Related papers: Integrable Quantum Mappings and Quantization Aspec…
The star-triangle relation plays an important role in the realm of exactly solvable models, offering exact results for classical two-dimensional statistical mechanical models. In this article, we construct integrable quantum circuits using…
The Yang-Baxter Equation (YBE) plays a crucial role for studying integrable many-body quantum systems. Many known YBE solutions provide various examples ranging from quantum spin chains to superconducting systems. Models of solvable…
We establish a correspondence between the invariant subsets of a non-degenerate symmetric set-theoretical solution of the quantum Yang-Baxter equation and the parabolic subgroups of its structure group, equipped with its canonical Garside…
The calculation of quantum canonical time correlation functions is considered in this paper. Transport properties, such as diffusion and reaction rate coefficients, can be determined from time integrals of these correlation functions.…
Starting from known solutions of the functional Yang-Baxter equations, we exhibit Miura type of transformations leading to various known integrable quad equations. We then construct, from the same list of Yang-Baxter maps, a series of…
By means of left quasigroups L=(L, .) and ternary systems, we construct dynamical Yang-Baxter maps associated with L, L, and (.) satisfying an invariance condition that the binary operation (.) of the left quasigroup L defines. Conversely,…
We present Yang-Baxter maps associated to elliptic curves. They are related to discrete versions of the Krichever-Novikov and the Landau-Lifshits equations. A lifting of scalar integrable quad-graph equations to two-field equations is also…
We show explicitly how to construct the quantum Lax pair for systems with open boundary conditions. We demonstrate the method by applying it to the Heisenberg XXZ model with general integrable boundary terms.
Hamiltonian systems of ordinary and partial differential equations are fundamental mathematical models spanning virtually all physical scales. A critical property for the robustness and stability of computational methods in such systems is…
A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang-Mills theory is constructed and used to examine some generic properties of noncommutative quantum…
We address a conceptual issue of reconciling the traditional canonical quantization framework of quantum theory with the spatially restricted quantum dynamics and the related spectral problems for confined and global observables of the…
We construct lattice gauge theories in which the elements of the link matrices are represented by non-commuting operators acting in a Hilbert space. These quantum link models are related to ordinary lattice gauge theories in the same way as…
In a previous paper [Nijhoff,Puttock,2003], a 2-parameter extension of the lattice potential KdV equation was derived, associated with an elliptic curve. This comprises a rather complicated 3-component system on the quad lattice which…
We discuss the problem of recovering geometric objects from the spectrum of a quantum integrable system. In the case of one degree of freedom, precise results exist. In the general case, we report on the recent notion of good labellings of…
We investigate the quantum properties of the truly gauge-invariant and conserved charges of two-dimensional Yang-Mills theories, focusing on lattice QCD in the strong coupling regime. The construction of those charges uses the integral…
Quantum baker`s map is a model of chaotic system. We study quantum dynamics for the quantum baker's map. We use the Schack and Caves symbolic description of the quantum baker`s map. We find an exact expression for the expectation value of…
This is a continuation of a previous study of quantum vertex algebras of Zamolodchikov-Faddeev type. In this paper, we focus our attention on the special case associated to diagonal unitary rational quantum Yang-Baxter operators. We prove…
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…
We clarify the algebraic structure of continuous and discrete quasi-exactly solvable spectral problems by embedding them into the framework of the quantum inverse scattering method. The quasi-exactly solvable hamiltonians in one dimension…
We obtain two series of spectral parameter dependent solutions to the generalized Yang-Baxter equations (GYBE), for definite types of $N_1^2\times N_2^2$ matrices with general dimensions $N_1$ and $N_2$. Appropriate extensions are presented…