Related papers: Baxter operators in Ruijsenaars hyperbolic system …
An arbitrary form of complex potential perturbation in an oscillator consists of many exciting questions in open quantum systems. These often provide valuable insights in a realistic scenario when a quantum system interacts with external…
In this paper, we introduce operators that are represented by upper triangular $2\times 2$ block matrices whose entries satisfy some algebraic constraints. We call them Brownian-type operators of class $\mathcal Q,$ briefly operators of…
The structure of a cotangent bundle is investigated for quantum linear groups GLq(n) and SLq(n). Using a q-version of the Cayley-Hamilton theorem we construct an extension of the algebra of differential operators on SLq(n) (otherwise called…
We derive covariant wave functions for hadrons composed of two constituents for arbitrary Lorentz boosts. Focussing explicitly on baryons as quark-diquark systems, we reduce their manifestly covariant Bethe-Salpeter equation to covariant…
Baxter's Q-operator is generally believed to be the most powerful tool for the exact diagonalization of integrable models. Curiously, it has hitherto not yet been properly constructed in the simplest such system, the compact spin-1/2…
We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct non-selfadjoint operators representing operator roots of the transfer…
A method is presented for the systematic derivation of a hierarchy of coupled equations for the computation of two-time correlation functions of operators for open many-body quantum systems. We show how these systems of equations can be…
We use the functorial properties of Rieffel's pseudodifferential calculus to study families of operators associated to topological dynamical systems acted by a symplectic space. Information about the spectra and the essential spectra are…
A quantum integrable model is considered which describes a quantization of affine hyper-elliptic Jacobian. This model is shown to possess the property of duality: a dual model with inverse Planck constant exists such that the…
Factorization of quantum mechanical Hamiltonians has been a useful technique for some time. This procedure has been given an elegant description by supersymmetric quantum mechanics, and the subject has become well-developed. We demonstrate…
For any variable number, a non-stationary Ruijsenaars function was recently introduced as a natural generalization of an explicitly known asymptotically free solution of the trigonometric Ruijsenaars model, and it was conjectured that this…
We discuss the construction of Baxter's Q-operator. The suggested approach leads to the one-parametric family of Q-operators, satisfying to the wronslian-type relations. Also we have found the generalization of Baxter operators, with…
Weak-strong coupling duality relations are shown to be present in the quantum-mechanical many-body system with the interacting potential proportional to the pair-wise inverse-squared distance in addition to the harmonic potential. Using…
In this paper the proofs are given of important properties of deformed Abelian differentials introduced earlier in connection with quantum integrable systems. The starting point of the construction is Baxter equation. In particular, we…
We obtain the Baxter Q-operators in the $U_q(\hat{sl}_2)$ invariant integrable models as a special limits of the quantum transfer matrices corresponding to different spins in the auxiliary space both from the functional relations and from…
We present a method for the explicit diagonalization of some Hankel operators. This method allows us to recover classical results on the diagonalization of Hankel operators with the absolutely continuous spectrum. It leads also to new…
Generalized trigonometric functions and generalized hyperbolic functions can be converted to each other by the duality formulas previously discovered by the authors. In this paper, we apply the duality formulas to prove dual pairs of…
A result from Dodd and Gibbs[1] for the second virial coefficient of particles in 1 dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be…
We study the Kramers-Wannier duality for the transverse-field Ising lattice on a ring. A careful consideration of the ring boundary conditions shows that the duality has to be implemented with a proper treatment of different charge sectors…
Macdonald operators are well known as the 'commutative family' acting on the symmetric functions over Q(q,t). If we suppose that q=exp(h) and t=exp(beta h) and observe the Taylor expansion around h=0, we can see the second-degree Dunkl…