Single temperature for Monte Carlo optimization on complex landscapes

We propose a new strategy for Monte Carlo (MC) optimization on rugged multidimensional landscapes. The strategy is based on querying the statistical properties of the landscape in order to find the temperature at which the mean first passage time across the current region of the landscape is minimized. Thus, in contrast to other algorithms such as simulated annealing (SA), we explicitly match the temperature schedule to the statistics of landscape irregularities. In cases where this statistics is approximately the same over the entire landscape, or where non-local moves couple distant parts of the landscape, single-temperature MC will outperform any other MC algorithm with the same move set. We also find that in strongly anisotropic Coulomb spin glass and traveling salesman problems, the only relevant statistics (which we use to assign a single MC temperature) is that of irregularities in low-energy funnels. Our results may explain why protein folding in nature is efficient at room temperatures.Comment: 5 pages, 3 figure

Surface EM waves on 1D Photonic Crystals

We study surface states of 1D photonic crystals using a semiclassical coupled wave theory. Both TE and TM modes are treated. We derive analytic approximations that clarify the systematics of the dispersion relations, and the roles of the various parameters defining the crystal.Comment: 7 pages, 8 figure

Short time dynamics with initial correlations

The short-time dynamics of correlated systems is strongly influenced by initial correlations giving rise to an additional collision integral in the non-Markovian kinetic equation. Exact cancellation of the two integrals is found if the initial state is thermal equilibrium which is an important consistency criterion. Analytical results are given for the time evolution of the correlation energy which are confirmed by comparisons with molecular dynamics simulations (MD)

SDiff(2) and uniqueness of the Pleba\'{n}ski equation

The group of area preserving diffeomorphisms showed importance in the problems of self-dual gravity and integrability theory. We discuss how representations of this infinite-dimensional Lie group can arise in mathematical physics from pure local considerations. Then using Lie algebra extensions and cohomology we derive the second Pleba\'{n}ski equation and its geometry. We do not use K\"ahler or other additional structures but obtain the equation solely from the geometry of area preserving transformations group. We conclude that the Pleba\'{n}ski equation is Lie remarkable

Kadanoff-Baym equations and non-Markovian Boltzmann equation in generalized T-matrix approximation

A recently developed method for incorporating initial binary correlations into the Kadanoff-Baym equations (KBE) is used to derive a generalized T-matrix approximation for the self-energies. It is shown that the T-matrix obtains additional contributions arising from initial correlations. Using these results and taking the time-diagonal limit of the KBE, a generalized quantum kinetic equation in binary collision approximation is derived. This equation is a far-reaching generalization of Boltzmann-type kinetic equations: it selfconsistently includes memory effects (retardation, off-shell T-matrices) as well as many-particle effects (damping, in-medium T-Matrices) and spin-statistics effects (Pauli-blocking).Comment: 9 pages, 7 figures, corrected misprints in eqs. 48-5

Dynamical lattice instability versus spin liquid state in a frustrated spin chain system

The low-dimensional s=1/2 compound (NO)[Cu(NO3)3] has recently been suggested to follow the Nersesyan-Tsvelik model of coupled spin chains. Such a system shows unbound spinon excitations and a resonating valence bond ground state due spin frustration. Our Raman scattering study demonstrates phonon anomalies as well as the suppression of a broad magnetic scattering continuum for temperatures below a characteristic temperature, T<T*=100K. We interpret these effects as evidence for a dynamical interplay of spin and lattice degrees of freedom that might lead to a further transition into a dimerized or structurally distorted phase at lower temperatures.Comment: 5 pages, 6 figure