257 research outputs found
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
Coarsening scenarios in unstable crystal growth
Crystal surfaces may undergo thermodynamical as well kinetic,
out-of-equilibrium instabilities. We consider the case of mound and pyramid
formation, a common phenomenon in crystal growth and a long-standing problem in
the field of pattern formation and coarsening dynamics. We are finally able to
attack the problem analytically and get rigorous results. Three dynamical
scenarios are possible: perpetual coarsening, interrupted coarsening, and no
coarsening. In the perpetual coarsening scenario, mound size increases in time
as L=t^n, where the coasening exponent is n=1/3 when faceting occurs, otherwise
n=1/4.Comment: Changes in the final part. Accepted for publication in Phys. Rev.
Let
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 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
Singular forces and point-like colloids in lattice Boltzmann hydrodynamics
We present a second-order accurate method to include arbitrary distributions
of force densities in the lattice Boltzmann formulation of hydrodynamics. Our
method may be used to represent singular force densities arising either from
momentum-conserving internal forces or from external forces which do not
conserve momentum. We validate our method with several examples involving point
forces and find excellent agreement with analytical results. A minimal model
for dilute sedimenting particles is presented using the method which promises a
substantial gain in computational efficiency.Comment: 22 pages, 9 figures. Submitted to Phys. Rev.
A bipartite class of entanglement monotones for N-qubit pure states
We construct a class of algebraic invariants for N-qubit pure states based on
bipartite decompositions of the system.
We show that they are entanglement monotones, and that they differ from the
well know linear entropies of the sub-systems. They therefore capture new
information on the non-local properties of multipartite systems.Comment: 6 page
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