相关论文: Structure of Matrix Elements in Quantum Toda Chain

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 conjecture an explicit construction of integral operators intertwining various quantum Toda chains. Compositions of the intertwining operators provide recursive and Q-operators for quantum Toda chains. In particular we propose a…

We reconstruct the canonical operators $p_i,q_i$ of the quantum closed Toda chain in terms of Sklyanin's separated variables.

We generalize Babelon's approach to equations in dual variables so as to be able to treat new types of operators which we build out of the sub-constituents of the model's monodromy matrix. Further, we also apply Sklyanin's recent monodromy…

We suggest the procedure of the construction of Baxter Q-operators for Toda chain . Apart from the one-paramitric family of Q-operators, considered in our recent paper (hep-th/9908179) we also give the construction of two basic Q-operators…

We declare briefly several interesting features of the quantum relativistic Toda chain at N-th root of unity. We consider the finite dimensional representation of the Weyl algebra. The origin of the features mentioned is that we consider…

Investigated is the relativistic periodic Toda chain, to each site of which the ultra-local Weyl algebra is associated. Weyl's $q$ we are considering here is restricted to be inside the unit circle. Quantum Lax operators of the model are…

We construct the Baxter operator $\boldsymbol{ \texttt{Q} }(\lambda)$ for the $q$-Toda chain and the Toda$_2$ chain (the Toda chain in the second Hamiltonian structure). Our construction builds on the relation between the Baxter operator…

A new integrable class of quantum models representing a family of different discrete-time or relativistic generalisations of the periodic Toda chain (TC), including that of a recently proposed classical close to TC model [7] is presented.…

We analyze the stationary problem for the Toda chain, and show that arising geometric data exactly correspond to the multi-support solutions of one-matrix model with a polynomial potential. For the first nontrivial examples the Hamiltonians…

A quantum $n$-particle model consisting of an open $q$-difference Toda chain with two-sided boundary interactions is placed on a finite integer lattice. The spectrum and eigenbasis are computed by establishing the equivalence with a…

We analyze multi--matrix chain models. They can be considered as multi--component Toda lattice hierarchies subject to suitable coupling conditions. The extension of such models to include extra discrete states requires a weak form of…

We investigate an N-state spin model called quantum relativistic Toda chain and based on the unitary finite dimensional representations of the Weyl algebra with q being N-th primitive root of unity. Parameters of the finite dimensional…

Using a contraction procedure, we obtain Toda theories and their structures, from affine Toda theories and their corresponding structures. By structures, we mean the equation of motion, the classical Lax pair, the boundary term for half…

An alternative to Babelon's (2003) construction of dual variables for the quantum open Toda chain is proposed that is based on the 2x2 Lax matrix and the corresponding quadratic R-matrix algebra.

We obtain Gauss-Givental integral representation for the eigenfunctions of quantum Toda chain with boundary interaction of BC type. For this we introduce reflection operator satisfying reflection equation with DST chain Lax matrices.…

The quantum separation of variables method consists in mapping the original Hilbert space where a spectral problem is formulated onto one where the spectral problem takes a simpler "separated" form. In order to realise such a program, one…

The paper deals with the analytic theory of the quantum q-deformed Toda chain; the technique used combines the methods of representation theory and the Quantum Inverse Scattering Method. The key phenomenon which is under scrutiny is the…

We analyse the $n$-dimensional superintegrable Kepler-Coulomb system with non-central terms. We find a novel underlying chain structure of quadratic algebras formed by the integrals of motion. We identify the elements for each sub-structure…

Precision tests of the Standard Model and searches for beyond the Standard Model physics often require nuclear structure input. There has been a tremendous progress in the development of nuclear ab initio techniques capable of providing…