160 research outputs found
Non-exponential relaxation for anomalous diffusion
We study the relaxation process in normal and anomalous diffusion regimes for
systems described by a generalized Langevin equation (GLE). We demonstrate the
existence of a very general correlation function which describes the relaxation
phenomena. Such function is even; therefore, it cannot be an exponential or a
stretched exponential. However, for a proper choice of the parameters, those
functions can be reproduced within certain intervals with good precision. We
also show the passage from the non-Markovian to the Markovian behaviour in the
normal diffusion regime. For times longer than the relaxation time, the
correlation function for anomalous diffusion becomes a power law for broad-band
noise.Comment: 6 pages, 2 figure
Entropy, non-ergodicity and non-Gaussian behaviour in ballistic transport
Ballistic transportation introduces new challenges in the thermodynamic
properties of a gas of particles. For example, violation of mixing, ergodicity
and of the fluctuation-dissipation theorem may occur, since all these processes
are connected. In this work, we obtain results for all ranges of diffusion,
i.e., both for subdiffusion and superdiffusion, where the bath is such that it
gives origin to a colored noise. In this way we obtain the skewness and the
non-Gaussian factor for the probability distribution function of the dynamical
variable. We put particular emphasis on ballistic diffusion, and we demonstrate
that in this case, although the second law of thermodynamics is preserved, the
entropy does not reach a maximum and a non-Gaussian behavior occurs. This
implies the non-applicability of the central limit theorem.Comment: 9 pages, 2 figure
Accurate numerical verification of the instanton method for macroscopic quantum tunneling: dynamics of phase slips
Instanton methods, in which imaginary-time evolution gives the tunneling
rate, have been widely used for studying quantum tunneling in various contexts.
Nevertheless, how accurate instanton methods are for the problems of
macroscopic quantum tunneling (MQT) still remains unclear because of lack of
their direct comparison with exact time evolution of the many-body Schroedinger
equation. Here, we verify instanton methods applied to coherent MQT.
Specifically applying the quasi-exact numerical method of time-evolving block
decimation to the system of bosons in a ring lattice, we directly simulate the
real-time quantum dynamics of supercurrents, where a coherent oscillation
between two macroscopically distinct current states occurs due to MQT. The
tunneling rate extracted from the coherent oscillation is compared with that
given by the instanton method. We show that the error is within 10% when the
effective Planck's constant is sufficiently small. We also discuss phase slip
dynamics associated with the coherent oscillations.Comment: 19 pages, 14 figures, 1 tabl
Collisional Plasma Models with APEC/APED: Emission Line Diagnostics of Hydrogen-like and Helium-like Ions
New X-ray observatories (Chandra and XMM-Newton) are providing a wealth of
high-resolution X-ray spectra in which hydrogen- and helium-like ions are
usually strong features. We present results from a new collisional-radiative
plasma code, the Astrophysical Plasma Emission Code (APEC), which uses atomic
data in the companion Astrophysical Plasma Emission Database (APED) to
calculate spectral models for hot plasmas. APED contains the requisite atomic
data such as collisional and radiative rates, recombination cross sections,
dielectronic recombination rates, and satellite line wavelengths. We compare
the APEC results to other plasma codes for hydrogen- and helium-like
diagnostics, and test the sensitivity of our results to the number of levels
included in the models. We find that dielectronic recombination with
hydrogen-like ions into high (n=6-10) principal quantum numbers affects some
helium-like line ratios from low-lying (n=2) transitions.Comment: 5 pages, 6 figures, accepted by ApJ Letter
Super Multi-Instantons in Conformal Chiral Superspace
We reformulate self-dual supersymmetric theories directly in conformal chiral
superspace, where superconformal invariance is manifest. The superspace can be
interpreted as the generalization of the usual Atiyah-Drinfel'd-Hitchin-Manin
twistors (the quaternionic projective line), the real projective light-cone in
six dimensions, or harmonic superspace, but can be reduced immediately to
four-dimensional chiral superspace. As an example, we give the 't Hooft and
ADHM multi-instanton constructions for self-dual super Yang-Mills theory. In
both cases, all the parameters are represented as a single, irreducible,
constant tensor.Comment: 21 pg., uuencoded compressed postscript file (twist.ps.Z.uu), other
formats (.dvi, .ps, .ps.Z, 8-bit .tex) available at
http://insti.physics.sunysb.edu/~siegel/preprints or at
ftp://max.physics.sunysb.edu/preprints/siege
Novel approach to a perfect lens
Within the framework of an exact analytical solution of Maxwell equations in
a space domain, it is shown that optical scheme based on a slab with negative
refractive index () (Veselago lens or Pendry lens) does not possess
focusing properties in the usual sense . In fact, the energy in such systems
does not go from object to its "image", but from object and its "image" to an
intersection point inside a metamaterial layer, or vice versa. A possibility of
applying this phenomenon to a creation of entangled states of two atoms is
discussed.Comment: 4 pages, 6 figure
Anomalous diffusion : a basic mechanism for the evolution of inhomogeneous systems
In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be given to some methods applied in the analysis and characterization of diffusive regimes through the memory function, the mixing condition (or irreversibility), and ergodicity. Those methods can be used in the study of small-scale systems, ranging in size from single-molecule to particle clusters and including among others polymers, proteins, ion channels and biological cells, whose diffusive properties have received much attention lately
The role of fluctuations in the response of coupled bistable units to weak driving time-periodic forces
We analyze the stochastic response of a finite set of globally coupled noisy
bistable units driven by rather weak time-periodic forces. We focus on the
stochastic resonance and phase frequency synchronization of the collective
variable, defined as the arithmetic mean of the variable characterizing each
element of the array. For single unit systems, stochastic resonance can be
understood with the powerful tools of linear response theory. Proper noise
induced phase frequency synchronization for a single unit system in this linear
response regime does not exist. For coupled arrays, our numerical simulations
indicate an enhancement of the stochastic resonance effects leading to gains
larger than unity as well as genuine phase frequency synchronization. The
non-monotonicity of the response with the strength of the coupling strength is
investigated. Comparison with simplifying schemes proposed in the literature to
describe the random response of the collective variable is carried out
The Origin of Magnetic Fields in Galaxies
Microgauss magnetic fields are observed in all galaxies at low and high
redshifts. The origin of these intense magnetic fields is a challenging
question in astrophysics. We show here that the natural plasma fluctuations in
the primordial universe (assumed to be random), predicted by the
Fluctuation-Dissipation-Theorem, predicts fields over kpc regions in galaxies.
If the dipole magnetic fields predicted by the
Fluctuation-Dissipation-Theorem are not completely random, microgauss fields
over regions kpc are easily obtained. The model is thus a strong
candidate for resolving the problem of the origin of magnetic fields in
years in high redshift galaxies.Comment: 10 pages, 3 figure
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