共查询到20条相似文献,搜索用时 312 毫秒
1.
We study a model of mass-bearing coagulating-fragmenting planar Brownian particles. Coagulation occurs when two particles
are within a distance of order ε. Our model is macroscopically described by an inhomogeneous Smoluchowski’s equation in the low ε limit provided that the initial number of particles N is of order |log ε|. When a detailed balance condition is satisfied, we establish a central limit theorem by showing that in the low ε limit, the particle density fluctuation fields obey an Ornstein-Uhlenbeck stochastic differential equation. 相似文献
2.
Consider an infinite system of particles evolving in a one dimensional lattice according to symmetric random walks with hard
core interaction. We investigate the behavior of a tagged particle under the action of an external constant driving force.
We prove that the diffusively rescaled position of the test particle εX(ε-2
t), t > 0, converges in probability, as ε→ 0, to a deterministic function v(t). The function v(⋅) depends on the initial distribution of the random environment through a non-linear parabolic equation. This law of large
numbers for the position of the tracer particle is deduced from the hydrodynamical limit of an inhomogeneous one dimensional
symmetric zero range process with an asymmetry at the origin. An Einstein relation is satisfied asymptotically when the external
force is small.
Received: 5 December 1996 / Accepted: 30 June 1997 相似文献
3.
We investigate numerically the common α+β and the pure β FPU models, as well as some higher order generalizations. We consider initial conditions in which only low-frequency normal
modes are excited, and perform a very accurate systematic study of the equilibrium time as a function of the number N of particles, the specific energy ε, and the parameters α and β. While at any fixed N the equilibrium time is found to be a stretched exponential in 1/ε, in the thermodynamic limit, i.e. for N→∞ at fixed ε, we observe a crossover to a power law. Concerning the (usually disregarded) dependence of T
eq on α and β, we find it is nontrivial, and propose and test a general law. A central role is played by the comparison of the FPU models
with the Toda model. 相似文献
4.
We consider a billiard in the plane with periodic configuration of convex scatterers. This system is recurrent, in the sense
that almost every orbit comes back arbitrarily close to the initial point. In this paper we study the time needed to get back
in an ε-ball about the initial point, in the phase space and also for the position, in the limit when ε → 0. We establish the existence of an almost sure convergence rate, and prove a convergence in distribution for the rescaled
return times. 相似文献
5.
We compute the normalisation factor for the large order asymptotics of perturbation theory for the self-avoiding manifold
(SAM) model describing flexible tethered (D-dimensional) membranes in d-dimensional space, and the ε-expansion for this problem. For that purpose, we develop the methods inspired from instanton
calculus, that we introduced in a previous publication (Nucl. Phys. B 534 (1998) 555), and we compute the functional determinant
of the fluctuations around the instanton configuration. This determinant has UV divergences and we show that the renormalized
action used to make perturbation theory finite also renders the contribution of the instanton UV-finite. To compute this determinant,
we develop a systematic large-d expansion. For the renormalized theory, we point out problems in the interplay between the limits ε→ 0 and d→∞, as well as IR divergences when ε=0. We show that many cancellations between IR divergences occur, and argue that the remaining
IR-singular term is associated to amenable non-analytic contributions in the large-d limit when ε=0. The consistency with the standard instanton-calculus results for the self-avoiding walk is checked for D=1. 相似文献
6.
We consider a system of N non-relativistic spinless quantum particles (“electrons”) interacting with a quantized scalar Bose field (whose excitations
we call “photons”). We examine the case when the velocity v of the electrons is small with respect to the one of the photons, denoted by c (v/c = ε ≪ 1). We show that dressed particle states exist (particles surrounded by “virtual photons”), which, up to terms of order
(v/c)3, follow Hamiltonian dynamics. The effective N-particle Hamiltonian contains the kinetic energies of the particles and Coulomb-like pair potentials at order (v/c)0 and the velocity dependent Darwin interaction and a mass renormalization at order (v/c)2. Beyond that order the effective dynamics are expected to be dissipative.
The main mathematical tool we use is adiabatic perturbation theory. However, in the present case there is no eigenvalue which
is separated by a gap from the rest of the spectrum, but its role is taken by the bottom of the absolutely continuous spectrum,
which is not an eigenvalue. Nevertheless we construct approximate dressed electron subspaces, which are adiabatically invariant
for the dynamics up to order . We also give an explicit expression for the non-adiabatic transitions corresponding to emission of free photons. For the
radiated energy we obtain the quantum analogue of the Larmor formula of classical electrodynamics. 相似文献
7.
Controlling the noise enhanced stability effect via noise recycling in a metastable system 总被引:1,自引:0,他引:1
Z. L. Jia D. C. Mei 《The European Physical Journal B - Condensed Matter and Complex Systems》2012,85(4):139
We analyze the role of the delay time τ
d
and the fraction ε of recycled noise on the enhancement of the mean first-passage time (MFPT) in a metastable system with recycled noise, generated
by the superposition of a primary Gaussian noise source with a second component of constant delay. The results indicate that
MFPT as a function of the noise intensity D shows either a non-monotonic behavior with a maximum or a divergent behavior, which is the identifying characteristic of
the noise enhanced stability (NES) phenomenon. The increasing of τ
d
or ε strengthens the NES effect for ε > 0. However, for ε < 0, there is a critical value of τ
d
, below which we observe an increase of MFPT whose maximum goes to infinity, and above which the divergent behavior tends
to disappear and MFPT versus D shows a transition from one peak to two peaks and eventually one peak as τ
d
or |ε| increases. Moreover, we also discuss the effect of different initial conditions. These observations illustrate that the
noise recycling may be used as an effective scheme for controlling the NES effect. 相似文献
8.
The dynamics of an electron gas in a constant ion background can be decribed by the Vlasov-Poisson-Boltzmann system at the
kinetic level, or by the compressible Euler-Poisson system at the fluid level. We prove that any solution of the Vlasov-Poisson-Boltzmann
system near a smooth local Maxwellian with a small irrotational velocity converges global in time to the corresponding solution
to the Euler-Poisson system, as the mean free path ε goes to zero. We use a recent L
2 − L
∞ framework in the Boltzmann theory to control the higher order remainder in the Hilbert expansion uniformly in ε and globally in time. 相似文献
9.
Nicholas Crawford 《Journal of statistical physics》2011,142(1):11-42
Consider the classical XY model in a weak random external field pointing along the Y axis with strength ε. We study the behavior of this model as the range of the interaction is varied. We prove that in any dimension d≥2 and for all ε sufficiently small, there is a range L=L(ε) so that whenever the inverse temperature β is larger than some β(ε), there is strong residual ordering along the X direction. 相似文献
10.
Jean Bertoin 《Communications in Mathematical Physics》2002,232(1):59-81
We consider the following elementary model for clustering by ballistic aggregation in an expanding universe. At the initial
time, there is a doubly infinite sequence of particles lying in a one-dimensional universe that is expanding at constant rate.
We suppose that each particle p attracts points at a certain rate a(p)/2 depending only on p, and when two particles, say p and q, collide by the effect of attraction, they merge as a single particle p*q. The main purpose of this work is to point at the following remarkable property of Poisson clouds in these dynamics. Under
certain technical conditions, if at the initial time the system is distributed according to a spatially stationary Poisson
cloud with intensity μ
0
, then at any time t > 0, the system will again have a Poissonian distribution, now with intensity μ
t
, where the family solves a generalization of Smoluchowski's coagulation equation.
Received: 15 February 2002 / Accepted: 8 July 2002 Published online: 7 November 2002 相似文献
11.
Debendranath Sahoo 《Pramana》1977,8(6):545-562
We consider a graded algebra with two products (σ, α) over anε-factor commutation. One of the products (σ) isε-commutative, but, in general non-associative; and the other (α) is a graded Lieε-product and a gradedε-derivative with respect to the first (σ). Using the obvious mathematical condition, namely—the tensor product of two graded algebras with the sameε-factors is another with the sameε-factor, we determine the complete structure of a two-product (σ, α) graded algebra.
When theε-factors are taken to be unity and the gradation structure is ignored, we recover the algebras of the physical variables of
classical and quantum systems, considered by Grgin and Petersen.
With the retention of the gradation structure and the possible choice of two ε-factors we recover the algebras of the canonical
formalism of boson and fermion systems for the above classical and quantum theories. We also recover in this case the algebra
of anticommutative classical systems considered by Martin along with its quantum analogue. 相似文献
12.
We analyze the fusion process involving two deuterium nuclei in the case of deceleration of a fast deuteron with an energy
of approximately 100 keV located in a deuterium target. We calculate the probability ω
fus(ε) of generating a neutron by a fast deuteron with an initial kinetic energy ε during its deceleration. The mean free path
of fast deuterons with respect to their relaxation is found for various deuterium targets. The data are analyzed for neutron
generation in deuterium cluster beams under laser irradiation. The method of neutron generation in the collision of two deuterium
cluster beams is suggested.
The text was submitted by the author in English. 相似文献
13.
A class of Fourier Integral Operators which converge to the unitary group of the Schr?dinger equation in the semiclassical
limit ε → 0 in the uniform operator norm is constructed. The convergence allows for an error bound of order O(ε), which can be improved to arbitrary order in ε upon the introduction of corrections in the symbol. On the Ehrenfest-timescale, the result holds with a slightly weaker error
bound. In the chemical literature the approximation is known as the Herman-Kluk propagator. 相似文献
14.
Dirk Blömker Stanislaus Maier-Paape Thomas Wanner 《Communications in Mathematical Physics》2001,223(3):553-582
This paper gives theoretical results on spinodal decomposition for the stochastic Cahn–Hilliard–Cook equation, which is a
Cahn–Hilliard equation perturbed by additive stochastic noise. We prove that most realizations of the solution which start
at a homogeneous state in the spinodal interval exhibit phase separation, leading to the formation of complex patterns of
a characteristic size.
In more detail, our results can be summarized as follows. The Cahn–Hilliard–Cook equation depends on a small positive parameter
ε which models atomic scale interaction length. We quantify the behavior of solutions as ε→ 0. Specifically, we show that
for the solution starting at a homogeneous state the probability of staying near a finite-dimensional subspace ?ε is high as long as the solution stays within distance r
ε=O(ε
R
) of the homogeneous state. The subspace ?ε is an affine space corresponding to the highly unstable directions for the linearized deterministic equation. The exponent
R depends on both the strength and the regularity of the noise.
Received: 2 May 2000 / Accepted: 8 July 2001 相似文献
15.
A local derivative coupling model is used to study theφ′→ππ and other dipionic decays ofφ andφ″, as an alternative to theε-model. The results obtained are quite satisfactory. We findt hat the existence of theε-resonance is not essential in order to understand the dipionic decays of the psions at the present level of experimental
data available.
A preliminary version of this paper was presented at the 3rd High Energy Phys. Symp. held in Nov. 1976 at Bhubaneswar. 相似文献
16.
We study the Gross-Pitaevskii (GP) energy functional for a fast rotating Bose-Einstein condensate on the unit disc in two
dimensions. Writing the coupling parameter as 1/ε
2 we consider the asymptotic regime ε → 0 with the angular velocity Ω proportional to (ε
2|log ε|)−1. We prove that if Ω = Ω0(ε
2|log ε|)−1 and Ω0 > 2(3π)−1 then a minimizer of the GP energy functional has no zeros in an annulus at the boundary of the disc that contains the bulk
of the mass. The vorticity resides in a complementary ‘hole’ around the center where the density is vanishingly small. Moreover,
we prove a lower bound to the ground state energy that matches, up to small errors, the upper bound obtained from an optimal
giant vortex trial function, and also that the winding number of a GP minimizer around the disc is in accord with the phase
of this trial function. 相似文献
17.
18.
G. A. Gogadze 《Il Nuovo Cimento D》1988,10(12):1519-1524
Summary The effect of non-Josephson generation (high-frequency oscillations of voltage) in the resistive state of the superconducting
film is studied theoretically in the presence of a constant magnetic field. The density of the generation current in the magnetic
field is calculated. The consideration is based on the earlier developed model, in which the above effect is due to the bremsstrahlung
radiation from the particles with the energy ε>Δ which are injected from the quasi-normal layer of the phase slip centre to
the superconducting bank. The quasi-particles pick up the energy in the process of the multiple Andreev scattering at theN-S boundaries, and the bremsstrahlung radiation is only possible if ε-Δ is of the order of the perturbation energy of the off-diagonal
potential
at theN-S boundary (~ΔΓ
3/2, where γ is the depairing factor of the super-conductor). 相似文献
19.
In the classical theory of electromagnetism, the permittivity ε
0 and the permeability μ
0 of free space are constants whose magnitudes do not seem to possess any deeper physical meaning. By replacing the free space
of classical physics with the quantum notion of the vacuum, we speculate that the values of the aforementioned constants could
arise from the polarization and magnetization of virtual pairs in vacuum. A classical dispersion model with parameters determined
by quantum and particle physics is employed to estimate their values. We find the correct orders of magnitude. Additionally,
our simple assumptions yield an independent estimate for the number of charged elementary particles based on the known values
of ε
0 and μ
0 and for the volume of a virtual pair. Such an interpretation would provide an intriguing connection between the celebrated
theory of classical electromagnetism and the quantum theory in the weak-field limit. 相似文献