Vector modulation instability induced by vacuum fluctuations in highly birefringent fibers in the anomalous dispersion regime

We report a detailed experimental study of vector modulation instability in highly birefringent optical fibers in the anomalous dispersion regime. We prove that the observed instability is mainly induced by vacuum fluctuations. The detuning of the spectral peaks agrees with linear perturbation analysis. The exact shape of the spectrum is well reproduced by numerical integration of stochastic nonlinear Schrodinger equations describing quantum propagation.Comment: 11 pages, 4 figures, to be published in Optics Letter

Decay of Resonance Structure and Trapping Effect in Potential Scattering Problem of Self-Focusing Wave Packet

Potential scattering problems governed by the time-dependent Gross-Pitaevskii equation are investigated numerically for various values of coupling constants. The initial condition is assumed to have the Gaussian-type envelope, which differs from the soliton solution. The potential is chosen to be a box or well type. We estimate the dependences of reflectance and transmittance on the width of the potential and compare these results with those given by the stationary Schr\"odinger equation. We attribute the behaviors of these quantities to the limitation on the width of the nonlinear wave packet. The coupling constant and the width of the potential play an important role in the distribution of the waves appearing in the final state of scattering.Comment: 18 pages, 12 figures; added 2 figure

Theoretical description of phase coexistence in model C60

We have investigated the phase diagram of the Girifalco model of C60 fullerene in the framework provided by the MHNC and the SCOZA liquid state theories, and by a Perturbation Theory (PT), for the free energy of the solid phase. We present an extended assessment of such theories as set against a recent Monte Carlo study of the same model [D. Costa et al, J. Chem. Phys. 118:304 (2003)]. We have compared the theoretical predictions with the corresponding simulation results for several thermodynamic properties. Then we have determined the phase diagram of the model, by using either the SCOZA, or the MHNC, or the PT predictions for one of the coexisting phases, and the simulation data for the other phase, in order to separately ascertain the accuracy of each theory. It turns out that the overall appearance of the phase portrait is reproduced fairly well by all theories, with remarkable accuracy as for the melting line and the solid-vapor equilibrium. The MHNC and SCOZA results for the liquid-vapor coexistence, as well as for the corresponding critical points, are quite accurate. All results are discussed in terms of the basic assumptions underlying each theory. We have selected the MHNC for the fluid and the first-order PT for the solid phase, as the most accurate tools to investigate the phase behavior of the model in terms of purely theoretical approaches. The overall results appear as a robust benchmark for further theoretical investigations on higher order C(n>60) fullerenes, as well as on other fullerene-related materials, whose description can be based on a modelization similar to that adopted in this work.Comment: RevTeX4, 15 pages, 7 figures; submitted to Phys. Rev.

STM observation of electronic wave interference effect in finite-sized graphite with dislocation-network structures

Superperiodic patterns near a step edge were observed by STM on several-layer-thick graphite sheets on a highly oriented pyrolitic graphite substrate, where a dislocation network is generated at the interface between the graphite overlayer and the substrate. Triangular- and rhombic-shaped periodic patterns whose periodicities are around 100 nm were observed on the upper terrace near the step edge. In contrast, only outlines of the patterns similar to those on the upper terrace were observed on the lower terrace. On the upper terrace, their geometrical patterns gradually disappeared and became similar to those on the lower terrace without any changes of their periodicity in increasing a bias voltage. By assuming a periodic scattering potential at the interface due to dislocations, the varying corrugation amplitudes of the patterns can be understood as changes in LDOS as a result of the beat of perturbed and unperturbed waves, i.e. the interference in an overlayer. The observed changes in the image depending on an overlayer height and a bias voltage can be explained by the electronic wave interference in the ultra-thin overlayer distorted under the influence of dislocation-network structures.Comment: 8 pages; 6 figures; Paper which a part of cond-mat/0311068 is disscussed in detai

Effect of temperature anisotropy on various modes and instabilities for a magnetized non-relativistic bi-Maxwellian plasma

Using kinetic theory for homogeneous collisionless magnetized plasmas, we present an extended review of the plasma waves and instabilities and discuss the anisotropic response of generalized relativistic dielectric tensor and Onsager symmetry properties for arbitrary distribution functions. In general, we observe that for such plasmas only those electromagnetic modes whose magnetic field perturbations are perpendicular to the ambient magneticeld, i.e.,B1 \perp B0, are effected by the anisotropy. However, in oblique propagation all modes do show such anisotropic effects. Considering the non-relativistic bi-Maxwellian distribution and studying the relevant components of the general dielectric tensor under appropriate conditions, we derive the dispersion relations for various modes and instabilities. We show that only the electromagnetic R- and L- waves, those derived from them and the O-mode are affected by thermal anisotropies, since they satisfy the required condition B1\perpB0. By contrast, the perpendicularly propagating X-mode and the modes derived from it (the pure transverse X-mode and Bernstein mode) show no such effect. In general, we note that the thermal anisotropy modifies the parallel propagating modes via the parallel acoustic effect, while it modifies the perpendicular propagating modes via the Larmor-radius effect. In oblique propagation for kinetic Alfven waves, the thermal anisotropy affects the kinetic regime more than it affects the inertial regime. The generalized fast mode exhibits two distinct acoustic effects, one in the direction parallel to the ambient magnetic field and the other in the direction perpendicular to it. In the fast-mode instability, the magneto-sonic wave causes suppression of the firehose instability. We discuss all these propagation characteristics and present graphic illustrations

Nanoscopic Tunneling Contacts on Mesoscopic Multiprobe Conductors

We derive Bardeen-like expressions for the transmission probabilities between two multi-probe mesoscopic conductors coupled by a weak tunneling contact. We emphasize especially the dual role of a weak coupling contact as a current source and sink and analyze the magnetic field symmetry. In the limit of a point-like tunneling contact the transmission probability becomes a product of local, partial density of states of the two mesoscopic conductors. We present expressions for the partial density of states in terms of functional derivatives of the scattering matrix with respect to the local potential and in terms of wave functions. We discuss voltage measurements and resistance measurements in the transport state of conductors. We illustrate the theory for the simple case of a scatterer in an otherwise perfect wire. In particular, we investigate the development of the Hall-resistance as measured with weak coupling probes.Comment: 10 pages, 5 figures, revte

Dark soliton states of Bose-Einstein condensates in anisotropic traps

Dark soliton states of Bose-Einstein condensates in harmonic traps are studied both analytically and computationally by the direct solution of the Gross-Pitaevskii equation in three dimensions. The ground and self-consistent excited states are found numerically by relaxation in imaginary time. The energy of a stationary soliton in a harmonic trap is shown to be independent of density and geometry for large numbers of atoms. Large amplitude field modulation at a frequency resonant with the energy of a dark soliton is found to give rise to a state with multiple vortices. The Bogoliubov excitation spectrum of the soliton state contains complex frequencies, which disappear for sufficiently small numbers of atoms or large transverse confinement. The relationship between these complex modes and the snake instability is investigated numerically by propagation in real time.Comment: 11 pages, 8 embedded figures (two in color

Beyond the Fokker-Planck equation: Pathwise control of noisy bistable systems

We introduce a new method, allowing to describe slowly time-dependent Langevin equations through the behaviour of individual paths. This approach yields considerably more information than the computation of the probability density. The main idea is to show that for sufficiently small noise intensity and slow time dependence, the vast majority of paths remain in small space-time sets, typically in the neighbourhood of potential wells. The size of these sets often has a power-law dependence on the small parameters, with universal exponents. The overall probability of exceptional paths is exponentially small, with an exponent also showing power-law behaviour. The results cover time spans up to the maximal Kramers time of the system. We apply our method to three phenomena characteristic for bistable systems: stochastic resonance, dynamical hysteresis and bifurcation delay, where it yields precise bounds on transition probabilities, and the distribution of hysteresis areas and first-exit times. We also discuss the effect of coloured noise.Comment: 37 pages, 11 figure

Burgers' Flows as Markovian Diffusion Processes

We analyze the unforced and deterministically forced Burgers equation in the framework of the (diffusive) interpolating dynamics that solves the so-called Schr\"{o}dinger boundary data problem for the random matter transport. This entails an exploration of the consistency conditions that allow to interpret dispersion of passive contaminants in the Burgers flow as a Markovian diffusion process. In general, the usage of a continuity equation $\partial_t\rho =-\nabla (\vec{v}\rho)$, where $\vec{v}=\vec{v}(\vec{x},t)$ stands for the Burgers field and $\rho$ is the density of transported matter, is at variance with the explicit diffusion scenario. Under these circumstances, we give a complete characterisation of the diffusive transport that is governed by Burgers velocity fields. The result extends both to the approximate description of the transport driven by an incompressible fluid and to motions in an infinitely compressible medium. Also, in conjunction with the Born statistical postulate in quantum theory, it pertains to the probabilistic (diffusive) counterpart of the Schr\"{o}dinger picture quantum dynamics.Comment: Latex fil

Planetary population synthesis

In stellar astrophysics, the technique of population synthesis has been successfully used for several decades. For planets, it is in contrast still a young method which only became important in recent years because of the rapid increase of the number of known extrasolar planets, and the associated growth of statistical observational constraints. With planetary population synthesis, the theory of planet formation and evolution can be put to the test against these constraints. In this review of planetary population synthesis, we first briefly list key observational constraints. Then, the work flow in the method and its two main components are presented, namely global end-to-end models that predict planetary system properties directly from protoplanetary disk properties and probability distributions for these initial conditions. An overview of various population synthesis models in the literature is given. The sub-models for the physical processes considered in global models are described: the evolution of the protoplanetary disk, the planets' accretion of solids and gas, orbital migration, and N-body interactions among concurrently growing protoplanets. Next, typical population synthesis results are illustrated in the form of new syntheses obtained with the latest generation of the Bern model. Planetary formation tracks, the distribution of planets in the mass-distance and radius-distance plane, the planetary mass function, and the distributions of planetary radii, semimajor axes, and luminosities are shown, linked to underlying physical processes, and compared with their observational counterparts. We finish by highlighting the most important predictions made by population synthesis models and discuss the lessons learned from these predictions - both those later observationally confirmed and those rejected.Comment: 47 pages, 12 figures. Invited review accepted for publication in the 'Handbook of Exoplanets', planet formation section, section editor: Ralph Pudritz, Springer reference works, Juan Antonio Belmonte and Hans Deeg, Ed