerate, finite set theoretic solutions of the Yang-Baxter equation. Such solutions can be always obtained using certain algebraic structures that ge…
An algebraic approach to discrete time integrability
Anastasia Doikou, Iain Findlay
We propose the systematic construction of classical and quantum two dimensional space-time lattices primarily based on algebraic considerations, i.e. on the existence of associated…
Set theoretic Yang-Baxter & reflection equations and quantum group symmetries
Anastasia Doikou, Agata Smoktunowicz
Connections between set-theoretic Yang-Baxter and reflection equations and quantum integrable systems are investigated. We show that set-theoretic -matrices are expressed as twi…
Time evolution in quantum systems and stochastics
Anastasia Doikou, Simon J. A. Malham, Anke Wiese
The time evolution problem for non-self adjoint second order differential operators is studied by means of the path integral formulation. Explicit computation of the path integral…
From Braces to Hecke algebras & Quantum Groups
Anastasia Doikou, Agata Smoktunowicz
We examine links between the theory of braces and set theoretical solutions of the Yang-Baxter equation, and fundamental concepts from the theory of quantum integrable systems. Mor…
Discretizations of the generalized AKNS scheme
Anastasia Doikou, Spyridoula Sklaveniti
We consider space discretizations of the matrix Zakharov-Shabat AKNS scheme, in particular the discrete matrix non-linear Scrhrödinger (DNLS) model, and the matrix generalization o…
Time-like boundary conditions in the NLS model
Anastasia Doikou, Iain Findlay, Spyridoula Sklaveniti
We focus on the non-linear Schrodinger model and we extend the notion of space-time dualities in the presence of integrable time-like boundary conditions. We identify the associate…
Solitons: conservation laws & dressing methods
Anastasia Doikou, Iain Findlay
We review some of the fundamental notions associated to the theory of solitons. More precisely, we focus on the issue of conservation laws via the existence of the Lax pair and als…
Non-commutative NLS-type hierarchies: dressing & solutions
Anastasia Doikou, Iain Findlay, Spyridoula Sklaveniti
We consider the generalized matrix non-linear Schrodinger (NLS) hierarchy. By employing the universal Darboux-dressing scheme we derive solutions for the hierarchy of integrable PD…
Stochastic analysis & discrete quantum systems
Anastasia Doikou, Simon J. A. Malham, Anke Wiese
We explore the connections between the theories of stochastic analysis and discrete quantum mechanical systems. Naturally these connections include the Feynman-Kac formula, and the…
The quantum auxiliary linear problem & Darboux-Backlund transformations
Anastasia Doikou, Iain Findlay
We explore the notion of the quantum auxiliary linear problem and the associated problem of quantum Backlund transformations (BT). In this context we systematically construct the a…
Darboux-Backlund transformations, dressing & impurities in multi-component NLS
Panagiota Adamopoulou, Anastasia Doikou, Georgios Papamikos
We consider the discrete and continuous vector non-linear Schrodinger (NLS) model. We focus on the case where space-like local discontinuities are present, and we are primarily int…
Space & time discontinuities in Liouville theory and the deformed oscillator model
Anastasia Doikou, Iain Findlay
We consider the deformed harmonic oscillator as a discrete version of the Liouville theory and study this model in the presence of local integrable defects. From this, the time evo…
Lagrangian and Hamiltonian structures in an integrable hierarchy and space-time duality
Jean Avan, Vincent Caudrelier, Anastasia Doikou +1
We define and illustrate the novel notion of dual integrable hierarchies, on the example of the nonlinear Schrödinger (NLS) hierarchy. For each integrable nonlinear evolution equat…
The sl(N) twisted Yangian: bulk-boundary scattering & defects
Jean Avan, Anastasia Doikou, Nikos Karaiskos
We consider the sl(N) twisted Yangian quantum spin chain. In particular, we study the bulk and boundary scattering of the model via the solution of the Bethe ansatz equations in th…
A note on gl_N type-I integrable defects
Anastasia Doikou
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…
Type-I integrable quantum impurities in the Heisenberg model
Anastasia Doikou
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 transmi…
Transmission amplitudes from Bethe ansatz equations
Anastasia Doikou, Nikos Karaiskos
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 descri…
Selected Topics in Classical Integrability
Anastasia Doikou
Basic notions regarding classical integrable systems are reviewed. An algebraic description of the classical integrable models together with the zero curvature condition descriptio…
Junction type representations of the Temperley-Lieb algebra and associated symmetries
Anastasia Doikou, Nikos Karaiskos
Inspired by earlier works on representations of the Temperley-Lieb algebra we introduce a novel family of representations of the algebra. This may be seen as a generalization of th…
Introduction to Quantum Integrability
Anastasia Doikou, Stefano Evangelisti, Giovanni Feverati +1
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are e…
On boundary super algebras
Anastasia Doikou
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 bo…
New reflection matrices for the U_q(gl(m|n)) case
Anastasia Doikou, Nikos Karaiskos
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 t…