Related papers: Quantum Integrable Systems: Construction, Solution…
This article reviews a recently-discovered link between integrable quantum field theories and certain ordinary differential equations in the complex domain. Along the way, aspects of PT-symmetric quantum mechanics are discussed, and some…
By resorting to the Fock--Bargmann representation, we incorporate the quantum Weyl--Heisenberg ($q$-WH) algebra into the theory of entire analytic functions. The main tool is the realization of the $q$--WH algebra in terms of finite…
We present an algebraic framework for interacting extended quantum systems to study complex phenomena characterized by the coexistence and competition of different states of matter. We start by showing how to connect different…
In the paper we investigate the theory of quantum optical systems. As an application we integrate and describe the quantum optical systems which are generically related to the classical orthogonal polynomials. The family of coherent states…
The rational quantum algebraically integrable systems are non-trivial generalizations of Laplacian operators to the case of elliptic operators with variable coefficients. We study corresponding extensions of Laplacian growth connected with…
We consider in general terms dynamical systems with finite-dimensional, non-simply connected configuration-spaces. The fundamental group is assumed to be finite. We analyze in full detail those ambiguities in the quantization procedure that…
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic…
The central object of the quantum algebraic approach to the study of quantum integrable models is the universal $R$-matrix, which is an element of a completed tensor product of two copies of quantum algebra. Various integrability objects…
We define an integrable lattice model which, in the notation of Yang, in addition to the conventional 2-particle $R$-matrices also contains non-reducible 3-particle $R$-matrices. The corresponding modified Yang-Baxter equations are solved…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
We propose a novel quantum integrable model for every non-simply laced simple Lie algebra ${\mathfrak g}$, which we call the folded integrable model. Its spectra correspond to solutions of the Bethe Ansatz equations obtained by folding the…
One of the few schemes for obtaining an integrable nonultralocal quantum model is its possible generation from an ultralocal model by a suitable gauge transformation. Applying this scheme we discover two new nonultralocal models, which fit…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
The first part of this paper explains what super-integrability is and how it differs in the classical and quantum cases. This is illustrated with an elementary example of the resonant harmonic oscillator. For Hamiltonians in "natural form",…
We attempt to contribute some novel points of view to the "foundations of quantum mechanics", using mathematical tools from "quantum probability theory" (such as the theory of operator algebras). We first introduce an abstract algebraic…
This is a self-contained review on the theory of quantum group and its applications to modern physics. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics. The quantum…
We apply the algebraic Bethe ansatz developed in our previous paper \cite{CM} to three different families of U(1) integrable vertex models with arbitrary $N$ bond states. These statistical mechanics systems are based on the higher spin…
The basic methods of constructing the sets of mutually unbiased bases in the Hilbert space of an arbitrary finite dimension are discussed and an emerging link between them is outlined. It is shown that these methods employ a wide range of…
Integrable systems have provided various insights into physical phenomena and mathematics. The way of constructing many-body integrable systems is limited to few ansatzes for the Lax pair, except for highly inventive findings of conserved…
We explain the relationship between the classical description of an integrable system in terms of invariant tori and action-angle variables, and the quantum description in terms of the asymptotic Bethe ansatz.