Spherical Location Under Restricted Distance

This paper deals with the problem of locating a new facility with respect to n given demand points on earth, with upper bounds imposed on distances between the new facility and each demand points. Distances are measured as the length of the shortest arc of great circle. The proposed algorithm makes use of a Lagrangean relaxation in which the distance constraints, which are not satisfied by the associated unconstrained solution, are incorporated in the economic function. Computational results of a limited number of test problems are presented

Sequence of phase transitions in a model of interacting rods

In a system of interacting thin rigid rods of equal length $2 \ell$ on a two-dimensional grid of lattice spacing $a$, we show that there are multiple phase transitions as the coupling strength $\kappa=\ell/a$ and the temperature are varied. There are essentially two classes of transitions. One corresponds to the Ising-type spontaneous symmetry breaking transition and the second belongs to less-studied phase transitions of geometrical origin. The latter class of transitions appear at fixed values of $\kappa$ irrespective of the temperature, whereas the critical coupling for the spontaneous symmetry breaking transition depends on it. By varying the temperature, the phase boundaries may cross each other, leading to a rich phase behaviour with infinitely many phases. Our results are based on Monte Carlo simulations on the square lattice, and a fixed-point analysis of a functional flow equation on a Bethe lattice.Comment: 6 pages, 4 figure

Field-dependent nonlinear luminescence response of (In,Ga)N/GaN quantum wells

We have investigated the electric-field- and excitation-density-induced variation of the optical transition energy and cathodoluminescence (CL) as well as photoluminescence intensity of a single (In,Ga)N/GaN quantum well deposited in the depletion region of a p-n junction. The electric-field dependence of the transition energy is significantly influenced by field screening in the depletion region due to the excited carriers and by filling of band tail states of localized excitons. The electric-field dependence of the CL intensity is characterized by an abrupt and strong quenching mainly due to drift of excited carriers in the depletion region. A gradual screening of the p-n junction field with increasing excitation density causes a strongly nonlinear CL response. We describe this nonlinear behavior theoretically by a rate equation model

Classical limit of master equation for harmonic oscillator coupled to oscillator bath with separable initial conditions

The equation for the Wigner function describing the reduced dynamics of a single harmonic oscillator, coupled to an oscillator bath, was obtained by Karrlein and Grabert [Phys. Rev. E, vol. 55, 153 (1997)]. It was shown that for some special correlated initial conditions the equation reduces, in the classical limit, to the corresponding classical Fokker-Planck equation obtained by Adelman [J. Chem Phys., vol. 64, 124 (1976)]. However for separable initial conditions the Adelman equations were not recovered. We resolve this problem by showing that, for separable initial conditions, the classical Langevin equation obtained from the oscillator bath model is somewhat different from the one considered by Adelman. We obtain the corresponding Fokker-Planck equation and show that it exactly matches the classical limit of the equation for the Wigner function obtained from the master equation for separable initial conditions. We also discuss why the special correlated initial conditions correspond to Adelman's solution.Comment: 12 page

Geometry versus Entanglement in Resonating Valence Bond Liquids

We investigate the behavior of bipartite as well as genuine multipartite entanglement of a resonating valence bond state on a ladder. We show that the system possesses significant amounts of bipartite entanglement in the steps of the ladder while no substantial bipartite entanglement is present in the rails. Genuine multipartite entanglement present in the system is negligible. The results are in stark contrast with the entanglement properties of the same state on isotropic lattices in two and higher dimensions, indicating that the geometry of the lattice can have important implications on the quality of quantum information and other tasks that can be performed by using multiparty states on that lattice.Comment: 6 pages, 8 figures, RevTeX

Heat transport in ordered harmonic lattices

We consider heat conduction across an ordered oscillator chain with harmonic interparticle interactions and also onsite harmonic potentials. The onsite spring constant is the same for all sites excepting the boundary sites. The chain is connected to Ohmic heat reservoirs at different temperatures. We use an approach following from a direct solution of the Langevin equations of motion. This works both in the classical and quantum regimes. In the classical case we obtain an exact formula for the heat current in the limit of system size N to infinity. In special cases this reduces to earlier results obtained by Rieder, Lebowitz and Lieb and by Nakazawa. We also obtain results for the quantum mechanical case where we study the temperature dependence of the heat current. We briefly discuss results in higher dimensions.Comment: 8 pages, 2 figures, published versio

Field-dependent nonlinear luminescence response of (In,Ga)N/GaN quantum wells

We have investigated the electric-field- and excitation-density-induced variation of the optical transition energy and cathodoluminescence (CL) as well as photoluminescence intensity of a single (In,Ga)N/GaN quantum well deposited in the depletion region of a p-n junction. The electric-field dependence of the transition energy is significantly influenced by field screening in the depletion region due to the excited carriers and by filling of band tail states of localized excitons. The electric-field dependence of the CL intensity is characterized by an abrupt and strong quenching mainly due to drift of excited carriers in the depletion region. A gradual screening of the p-n junction field with increasing excitation density causes a strongly nonlinear CL response. We describe this nonlinear behavior theoretically by a rate equation model

Equilibration problem for the generalized Langevin equation

We consider the problem of equilibration of a single oscillator system with dynamics given by the generalized Langevin equation. It is well-known that this dynamics can be obtained if one considers a model where the single oscillator is coupled to an infinite bath of harmonic oscillators which are initially in equilibrium. Using this equivalence we first determine the conditions necessary for equilibration for the case when the system potential is harmonic. We then give an example with a particular bath where we show that, even for parameter values where the harmonic case always equilibrates, with any finite amount of nonlinearity the system does not equilibrate for arbitrary initial conditions. We understand this as a consequence of the formation of nonlinear localized excitations similar to the discrete breather modes in nonlinear lattices.Comment: 5 pages, 2 figure