861 research outputs found
Quantum optomechanics of a multimode system coupled via photothermal and radiation pressure force
We provide a full quantum description of the optomechanical system formed by
a Fabry-Perot cavity with a movable micro-mechanical mirror whose
center-of-mass and internal elastic modes are coupled to the driven cavity mode
by both radiation pressure and photothermal force. Adopting a quantum Langevin
description, we investigate simultaneous cooling of the micromirror elastic and
center-of-mass modes, and also the entanglement properties of the
optomechanical multipartite system in its steady state.Comment: 11 pages, 7 figure
On the derivative of the associated Legendre function of the first kind of integer order with respect to its degree
In our recent works [R. Szmytkowski, J. Phys. A 39 (2006) 15147; corrigendum:
40 (2007) 7819; addendum: 40 (2007) 14887], we have investigated the derivative
of the Legendre function of the first kind, , with respect to its
degree . In the present work, we extend these studies and construct
several representations of the derivative of the associated Legendre function
of the first kind, , with respect to the degree , for
. At first, we establish several contour-integral
representations of . They are then
used to derive Rodrigues-type formulas for with . Next, some closed-form
expressions for are
obtained. These results are applied to find several representations, both
explicit and of the Rodrigues type, for the associated Legendre function of the
second kind of integer degree and order, ; the explicit
representations are suitable for use for numerical purposes in various regions
of the complex -plane. Finally, the derivatives
, and , all with , are evaluated in terms
of .Comment: LateX, 40 pages, 1 figure, extensive referencin
Opinion dynamics: rise and fall of political parties
We analyze the evolution of political organizations using a model in which
agents change their opinions via two competing mechanisms. Two agents may
interact and reach consensus, and additionally, individual agents may
spontaneously change their opinions by a random, diffusive process. We find
three distinct possibilities. For strong diffusion, the distribution of
opinions is uniform and no political organizations (parties) are formed. For
weak diffusion, parties do form and furthermore, the political landscape
continually evolves as small parties merge into larger ones. Without diffusion,
a pattern develops: parties have the same size and they possess equal niches.
These phenomena are analyzed using pattern formation and scaling techniques.Comment: 5 pages, 5 figure
Asymptotics of relative heat traces and determinants on open surfaces of finite area
The goal of this paper is to prove that on surfaces with asymptotically cusp
ends the relative determinant of pairs of Laplace operators is well defined. We
consider a surface with cusps (M,g) and a metric h on the surface that is a
conformal transformation of the initial metric g. We prove the existence of the
relative determinant of the pair under suitable
conditions on the conformal factor. The core of the paper is the proof of the
existence of an asymptotic expansion of the relative heat trace for small
times. We find the decay of the conformal factor at infinity for which this
asymptotic expansion exists and the relative determinant is defined. Following
the paper by B. Osgood, R. Phillips and P. Sarnak about extremal of
determinants on compact surfaces, we prove Polyakov's formula for the relative
determinant and discuss the extremal problem inside a conformal class. We
discuss necessary conditions for the existence of a maximizer.Comment: This is the final version of the article before it gets published. 51
page
From the solutions of diffusion equation to the solutions of subdiffusive one
Starting with the Green's functions found for normal diffusion, we construct
exact time-dependent Green's functions for subdiffusive equation (with
fractional time derivatives), with the boundary conditions involving a linear
combination of fluxes and concentrations. The method is particularly useful to
calculate the concentration profiles in a multi-part system where different
kind of transport occurs in each part of it. As an example, we find the
solutions of subdiffusive equation for the system composed from two parts with
normal diffusion and subdiffusion, respectively.Comment: 11 pages, 2 figure
Diffusion of particles in an expanding sphere with an absorbing boundary
We study the problem of particles undergoing Brownian motion in an expanding
sphere whose surface is an absorbing boundary for the particles. The problem is
akin to that of the diffusion of impurities in a grain of polycrystalline
material undergoing grain growth. We solve the time dependent diffusion
equation for particles in a d-dimensional expanding sphere to obtain the
particle density function (function of space and time). The survival rate or
the total number of particles per unit volume as a function of time is
evaluated. We have obtained particular solutions exactly for the case where d=3
and a parabolic growth of the sphere. Asymptotic solutions for the particle
density when the sphere growth rate is small relative to particle diffusivity
and vice versa are derived.Comment: 12 pages. To appear in J. Phys. A: Math. Theor. 41 (2008
Uniform approximation for diffractive contributions to the trace formula in billiard systems
We derive contributions to the trace formula for the spectral density
accounting for the role of diffractive orbits in two-dimensional billiard
systems with corners. This is achieved by using the exact Sommerfeld solution
for the Green function of a wedge. We obtain a uniformly valid formula which
interpolates between formerly separate approaches (the geometrical theory of
diffraction and Gutzwiller's trace formula). It yields excellent numerical
agreement with exact quantum results, also in cases where other methods fail.Comment: LaTeX, 41 pages including 12 PostScript figures, submitted to Phys.
Rev.
Interaction of magnetization and heat dynamics for pulsed domain wall movement with Joule heating
Pulsed domain wall movement is studied here in Ni80Fe20 nanowires on SiO2, using a fully integrated electrostatic, thermoelectric, and micromagnetics solver based on the Landau-Lifshitz- Bloch equation, including Joule heating, anisotropic magneto-resistance, and Oersted field contributions.
During the applied pulse, the anisotropic magneto-resistance of the domain wall generates a dynamic heat gradient, which increases the current-driven velocity by up to 15%. Using a temperature-dependent conductivity, significant differences are found between the constant voltage-pulsed and constant current-pulsed domain wall movement: constant voltage pulses are
shown to be more efficient at displacing domain walls whilst minimizing the increase in temperature,
with the total domain wall displacement achieved over a fixed pulse duration having a maximum with respect to the driving pulse strength
On the Mixing of Diffusing Particles
We study how the order of N independent random walks in one dimension evolves
with time. Our focus is statistical properties of the inversion number m,
defined as the number of pairs that are out of sort with respect to the initial
configuration. In the steady-state, the distribution of the inversion number is
Gaussian with the average ~N^2/4 and the standard deviation sigma N^{3/2}/6.
The survival probability, S_m(t), which measures the likelihood that the
inversion number remains below m until time t, decays algebraically in the
long-time limit, S_m t^{-beta_m}. Interestingly, there is a spectrum of
N(N-1)/2 distinct exponents beta_m(N). We also find that the kinetics of
first-passage in a circular cone provides a good approximation for these
exponents. When N is large, the first-passage exponents are a universal
function of a single scaling variable, beta_m(N)--> beta(z) with
z=(m-)/sigma. In the cone approximation, the scaling function is a root of a
transcendental equation involving the parabolic cylinder equation, D_{2
beta}(-z)=0, and surprisingly, numerical simulations show this prediction to be
exact.Comment: 9 pages, 6 figures, 2 table
Towards higher order lattice Boltzmann schemes
In this contribution we extend the Taylor expansion method proposed
previously by one of us and establish equivalent partial differential equations
of DDH lattice Boltzmann scheme at an arbitrary order of accuracy. We derive
formally the associated dynamical equations for classical thermal and linear
fluid models in one to three space dimensions. We use this approach to adjust
relaxation parameters in order to enforce fourth order accuracy for thermal
model and diffusive relaxation modes of the Stokes problem. We apply the
resulting scheme for numerical computation of associated eigenmodes and compare
our results with analytical references
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