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1.
Continuing our study of interrupted diffusion, we consider the problem of a particle executing a random walk interspersed
with localized oscillations during its halts (e.g., at lattice sites). Earlier approaches proceedvia approximation schemes for the solution of the Fokker-Planck equation for diffusion in a periodic potential. In contrast,
we visualize a two-state random walk in velocity space with the particle alternating between a state of flight and one of
localized oscillation. Using simple, physically plausible inputs for the primary quantities characterising the random walk,
we employ the powerful continuous-time random walk formalism to derive convenient and tractable closed-form expressions for
all the objects of interest: the velocity autocorrelation, generalized diffusion constant, dynamic mobility, mean square displacement,
dynamic structure factor (in the Gaussian approximation), etc. The interplay of the three characteristic times in the problem
(the mean residence and flight times, and the period of the ‘local mode’) is elucidated. The emergence of a number of striking
features of oscillatory diffusion (e.g., the local mode peak in the dynamic mobility and structure factor, and the transition between the oscillatory and diffusive
regimes) is demonstrated. 相似文献
2.
Diffusion with interruptions (arising from localized oscillations, or traps, or mixing between jump diffusion and fluid-like
diffusion, etc.) is a very general phenomenon. Its manifestations range from superionic conductance to the behaviour of hydrogen
in metals. Based on a continuous-time random walk approach, we present a comprehensive two-state random walk model for the
diffusion of a particle on a lattice, incorporating arbitrary holding-time distributions for both localized residence at the
sites and inter-site flights, and also the correct first-waiting-time distributions. A synthesis is thus achieved of the two
extremes of jump diffusion (zero flight time) and fluid-like diffusion (zero residence time). Various earlier models emerge
as special cases of our theory. Among the noteworthy results obtained are: closed-form solutions (ind dimensions, and with arbitrary directional bias) for temporally uncorrelated jump diffusion and for the ‘fluid diffusion’
counterpart; a compact, general formula for the mean square displacement; the effects of a continuous spectrum of time scales
in the holding-time distributions, etc. The dynamic mobility and the structure factor for ‘oscillatory diffusion’ are taken
up in part 2. 相似文献
3.
Our previous theoretical work one
− − H2O scattering has been modified and extended to intermediate and high energiesE
i. Using the Bethe plot, we compare the present inelastic cross-sections with the experimental ionization cross sections. Total
cross-sections are analytically represented asQ
TOT(cm2)=a.(E
ieV)
−b
and the parameters ‘a’ and ‘b’ are discussed for molecules H2O, NH3 and CH4 in the rangeE
i=100–1000eV. 相似文献
4.
A. E. Patrick 《Journal of statistical physics》2007,128(5):1211-1235
We investigate the properties of the Gibbs states and thermodynamic observables of the spherical model in a random field.
We show that on the low-temperature critical line the magnetization of the model is not a self-averaging observable, but it
self-averages conditionally. We also show that an arbitrarily weak homogeneous boundary field dominates over fluctuations
of the random field once the model transits into a ferromagnetic phase. As a result, a homogeneous boundary field restores
the conventional self-averaging of thermodynamic observables, like the magnetization and the susceptibility. We also investigate
the effective field created at the sites of the lattice by the random field, and show that at the critical temperature of
the spherical model the effective field undergoes a transition into a phase with long-range correlations ∼r
4−d
. 相似文献
5.
We solve analytically the problem of a biased random walk on a finite chain of ‘sites’ (1,2,…,N) in discrete time, with ‘myopic boundary conditions’—a walker at 1 (orN) at timen moves to 2 (orN − 1) with probability one at time (n + 1). The Markov chain has period two; there is no unique stationary distribution, and the moments of the displacement of
the walker oscillate about certain mean values asn → ∞, with amplitudes proportional to 1/N. In the continuous-time limit, the oscillating behaviour of the probability distribution disappears, but the stationary distribution
is depleted at the terminal sites owing to the boundary conditions. In the limit of continuous space as well, the problem
becomes identical to that of diffusion on a line segment with the standard reflecting boundary conditions. The first passage
time problem is also solved, and the differences between the walks with myopic and reflecting boundaries are brought out. 相似文献
6.
We consider wetting of a one-dimensional random walk on a half-line x≥0 in a short-ranged potential located at the origin x=0. We demonstrate explicitly how the presence of a quenched chemical disorder affects the pinning-depinning transition point.
For small disorders we develop a perturbative technique which enables us to compute explicitly the averaged temperature (energy)
of the pinning transition. For strong disorder we compute the transition point both numerically and using the renormalization
group approach. Our consideration is based on the following idea: the random potential can be viewed as a periodic potential
with the period n in the limit n→∞. The advantage of our approach stems from the ability to integrate exactly over all spatial degrees of freedoms in the
model and to reduce the initial problem to the analysis of eigenvalues and eigenfunctions of some special non-Hermitian random
matrix with disorder-dependent diagonal and constant off-diagonal coefficients. We show that even for strong disorder the
shift of the averaged pinning point of the random walk in the ensemble of random realizations of substrate disorder is indistinguishable
from the pinning point of the system with preaveraged (i.e. annealed) Boltzmann weight. 相似文献
7.
Andrzej Łuczak 《International Journal of Theoretical Physics》2008,47(1):236-244
We investigate a quantum counterpart of the classical notion of a stochastic process continuous with probability one, and
prove that the L
2-limit of quantum martingales ‘continuous with probability one’ is a quantum martingale ‘continuous with probability one’.
Applications of this result to a number of concrete situations is presented. 相似文献
8.
To explore the Coriolis attenuation problem we have carried out a schematici
13/2 rotor plus single quasi-particle band-mixing calculation. The results reveal that the calculations are largely insensitive
towards the location of the Fermi energy near the low-K single particle states only, and therefore are incapable of taking into account the transition from ‘full’ decoupling to
‘partial’ decoupling as the Fermi level is increased. We trace the possible reasons for this insensitivity and find that this
may be primarily due to thebcs approximation for calculating the quasiparticle energies. 相似文献
9.
10.
Leonard P. Gamberg 《Pramana》2009,72(1):55-68
The naive time reversal odd (‘T-odd’) parton distribution and fragmentation functions are explored. We use the spectator model
framework to study flavour dependence of the Boer-Mulders (h
1⊥ ) and Sivers (f
1T⊥) functions as well as the ‘T-even’ but chiral odd function h
1L⊥. These transverse momentum-dependent parton distribution functions are of significance for the analysis of azimuthal asymmetries
in semi-inclusive deep inelastic scattering, as well as for the overall physical understanding of the distribution of transversely
polarized quarks in unpolarized hadrons. In this context we also consider the Collins mechanism and the fragmentation function
H
1⊥. As a by-product of this analysis we calculate the leading twist unpolarized cos(2ϕ) asymmetry, and sin(2ϕ) single spin asymmetry for a longitudinally polarized target in semi-inclusive deep inelastic scattering.
相似文献
11.
Philippe A. Jacquet 《Journal of statistical physics》2009,134(4):709-748
We introduce a model for charge and heat transport based on the Landauer-Büttiker scattering approach. The system consists
of a chain of N quantum dots, each of them being coupled to a particle reservoir. Additionally, the left and right ends of the chain are
coupled to two particle reservoirs. All these reservoirs are independent and can be described by any of the standard physical
distributions: Maxwell-Boltzmann, Fermi-Dirac and Bose-Einstein. In the linear response regime, and under some assumptions,
we first describe the general transport properties of the system. Then we impose the self-consistency condition, i.e. we fix
the boundary values (T
L,μ
L) and (T
R,μ
R), and adjust the parameters (T
i
,μ
i
), for i=1,…,N, so that the net average electric and heat currents into all the intermediate reservoirs vanish. This condition leads to
expressions for the temperature and chemical potential profiles along the system, which turn out to be independent of the
distribution describing the reservoirs. We also determine the average electric and heat currents flowing through the system
and present some numerical results, using random matrix theory, showing that these currents are typically governed by Ohm
and Fourier laws. 相似文献
12.
Laser-induced periodic surface structures (LIPSS) were generated on oriented and amorphous thick, as well as on spin-coated
thin, poly-carbonate films by polarized ArF excimer laser light. The influence of the film structure and thickness on the
LIPSS formation was demonstrated. Below a critical thickness of the spin-coated films the line-shaped structures transformed
into droplets. This droplet formation was explained by the laser-induced melting across the whole film thickness and subsequent
de-wetting on the substrate. The thickness of the layer melted by laser illumination was computed by a heat-conduction model.
Very good agreement with the critical thickness for spin-coated films was found. The original polymer film structure influences
the index of refraction of the thin upper layer modified by the laser treatment, as was proven by the dependence of the structure’s
period on the angle of incidence both for ‘s’- and ‘p’-polarized beams. The effect of the original surface roughness – grains in thick films or holes in thin films –
was studied using atomic force microscopy. It was shown that the oblique incidence of ‘s’-polarized beams results in an intensity confinement in the direction of the forward scattering and in asymmetrical interference
pattern formation around these irregularities. A new, two-dimensional grating-like structure was generated on spin-coated
films. These gratings might be used as a special kind of mask.
Received: 10 July 2001 / Accepted: 23 July 2001 / Published online: 30 August 2001 相似文献
13.
According to recent progresses in the finite size scaling theory of
disordered systems, thermodynamic observables are not self-averaging
at critical points when the disorder is relevant in the
Harris criterion sense. This lack of
self-averageness at criticality is directly related to the distribution
of pseudo-critical temperatures Tc(i,L) over the ensemble of
samples (i) of size L. In this paper, we apply this analysis to
disordered Poland-Scheraga models with different loop exponents c,
corresponding to marginal and relevant disorder. In all cases, we
numerically obtain a Gaussian
histogram of pseudo-critical temperatures Tc(i,L) with mean
Tcav(L) and width ΔTc(L).
For the marginal case c=1.5 corresponding to two-dimensional wetting,
both the width ΔTc(L) and the shift
[Tc(∞)-Tcav(L)] decay as L-1/2, so the exponent is
unchanged (νrandom=2=νpure) but disorder is relevant and
leads to non self-averaging at criticality.
For relevant disorder
c=1.75, the width ΔTc(L) and the shift
[Tc(∞)-Tcav(L)] decay with the same new exponent
L-1/νrandom (where νrandom ∼2.7 > 2 > νpure) and
there is again no self-averaging at criticality. Finally for the value
c=2.15, of interest in the context of DNA denaturation, the
transition is first-order in the pure case. In the presence of
disorder, the width ΔTc(L) ∼L-1/2
dominates over the shift [Tc(∞)-Tcav(L)] ∼L-1,
i.e. there are two correlation length exponents ν=2 and
that govern respectively the averaged/typical loop distribution. 相似文献
14.
Fabio Lucio Toninelli 《Communications in Mathematical Physics》2008,280(2):389-401
We consider a renewal process τ = {τ
0, τ
1,...} on the integers, where the law of τ
i
− τ
i-1 has a power-like tail P(τ
i
− τ
i-1 = n) = n
−(α+1)
L(n) with α ≥ 0 and L(·) slowly varying. We then assign a random, n-dependent reward/penalty to the occurrence of the event that the site n belongs to τ. In such generality this class of problems includes, among others, (1 + d)-dimensional models of pinning of directed polymers on a one-dimensional random defect, (1 + 1)-dimensional models of wetting
of disordered substrates, and the Poland-Scheraga model of DNA denaturation. By varying the average of the reward, the system
undergoes a transition from a localized phase, where τ occupies a finite fraction of to a delocalized phase, where the density of τ vanishes. In absence of disorder (i.e., if the reward is independent of n), the transition is of first order for α > 1 and of higher order for α < 1. Moreover, for α ranging from 1 to 0, the transition ranges from first to infinite order. Presence of even an arbitrarily
small (but extensive) amount of disorder is known to modify the order of transition as soon as α > 1/2 [11]. In physical terms, disorder is relevant in this situation, in agreement with the heuristic Harris criterion.
On the other hand, for 0 < α < 1/2 it has been proven recently by K. Alexander [2] that, if disorder is sufficiently weak, critical exponents are not
modified by randomness: disorder is irrelevant. In this work, generalizing techniques which in the framework of spin glasses
are known as replica coupling and interpolation, we give a new, simpler proof of the main results of [2]. Moreover, we (partially) justify a small-disorder expansion worked
out in [9] for α < 1/2, showing that it provides a free energy upper bound which improves the annealed one. 相似文献
15.
We show that the classical de Finetti theorem has a canonical noncommutative counterpart if we strengthen “exchangeability”
(i.e., invariance of the joint distribution of the random variables under the action of the permutation group) to invariance
under the action of the quantum permutation group. More precisely, for an infinite sequence of noncommutative random variables
, we prove that invariance of the joint distribution of the x
i
’s under quantum permutations is equivalent to the fact that the x
i
’s are identically distributed and free with respect to the conditional expectation onto the tail algebra of the x
i
’s.
Research supported by Discovery and LSI grants from NSERC (Canada) and by a Killam Fellowship from the Canada Council for
the Arts. 相似文献
16.
Eckehard W. Mielke 《General Relativity and Gravitation》2008,40(6):1311-1325
The curvature-squared model of gravity, in the affine form proposed by Weyl and Yang, is deduced from a topological action
in 4D. More specifically, we start from the Pontrjagin (or Euler) invariant. Using the BRST antifield formalism with a double
duality gauge fixing, we obtain a consistent quantization in spaces of double dual curvature as classical instanton type background. However,
exact vacuum solutions with double duality properties exhibit a ‘vacuum degeneracy’. By modifying the duality via a scale breaking term, we demonstrate that only Einstein’s equations with an induced cosmological constant emerge for the topology of the macroscopic background. This may have repercussions on the problem of ‘dark energy’ as well as ‘dark matter’ modeled
by a torsion induced quintaxion. 相似文献
17.
M. G. Ryskin A. D. Martin V. A. Khoze 《The European Physical Journal C - Particles and Fields》2011,71(4):1617
We discuss the qualitative features of the recent data on multiparticle production observed at the LHC. The tolerable agreement
with Monte Carlos based on LO DGLAP evolution indicates that there is no qualitative difference between ‘hard’ and ‘soft’
interactions; and that a perturbative QCD approach may be extended into the soft domain. However, in order to describe the
data, these Monte Carlos need an additional infrared cutoff k
min with a value k
min ∼2–3 GeV which is not small, and which increases with collider energy. Here we explain the physical origin of the large k
min . Using an alternative model which matches the ‘soft’ high-energy hadron interactions smoothly on to perturbative QCD at small
x, we demonstrate that this effective cutoff k
min is actually due to the strong absorption of low k
t
partons. The model embodies the main features of the BFKL approach, including the diffusion in transverse momenta, ln k
t
, and an intercept consistent with resummed next-to-leading log corrections. Moreover, the model uses a two-channel eikonal
framework, and includes the contributions from the multi-Pomeron exchange diagrams, both non-enhanced and enhanced. The values
of a small number of physically-motivated parameters are chosen to reproduce the available total, elastic and proton dissociation
cross section (pre-LHC) data. Predictions are made for the LHC, and the relevance to ultra-high-energy cosmic rays is briefly
discussed. The low x inclusive integrated gluon PDF, and the diffractive gluon PDF, are calculated in this framework, using the parameters which
describe the high-energy pp and p[`(p)]p\bar{p} ‘soft’ data. Comparison with the PDFs obtained from the global parton analyses of deep inelastic and related hard scattering data and from diffractive deep inelastic data looks encouraging. 相似文献
18.
19.
In this easy introduction to higher gauge theory, we describe parallel transport for particles and strings in terms of 2-connections
on 2-bundles. Just as ordinary gauge theory involves a gauge group, this generalization involves a gauge ‘2-group’. We focus
on 6 examples. First, every abelian Lie group gives a Lie 2-group; the case of U(1) yields the theory of U(1) gerbes, which
play an important role in string theory and multisymplectic geometry. Second, every group representation gives a Lie 2-group;
the representation of the Lorentz group on 4d Minkowski spacetime gives the Poincaré 2-group, which leads to a spin foam model
for Minkowski spacetime. Third, taking the adjoint representation of any Lie group on its own Lie algebra gives a ‘tangent
2-group’, which serves as a gauge 2-group in 4d BF theory, which has topological gravity as a special case. Fourth, every Lie group has an ‘inner automorphism 2-group’, which
serves as the gauge group in 4d BF theory with cosmological constant term. Fifth, every Lie group has an ‘automorphism 2-group’, which plays an important role
in the theory of nonabelian gerbes. And sixth, every compact simple Lie group gives a ‘string 2-group’. We also touch upon
higher structures such as the ‘gravity 3-group’, and the Lie 3-superalgebra that governs 11-dimensional supergravity. 相似文献
20.
Y. Koide 《The European Physical Journal C - Particles and Fields》2007,52(3):617-623
Stimulated by Ma’s idea, which explains the tribimaximal neutrino mixing by assuming an A4 flavor symmetry, a lepton mass matrix model is investigated. A Frogatt–Nielsen-type model is assumed, and the flavor structures
of the masses and mixing are caused by the VEVs of SU(2)L singlet scalars φi
u and φi
d (i=1,2,3), which are assigned to 3
and (1
,1
’,1
”) of A4, respectively. Possible charged lepton and neutrino mass spectra and mixing are investigated. 相似文献