In this letter we present a general classification of integrable models of identical classical spins coupled via the isotropic Heisenberg Hamiltonian. Our constructive proof of integrability provides a solution scheme for the equations describing the time evolution of each spin. We show that for a broad class of Heisenberg couplings, it is possible to solve the equations of motion iteratively b...

We study a simplified Heisenberg spin model in order to clarify the idea of decoherence in closed quantum systems. For this purpose, we define a new concept: the decoherence function Ξ(t), which describes the dynamics of decoherence in the whole system, and which is linked with the total (von Neumann) entropy of all particles. As expected, decoherence is understood both as a statistical process...

Following the approach of [Alexandrov A., Kazakov V., Leurent S., Tsuboi Z., Zabrodin A., J. High Energy Phys. 2013 (2013), no. 9, 064, 65 pages, arXiv:1112.3310], we show how to construct the master T -operator for the quantum inhomogeneous GL(N) XXX spin chain with twisted boundary conditions. It satisfies the bilinear identity and Hirota equations for the classical mKP hierarchy. We also cha...

We perform a systematic exact algebraic search for integrable spin-S chains which are isotropic in spin space, i.e. are su(2)-invariant. The families of spin chains found for S ≤ 13.5 support recent arguments in favour of the complete classification of all such integrable chains. The integrable families of spin chains are discussed in the light of the conjectured spin-dependent properties of th...

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 defines the nondiagonal part of the monodromy.

We present certain classical continuum long wave-length limits of prototype integrable quantum spin chains, and define the corresponding construction of classical continuum Lax operators. We also provide two specific examples, i.e. the isotropic and anisotropic Heisenberg models. ∗Proceedings contribution to the Corfu Summer Institute on Elementary Particle Physics and Gravity Workshop on Non C...

Recent developments in the analysis of finite temperature dissipationless transport in inte-grable quantum many body problems are presented. In particular, we will discuss: (i) the role played by the conservation laws in systems as the spin 1/2 Heisenberg chain and the one-dimensional Hubbard model, (ii) exact results obtained using the Bethe ansatz method on the long time decay of current corr...

We point out that the claim of strong universality of [1] is incorrect, as it contradicts known rigorous results. AMS 2000 subject classification: 82B20, 82B26, 60K35.

in this paper, we study spacelike dual biharmonic curves. we characterize spacelike dual biharmonic curves in terms of their curvature and torsion in the lorentzian dual heisenberg group . we give necessary and sufficient conditions for spacelike dual biharmonic curves in the lorentzian dual heisenberg group . therefore, we prove that all spacelike dual biharmonic curves are spacelike dual heli...