"A Solvable Hamiltonian System" Integrability and Action-Angle Variables

We prove that the dynamical system charaterized by the Hamiltonian $H = \lambda N \sum_{j}^{N} p_j + \mu \sum_{j,k}^{N} {{(p_j p_k)}^{1\over 2}} \{ cos [ \nu ( q_j - q_k)] \}$ proposed and studied by Calogero [1,2] is equivalent to a system of {\it non-interacting} harmonic oscillators. We find the explicit form of the conserved currents which are in involution. We also find the action-angle variables and solve the initial value problem in simple form.Comment: 12 pages, Latex, No Figure

Reply to Comment on ''Quantum key distribution for d-level systems with generalized Bell states''

In a recent comment \cite{ch1} it has been claimed that an entangled-based quantum key distribution protocol proposed in \cite{zhang} and its generalization to d-level systems in \cite{v1} are insecure against an attack devised by the authors of the comment. We invalidate the arguments of the comment and show that the protocols are still secure.Comment: 4 pages, Latex, no figures, Accepted for Publication in Phys. Rev.

A new class of models for surface relaxation with exact mean-field solutions

We introduce a class of discrete models for surface relaxation. By exactly solving the master equation which governs the microscopic dynamics of the surface, we determine the steady state of the surface and calculate its roughness. We will also map our model to a diffusive system of particles on a ring and reinterpret our results in this new setting.Comment: 12 pages, 3 figures,references adde