15,047 research outputs found
Power law tails of time correlations in a mesoscopic fluid model
In a quenched mesoscopic fluid, modelling transport processes at high
densities, we perform computer simulations of the single particle energy
autocorrelation function C_e(t), which is essentially a return probability.
This is done to test the predictions for power law tails, obtained from mode
coupling theory. We study both off and on-lattice systems in one- and
two-dimensions. The predicted long time tail ~ t^{-d/2} is in excellent
agreement with the results of computer simulations. We also account for finite
size effects, such that smaller systems are fully covered by the present theory
as well.Comment: 11 pages, 12 figure
Irreversible Thermodynamics in Multiscale Stochastic Dynamical Systems
This work extends the results of the recently developed theory of a rather
complete thermodynamic formalism for discrete-state, continuous-time Markov
processes with and without detailed balance. We aim at investigating the
question that whether and how the thermodynamic structure is invariant in a
multiscale stochastic system. That is, whether the relations between
thermodynamic functions of state and process variables remain unchanged when
the system is viewed at different time scales and resolutions. Our results show
that the dynamics on a fast time scale contribute an entropic term to the
"internal energy function", , for the slow dynamics. Based on the
conditional free energy , one can then treat the slow dynamics as if
the fast dynamics is nonexistent. Furthermore, we show that the free energy,
which characterizes the spontaneous organization in a system without detailed
balance, is invariant with or without the fast dynamics: The fast dynamics is
assumed to reach stationarity instantaneously on the slow time scale; they have
no effect on the system's free energy. The same can not be said for the entropy
and the internal energy, both of which contain the same contribution from the
fast dynamics. We also investigate the consequences of time-scale separation in
connection to the concepts of quasi-stationaryty and steady-adiabaticity
introduced in the phenomenological steady-state thermodynamics
Low work function of the (1000) Ca2N surface
Polymer diodes require cathodes that do not corrode the polymer but do have
low work function to minimize the electron injection barrier. First-principles
calculations demonstrate that the work function of the (1000) surface of the
compound Ca2N is half an eV lower than that of the elemental metal Ca (2.35 vs.
2.87 eV). Moreover its reactivity is expected to be smaller. This makes Ca2N an
interesting candidate to replace calcium as cathode material for polymer light
emitting diode devices.Comment: 3 pages, 4 figures, accepted by J. Appl. Phy
Diffusion of multiple species with excluded-volume effects
Stochastic models of diffusion with excluded-volume effects are used to model
many biological and physical systems at a discrete level. The average
properties of the population may be described by a continuum model based on
partial differential equations. In this paper we consider multiple interacting
subpopulations/species and study how the inter-species competition emerges at
the population level. Each individual is described as a finite-size hard core
interacting particle undergoing Brownian motion. The link between the discrete
stochastic equations of motion and the continuum model is considered
systematically using the method of matched asymptotic expansions. The system
for two species leads to a nonlinear cross-diffusion system for each
subpopulation, which captures the enhancement of the effective diffusion rate
due to excluded-volume interactions between particles of the same species, and
the diminishment due to particles of the other species. This model can explain
two alternative notions of the diffusion coefficient that are often confounded,
namely collective diffusion and self-diffusion. Simulations of the discrete
system show good agreement with the analytic results
A Physical Realization of the Generalized PT-, C-, and CPT-Symmetries and the Position Operator for Klein-Gordon Fields
Generalized parity (P), time-reversal (T), and charge-conjugation
(C)operators were initially definedin the study of the pseudo-Hermitian
Hamiltonians. We construct a concrete realization of these operators for
Klein-Gordon fields and show that in this realization PT and C operators
respectively correspond to the ordinary time-reversal and charge-grading
operations. Furthermore, we present a complete description of the quantum
mechanics of Klein-Gordon fields that is based on the construction of a Hilbert
space with a relativistically invariant, positive-definite, and conserved inner
product. In particular we offer a natural construction of a position operator
and the corresponding localized and coherent states. The restriction of this
position operator to the positive-frequency fields coincides with the
Newton-Wigner operator. Our approach does not rely on the conventional
restriction to positive-frequency fields. Yet it provides a consistent quantum
mechanical description of Klein-Gordon fields with a genuine probabilistic
interpretation.Comment: 20 pages, published versio
Momentum of an electromagnetic wave in dielectric media
Almost a hundred years ago, two different expressions were proposed for the
energy--momentum tensor of an electromagnetic wave in a dielectric. Minkowski's
tensor predicted an increase in the linear momentum of the wave on entering a
dielectric medium, whereas Abraham's tensor predicted its decrease. Theoretical
arguments were advanced in favour of both sides, and experiments proved
incapable of distinguishing between the two. Yet more forms were proposed, each
with their advocates who considered the form that they were proposing to be the
one true tensor. This paper reviews the debate and its eventual conclusion:
that no electromagnetic wave energy--momentum tensor is complete on its own.
When the appropriate accompanying energy--momentum tensor for the material
medium is also considered, experimental predictions of all the various proposed
tensors will always be the same, and the preferred form is therefore
effectively a matter of personal choice.Comment: 23 pages, 3 figures, RevTeX 4. Removed erroneous factor of mu/mu_0
from Eq.(44
The Averaging Problem in Cosmology and Macroscopic Gravity
The averaging problem in cosmology and the approach of macroscopic gravity to
resolve the problem is discussed. The averaged Einstein equations of
macroscopic gravity are modified on cosmological scales by the macroscopic
gravitational correlation tensor terms as compared with the Einstein equations
of general relativity. This correlation tensor satisfies a system of structure
and field equations. An exact cosmological solution to the macroscopic gravity
equations for a constant macroscopic gravitational connection correlation
tensor for a flat spatially homogeneous, isotropic macroscopic space-time is
presented. The correlation tensor term in the macroscopic Einstein equations
has been found to take the form of either a negative or positive spatial
curvature term. Thus, macroscopic gravity provides a cosmological model for a
flat spatially homogeneous, isotropic Universe which obeys the dynamical law
for either an open or closed Universe.Comment: 8 pages, LaTeX, ws-ijmpa.cls, few style and typo corrections. Based
on the plenary talk given at the Second Stueckelberg Workshop, ICRANet
Coordinating Center, Pescara, Italy, September 3-7, 2007. To appear in
International Journal of Modern Physics A (2008
The applicability of causal dissipative hydrodynamics to relativistic heavy ion collisions
We utilize nonequilibrium covariant transport theory to determine the region
of validity of causal Israel-Stewart dissipative hydrodynamics (IS) and
Navier-Stokes theory (NS) for relativistic heavy ion physics applications. A
massless ideal gas with 2->2 interactions is considered in a 0+1D Bjorken
scenario, appropriate for the early longitudinal expansion stage of the
collision. In the scale invariant case of a constant shear viscosity to entropy
density ratio eta/s ~ const, we find that Israel-Stewart theory is 10% accurate
in calculating dissipative effects if initially the expansion timescale exceeds
half the transport mean free path tau0/lambda0 > ~2. The same accuracy with
Navier-Stokes requires three times larger tau0/lambda0 > ~6. For dynamics
driven by a constant cross section, on the other hand, about 50% larger
tau0/lambda0 > ~3 (IS) and ~9 (NS) are needed. For typical applications at RHIC
energies s_{NN}**(1/2) ~ 100-200 GeV, these limits imply that even the
Israel-Stewart approach becomes marginal when eta/s > ~0.15. In addition, we
find that the 'naive' approximation to Israel-Stewart theory, which neglects
products of gradients and dissipative quantities, has an even smaller range of
applicability than Navier-Stokes. We also obtain analytic Israel-Stewart and
Navier-Stokes solutions in 0+1D, and present further tests for numerical
dissipative hydrodynamics codes in 1+1, 2+1, and 3+1D based on generalized
conservation laws.Comment: 30 pages, 26 EPS figures, revtex stylefil
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