Vladimir Inozemtsev
141980, Dubna, Moscow region
Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Reserch
Publications:
Dittrich J., Inozemtsev V. I.
Towards the Proof of Complete Integrability of Quantum Elliptic Manybody Systems with Spin Degrees of Freedom
2009, vol. 14, no. 2, pp. 218222
Abstract
We consider the problem of finding integrals of motion for quantum elliptic Calogero–Moser systems with arbitrary number of particles extended by introducing spinexchange interaction. By direct calculation, after making certain ansatz, we found first two integrals — quite probably, lowest nontrivial members of the whole commutative ring. This result might be considered as the first step in constructing this ring of the operators which commute with the Hamiltonian of the model.

Inozemtsev V. I.
Equilibrium points of classical integrable particle systems, factorization of wave functions of their quantum analogs and polynomial solutions of the Hill equation
2008, vol. 13, no. 6, pp. 588592
Abstract
The relation between the characteristics of the equilibrium configurations of the classical Calogero–Moser integrable systems and properties of the ground state of their quantum analogs is found. It is shown that under the condition of factorization of the wave function of these systems the coordinates of classical particles at equilibrium are zeroes of the polynomial solutions of the secondorder linear differential equation. It turns out that, under these conditions, the dependence of classical and quantum minimal energies on the parameters of the interaction potential is the same.

Dittrich J., Inozemtsev V. I.
The Commutativity of Integrals of Motion for Quantum Spin Chains and Elliptic Functions Identities
2008, vol. 13, no. 1, pp. 1926
Abstract
We prove the commutativity of the first two nontrivial integrals of motion for quantum spin chains with elliptic form of the exchange interaction. We also show their liner independence for the number of spins larger than 4. As a byproduct, we obtained several identities between elliptic Weierstrass functions of three and four arguments.

Inozemtsev V. I.
On a Set of BetheAnsatz Equetions for Quantium Heisenberg Chains with Elliptic Exchange
2000, vol. 5, no. 3, pp. 243250
Abstract
The eigenvectors of the Hamiltonian $\mathscr{H}_N$ of $N$sites quantum spin chains with elliptic exchange are connected with the double Bloch meromorphic solutions of the quantum continuous elliptic Calogero–Moser problem. This fact allows one to find the eigenvectors via the solutions to the system of highly transcendental equations of Betheansatz type which is presented in explicit form.
