Closure of the Monte Carlo dynamical equation in the spherical Sherrington-Kirkpatrick model

We study the analytical solution of the Monte Carlo dynamics in the spherical Sherrington-Kirkpatrick model using the technique of the generating function. Explicit solutions for one-time observables (like the energy) and two-time observables (like the correlation and response function) are obtained. We show that the crucial quantity which governs the dynamics is the acceptance rate. At zero temperature, an adiabatic approximation reveals that the relaxational behavior of the model corresponds to that of a single harmonic oscillator with an effective renormalized mass.

Dark energy equation of state and anthropic selection

We explore the possibility that the dark energy is due to a potential of a scalar field and that the magnitude and the slope of this potential in our part of the Universe are largely determined by anthropic selection effects. We find that, in some models, the most probable values of the slope are very small, implying that the dark energy density stays constant to very high accuracy throughout cosmological evolution. In other models, however, the most probable values of the slope are such that the slow roll condition is only marginally satisfied, leading to a recollapse of the local universe on a time scale comparable to the lifetime of the Sun. In the latter case, the effective equation of state varies appreciably with the redshift, leading to a number of testable predictions.

Spatiotemporal stochastic resonance in the Swift-Hohenberg equation

We show the appearance of spatiotemporal stochastic resonance in the Swift-Hohenberg equation. This phenomenon emerges when a control parameter varies periodically in time around the bifurcation point. By using general scaling arguments and by taking into account the common features occurring in a bifurcation, we outline possible manifestations of the phenomenon in other pattern-forming systems.

Solutions of the telegrapher's equation in the presence of traps

Several problems in the theory of photon migration in a turbid medium suggest the utility of calculating solutions of the telegrapher¿s equation in the presence of traps. This paper contains two such solutions for the one-dimensional problem, the first being for a semi-infinite line terminated by a trap, and the second being for a finite line terminated by two traps. Because solutions to the telegrapher¿s equation represent an interpolation between wavelike and diffusive phenomena, they will exhibit discontinuities even in the presence of traps.

Continued fraction solution for the radiative transfer equation in three dimensions

Starting from the radiative transfer equation, we obtain an analytical solution for both the free propagator along one of the axes and an arbitrary phase function in the Fourier-Laplace domain. We also find the effective absorption parameter, which turns out to be very different from the one provided by the diffusion approximation. We finally present an analytical approximation procedure and obtain a differential equation that accurately reproduces the transport process. We test our approximations by means of simulations that use the Henyey-Greenstein phase function with very satisfactory results.

Solution to telegrapher's equation in the presence of reflecting and partly reflecting broundaries

We show that the reflecting boundary condition for a one-dimensional telegraphers equation is the same as that for the diffusion equation, in contrast to what is found for the absorbing boundary condition. The radiation boundary condition is found to have a quite complicated form. We also obtain exact solutions of the telegraphers equation in the presence of these boundaries.

Telegrapher's equation with variable propagation speeds

All derivations of the one-dimensional telegraphers equation, based on the persistent random walk model, assume a constant speed of signal propagation. We generalize here the model to allow for a variable propagation speed and study several limiting cases in detail. We also show the connections of this model with anomalous diffusion behavior and with inertial dichotomous processes.

Reply to "Comment on 'Solutions of the telegrapher's equation in the presence of traps'"

This reply adds a number of details to remarks by Foong and Kanno [preceding Comment, Phys. Rev. A 46, 5296 (1992)] on our paper [Phys. Rev. A 45, 2222 (1992)] regarding the discontinuities observed in the curves generated in that paper.

When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated data in three dimensions indicates that the solution to the telegrapher's equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation.

Strong coupling solution to Schrödinger Equation: the mixing of states

In this paper we give some ideas that can be useful to solve Schrödinger equations in the case when the Hamiltonian contains a large term. We obtain an expansion of the solution in reciprocal powers of the large coupling constant. The procedure followed consists in considering that the small part of the Hamiltonian engenders a motion adiabatic to the motion generated by the large part of the same.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Interaction of Spiral Waves in the Complex Ginzburg-Landau Equation

Solutions of the general cubic complex Ginzburg-Landau equation comprising multiple spiral waves are considered, and laws of motion for the centers are derived. The direction of the motion changes from along the line of centers to perpendicular to the line of centers as the separation increases, with the strength of the interaction algebraic at small separations and exponentially small at large separations. The corresponding asymptotic wave number and frequency are also determined, which evolve slowly as the spirals move

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schr odinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.

Symmetries of the free Schrödinger equation in the non-commutative plane

We study all the symmetries of the free Schrödinger equation in the non-commu- tative plane. These symmetry transformations form an infinite-dimensional Weyl algebra that appears naturally from a two-dimensional Heisenberg algebra generated by Galilean boosts and momenta. These infinite high symmetries could be useful for constructing non-relativistic interacting higher spin theories. A finite-dimensional subalgebra is given by the Schröodinger algebra which, besides the Galilei generators, contains also the dilatation and the expansion. We consider the quantization of the symmetry generators in both the reduced and extended phase spaces, and discuss the relation between both approaches.