Related papers: Vertex operator approach to semi-infinite spin cha…

This paper presents a matrix-free approach for implementing the shifted boundary method (SBM) in finite element analysis. The SBM is a versatile technique for solving partial differential equations on complex geometries by shifting boundary…

This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…

We classify operator systems $S\subseteq \mathcal B(H)$ that act on finite dimensional Hilbert spaces by making use of the noncommutative Choquet boundary. S is said to be {\em reduced} when its boundary ideal is 0. In the category of…

We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…

Algebraic framework for construction of a commuting set of operators that can be interpreted as integrals of motion of the open spin chain with boundary conditions and nearest neighbour interaction is investigated.

Generalized symmetry extends the usual notion of symmetry to ones that are of higher-form, acting on subsystems, non-invertible, etc. The concept was originally defined in the field theory context using the idea of topological defects. On…

The Koopman operator allows for handling nonlinear systems through a (globally) linear representation. In general, the operator is infinite-dimensional - necessitating finite approximations - for which there is no overarching framework.…

We consider the finite volume mean values of current operators in integrable spin chains with local interactions, and provide an alternative derivation of the exact result found recently by the author and two collaborators. We use a certain…

This paper addresses two different but related questions regarding an unbounded symmetric tridiagonal operator: its self-adjointness and the approximation of its spectrum by the eigenvalues of its finite truncations. The sufficient…

We derive an exact operator bosonization of a finite number of fermions in one space dimension. The fermions can be interacting or noninteracting and can have an arbitrary hamiltonian, as long as there is a countable basis of states in the…

We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…

We introduce a new concept of unbounded solutions to the operator Riccati equation $A_1 X - X A_0 - X V X + V^\ast = 0$ and give a complete description of its solutions associated with the spectral graph subspaces of the block operator…

We review aspects of quantisation of the 11-dimensional supermembrane world volume theory. We explicitly construct vertex operators for the massless states and study interactions of supermembranes. The open supermembrane and its vertex…

This thesis is dedicated to the study of open spin networks. We formulate quasi-local descriptions of loop quantum gravity. We investigate the coarse-graining procedure via tracing over bulk degrees of freedom, which encodes all that we can…

We study the mirror-field interaction in several frameworks: when it is driven, when it is affected by an environment and when a two-level atom is introduced in the cavity. By using operator techniques we show how these problems may be…

We study the tomography of multispin quantum states in the context of finite-dimensional Wigner representations. An arbitrary operator can be completely characterized and visualized using multiple shapes assembled from linear combinations…

In the present work, we demonstrate how the pseudoinverse concept from linear algebra can be used to represent and analyze the boundary conditions of linear systems of partial differential equations. This approach has theoretical and…

We present a general method of folding an integrable spin chain, defined on a line, to obtain an integrable open spin chain, defined on a half-line. We illustrate our method through two fundamental models with sl(2) Lie algebra symmetry:…

This paper is a contribution to a program to see symmetry breaking in a weakly interacting many Boson system on a three dimensional lattice at low temperature. It is part of an analysis of the "small field" approximation to the "parabolic…

We show that if an infinite-dimensional Banach space X has a symmetric basis then there exists a bounded, linear operator R : X --> X such that the set A = {x in X : ||R^n(x)|| --> infinity} is non-empty and nowhere dense in X. Moreover, if…