Related papers: Construction of the Bethe State for the $E_{\tau,\…
Let $\{E_{(p,q)}\}$ be a family of elliptic curves over a rational field such that we have $E_{(p,q)} : y^2 = x^3 - p^2x + q^2$, where $p$ and $q$ are prime numbers greater than five. Earlier work showed that the elliptic curve $E_{(p,q)}$…
We construct quantum supersymmetric pairs $({\bold U},{\bold U}^\imath)$ of type AIII and elucidate their fundamental properties. An $\imath$Schur duality between the $\imath$quantum supergroup ${\bold U}^\imath$ and the Hecke algebra of…
In Field theories with simple or semi-simple unitary, local or global symmetries, the electric charge is related to a global one. This is the case also in electroweak gauge theories even before the spontaneous symmetry breaking (SSB), where…
This work aims to develop a global quantization in the concrete settings of two graded nilpotent Lie groups of 3-step; namely of the Engel group and the Cartan group. We provide a preliminary analysis on the structure and the…
We analyze a new computational role of coherent multi-qubit quantum tunneling that gives rise to bands of non-ergodic extended (NEE) quantum states each formed by a superposition of a large number of computational states (deep local minima…
We study quantum integrable models with $GL(3)$ trigonometric $R$-matrix solvable by the nested algebraic Bethe ansatz. We analyze scalar products of generic Bethe vectors and obtain an explicit representation for them in terms of a sum…
We propose new inhomogeneous local integrability equations - combined equations, for statistical vertex models of general dimensions in the framework of the Algebraic Bethe Ansatz (ABA). For the low dimensional cases the efficiency of the…
The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their…
We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for particular case of scalar products of Bethe vectors. This representation can be used for the calculation of…
Matrix elements of quantum intertwiner as well as the modified Q-operator for the quantum relativistic Toda chain at root of unity are constructed explicitly. Modified Q-operators make isospectrality transformations of quantum transfer…
We construct an infinite-dimensional solution of the Yang-Baxter equation (YBE) of rank 1 which is represented as an integral operator with an elliptic hypergeometric kernel acting in the space of functions of two complex variables. This…
Generalizing the problem of counting rational points on curves and surfaces over finite fields, we consider the setting of $n \times n$ matrix points with finite field entries. We obtain exact formulas for matrix point counts on elliptic…
I briefly review the recently proposed construction of the Bethe ansatz which diagonalizes the Hamiltonian for quantum strings on AdS_5\times S^5 at large tension and restricted to the large charge states from a closed su(2) subsector.
In this paper, we look at the asymmetric simple exclusion process with open boundaries with a current-counting deformation. We construct a two-parameter family of transfer matrices which commute with the deformed Markov matrix of the…
We present an unambiguous characterization of the rotation group SO(3) biconnectedness topology using two-qubit maximally entangled states. We show how to generate cyclic evolutions of these states, which are in one-to-one correspondence to…
As is known, tetrahedron equations lead to the commuting family of transfer-matrices and provide the integrability of corresponding three-dimensional lattice models. We present the modified version of these equations which give the…
We construct models of exactly solvable two-particle quantum graphs with certain non-local two-particle interactions, establishing appropriate boundary conditions via suitable self-adjoint realisations of the two-particle Laplacian. Showing…
In this paper, we give a construction of a (C*-algebraic) quantum Heisenberg group. This is done by viewing it as the dual quantum group of the specific non-compact quantum group (A,\Delta) constructed earlier by the author. Our definition…
We re-examine the appearance of semiheaps and (para-associative) ternary algebras in quantum mechanics. In particular, we review the construction of a semiheap on a Hilbert space and the set of bounded operators on a Hilbert space. The new…
We compute the operator which creates the missing degenerate states in the algebraic Bethe ansatz of the 8 vertex model at roots of unity and relate it to the concept of an elliptic current operator. We find that in sharp contrast with the…