We study a model of two interacting Hamiltonian particles subject to a common potential in contact with two Langevin heat reservoirs: one at finite and one at infinite temperature. This is a toy model for ‘extreme’ non-equilibrium statistical mechanics. We provide a full picture of the long-time behaviour of such a system, including the existence / non-existence of a non-equilibrium steady stat...

A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the ⋆-quantization is an extension of the classical Poisson-Lie formalism which can be used as an efficient tool in the quantum phase space transformation theory. The purpose of this paper is to show that the Weyl correspondence in the quantum phase space can be...

The problem of reducing an algebraic Riccati equation XCX −AX − XD + B = 0 to a unilateral quadratic matrix equation (UQME) of the kind PX + QX + R = 0 is analyzed. New reductions are introduced which enable one to prove some theoretical and computational properties. In particular we show that the structure preserving doubling algorithm of B.D.O. Anderson [Internat. J. Control, 1978] is in fact...

We present an effective quantum action for the gauged WZW model G −k /H −k. It is conjectured that it is valid to all orders of the central extension (−k) on the basis that it reproduces the exact spacetime geometry of the zero modes that was previously derived in the algebraic Hamiltonian formalism. Besides the metric and dilaton, the new results that follow from this approach include the exac...

We report general properties of N -fold supersymmetry in one-dimensional quantum mechanics. N -fold supersymmetry is characterized by supercharges which are N -th polynomials of momentum. Relations between the anti-commutator of the supercharges and the Hamiltonian, the spectra, the Witten index, the non-renormalization theorems and the quasi-solvability are examined. We also present further in...

For a general K3 surface S of genus g, with 2 ≤ g ≤ 10, we prove that the intermediate Jacobians of the family of prime Fano threefolds of genus g containing S as a hyperplane section, form generically an algebraic completely integrable Hamiltonian system.

Lie algebraic methods are described which were used to optimize the d~ign of the PEP-II lattices. These methods include calculation of the nonlinear Hamiltonian for lattice modules, dimensionless normalized representation of resonance basis coefficients, correlation of coefficients with dynamic aperture determination, and techniques for coefficient control and compensation.

Preview control and fixed-lag smoothing allow a non-causal component in the controller/estimator. Time domain variational analysis is used in a reduction to an open loop differential game, leading to a complete, necessary and sufficient characterization of suboptimal values and an explicit state space design, in terms of a parameterized (non-standard) algebraic matrix Riccati equation in a gene...