Similarity Solutions of a Class of Perturbative Fokker-Planck Equation

In a previous work, a perturbative approach to a class of Fokker-Planck equations, which have constant diffusion coefficients and small time-dependent drift coefficients, was developed by exploiting the close connection between the Fokker-Planck equations and the Schrodinger equations. In this work, we further explore the possibility of similarity solutions of such a class of Fokker-Planck equations. These solutions possess definite scaling behaviors, and are obtained by means of the so-called similarity method

Green functions and nonlinear systems: Short time expansion

We show that Green function methods can be straightforwardly applied to nonlinear equations appearing as the leading order of a short time expansion. Higher order corrections can be then computed giving a satisfactory agreement with numerical results. The relevance of these results relies on the possibility of fully exploiting a gradient expansion in both classical and quantum field theory granting the existence of a strong coupling expansion. Having a Green function in this regime in quantum field theory amounts to obtain the corresponding spectrum of the theory.Comment: 7 pages, 3 figures. Version accepted for publication in International Journal of Modern Physics

Effects of disorder on quantum fluctuations and superfluid density of a Bose-Einstein condensate in a two-dimensional optical lattice

We investigate a Bose-Einstein condensate trapped in a 2D optical lattice in the presence of weak disorder within the framework of the Bogoliubov theory. In particular, we analyze the combined effects of disorder and an optical lattice on quantum fluctuations and superfluid density of the BEC system. Accordingly, the analytical expressions of the ground state energy and quantum depletion of the system are obtained. Our results show that the lattice still induces a characteristic 3D to 1D crossover in the behavior of quantum fluctuations, despite the presence of weak disorder. Furthermore, we use the linear response theory to calculate the normal fluid density of the condensate induced by disorder. Our results in the 3D regime show that the combined presence of disorder and lattice induce a normal fluid density that asymptotically approaches 4/3 of the corresponding condensate depletion. Conditions for possible experimental realization of our scenario are also proposed.Comment: 8 pages, 0 figure. To appear in Physical Review

Resolving velocity space dynamics in continuum gyrokinetics

Many plasmas of interest to the astrophysical and fusion communities are weakly collisional. In such plasmas, small scales can develop in the distribution of particle velocities, potentially affecting observable quantities such as turbulent fluxes. Consequently, it is necessary to monitor velocity space resolution in gyrokinetic simulations. In this paper, we present a set of computationally efficient diagnostics for measuring velocity space resolution in gyrokinetic simulations and apply them to a range of plasma physics phenomena using the continuum gyrokinetic code GS2. For the cases considered here, it is found that the use of a collisionality at or below experimental values allows for the resolution of plasma dynamics with relatively few velocity space grid points. Additionally, we describe implementation of an adaptive collision frequency which can be used to improve velocity space resolution in the collisionless regime, where results are expected to be independent of collision frequency.Comment: 20 pages, 11 figures, submitted to Phys. Plasma

Nonlinear dynamics in one dimension: On a criterion for coarsening and its temporal law

We develop a general criterion about coarsening for a class of nonlinear evolution equations describing one dimensional pattern-forming systems. This criterion allows one to discriminate between the situation where a coarsening process takes place and the one where the wavelength is fixed in the course of time. An intermediate scenario may occur, namely `interrupted coarsening'. The power of the criterion lies in the fact that the statement about the occurrence of coarsening, or selection of a length scale, can be made by only inspecting the behavior of the branch of steady state periodic solutions. The criterion states that coarsening occurs if lambda'(A)>0 while a length scale selection prevails if lambda'(A)<0, where $lambda$ is the wavelength of the pattern and A is the amplitude of the profile. This criterion is established thanks to the analysis of the phase diffusion equation of the pattern. We connect the phase diffusion coefficient D(lambda) (which carries a kinetic information) to lambda'(A), which refers to a pure steady state property. The relationship between kinetics and the behavior of the branch of steady state solutions is established fully analytically for several classes of equations. Another important and new result which emerges here is that the exploitation of the phase diffusion coefficient enables us to determine in a rather straightforward manner the dynamical coarsening exponent. Our calculation, based on the idea that |D(lambda)|=lambda^2/t, is exemplified on several nonlinear equations, showing that the exact exponent is captured. Some speculations about the extension of the present results to higher dimension are outlined.Comment: 16 pages. Only a few minor changes. Accepted for publication in Physical Review

One-parameter Darboux-transformed quantum actions in Thermodynamics

We use nonrelativistic supersymmetry, mainly Darboux transformations of the general (one-parameter) type, for the quantum oscillator thermodynamic actions. Interesting Darboux generalizations of the fundamental Planck and pure vacuum cases are discussed in some detail with relevant plots. It is shown that the one-parameter Darboux-transformed Thermodynamics refers to superpositions of boson and fermion excitations of positive and negative absolute temperature, respectively. Recent results of Arnaud, Chusseau, and Philippe physics/0105048 regarding a single mode oscillator Carnot cycle are extended in the same Darboux perspective. We also conjecture a Darboux generalization of the fluctuation-dissipation theoremComment: 14 pages, 13 figures, correction of the formula in the text after Eq. 7, accepted at Physica Script

Control and Dynamic Competition of Bright and Dark Lasing States in Active Nanoplasmonic Metamaterials

Active nanoplasmonic metamaterials support bright and dark modes that compete for gain. Using a Maxwell-Bloch approach incorporating Langevin noise we study the lasing dynamics in an active nano-fishnet structure. We report that lasing of the bright negative-index mode is possible if the higher-Q dark mode is discriminated by gain, spatially or spectrally. The nonlinear competition during the transient phase is followed by steady-state emission where bright and dark modes can coexist. We analyze the influence of pump intensity and polarization and explore methods for mode control.Comment: 5 pages, 4 figure

Exact Analytic Solution for the Rotation of a Rigid Body having Spherical Ellipsoid of Inertia and Subjected to a Constant Torque

The exact analytic solution is introduced for the rotational motion of a rigid body having three equal principal moments of inertia and subjected to an external torque vector which is constant for an observer fixed with the body, and to arbitrary initial angular velocity. In the paper a parametrization of the rotation by three complex numbers is used. In particular, the rows of the rotation matrix are seen as elements of the unit sphere and projected, by stereographic projection, onto points on the complex plane. In this representation, the kinematic differential equation reduces to an equation of Riccati type, which is solved through appropriate choices of substitutions, thereby yielding an analytic solution in terms of confluent hypergeometric functions. The rotation matrix is recovered from the three complex rotation variables by inverse stereographic map. The results of a numerical experiment confirming the exactness of the analytic solution are reported. The newly found analytic solution is valid for any motion time length and rotation amplitude. The present paper adds a further element to the small set of special cases for which an exact solution of the rotational motion of a rigid body exists.Comment: "Errata Corridge Postprint" In particular: typos present in Eq. 28 of the Journal version are HERE correcte

A Solvable Model of Two-Dimensional Dilaton-Gravity Coupled to a Massless Scalar Field

We present a solvable model of two-dimensional dilaton-gravity coupled to a massless scalar field. We locally integrate the field equations and briefly discuss the properties of the solutions. For a particular choice of the coupling between the dilaton and the scalar field the model can be interpreted as the two-dimensional effective theory of 2+1 cylindrical gravity minimally coupled to a massless scalar field.Comment: 6 pages, RevTeX, to be published in Phys. Rev.