Collision rate ansatz for quantum integrable systems

Bethe Ansatz works for integrable model

New Fundamental Symmetries of Integrable Systems and Partial Bethe Ansatz

We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasiYang-Baxrer algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and nd an unexpected and remarkable applications in quantum inverse scattering method (QISM). We show that applying to quasi-Yang-Baxter algebras the standard proced...

Applications of Quantum Integrable Systems

We present two applications of quantum integrable systems. First, we predict that it is possible to generate high harmonics from solid state devices by demonstrating that the emission spectrum of a minimally coupled laser field of frequency ω to an impurity system of a quantum wire, contains multiples of the incoming frequency. Second, by evaluating expressions for the conductance in the high t...

Integrable Systems and Quantum Groups

The main purpose of this lecture is to present the study of quantum integrable systems and its interplay with the study of quantum groups. The history of quantum integrable systems begins, following a certain historical path, with the rst attempts of W. Heisenberg to develop a microscopic theory that could explain ferromagnetism [1]. Later on a method was proposed by H. Bethe [2] in order to ob...

Integrable Systems as Quantum Mechanics

We review briefly some ideas and constructions for dKP (from KP) and its Hamiltonian dynamics, discuss its quantization via Moyal back to KP, and treat the KP hierarchy itself as a sequence of quantum Hamiltonian systems based on the dKP dynamics. Some connections to q-theories are also indicated. The constructions are all well known (cf. [6, 8, 11, 12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 29, 3...