157 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
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
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
Tunneling in a uniform one-dimensional superfluid: emergence of a complex instanton
In a uniform ring-shaped one-dimensional superfluid, quantum fluctuations
that unwind the order parameter need to transfer momentum to quasiparticles
(phonons). We present a detailed calculation of the leading exponential factor
governing the rate of such phonon-assisted tunneling in a weakly-coupled Bose
gas at a low temperature . We also estimate the preexponent. We find that
for small superfluid velocities the -dependence of the rate is given mainly
by , where is the momentum transfer, and is the
phonon speed. At low , this represents a strong suppression of the rate,
compared to the non-uniform case. As a part of our calculation, we identify a
complex instanton, whose analytical continuation to suitable real-time segments
is real and describes formation and decay of coherent quasiparticle states with
nonzero total momenta.Comment: 15 pages, 3 figures; to be published in Phys. Rev.
On the color suppressed contribution to $\bar{B_{d}^0} \rightarrow \, \pi^0 \pi^{0}
The decay modes of the type are dynamically
different. For the case there is a
substantial factorized contribution which dominates. In contrast, the decay
mode has a small factorized
contribution, being proportional to a small Wilson coefficient combination.
However, for the decay mode there
is a sizeable nonfactorizable (color suppressed) contribution due to soft (long
distance) interactions, which dominate the amplitude. We estimate the branching
ratio for the mode in the heavy
quark limit for the - quark. In order to estimate color suppressed
contributions we treat the energetic light () quark within a variant of
Large Energy Effective Theory combined with a recent extension of chiral quark
models in terms of model- dependent gluon condensates. We find that our
calculated color suppressed amplitude is suppressed by a factor of order
with respect to the factorizable amplitude, as it should
according to QCD-factorization. Further, for reasonable values of the
constituent quark mass and the gluon condensate, the calculated nonfactorizable
amplitude for can easily
accomodate the experimental value. Unfortunately, the color suppressed
amplitude is very sensitive to the values of these model dependent parameters.
Therefore fine-tuning is necessary in order to obtain an amplitude compatible
with the experimental result for .
A possible link to the triangle anomaly is discussed.Comment: The submitted Latex version correspond to 23 pages in ps-version and
contains 4 figure
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
Neutrino conversions in random magnetic fields and from the Sun
The magnetic field in the convective zone of the Sun has a random small-scale
component with the r.m.s. value substantially exceeding the strength of a
regular large-scale field. For two Majorana neutrino flavors two
helicities in the presence of a neutrino transition magnetic moment and nonzero
neutrino mixing we analyze the displacement of the allowed ()-parameter region reconciled for the SuperKamiokande(SK) and
radiochemical (GALLEX, SAGE, Homestake) experiments in dependence on the r.m.s.
magnetic field value , or more precisely, on a value assuming the
transition magnetic moment . In contrast to RSFP in
regular magnetic fields we find an effective production of electron
antineutrinos in the Sun even for small neutrino mixing through cascade
conversions , in a random magnetic field that would be a
signature of the Majorana nature of neutrino if will be
registered. Basing on the present SK bound on electron antineutrinos we have
also found an excluded area in the same -plane and
revealed a strong sensitivity to the random magnetic field correlation length
.Comment: LaTex 36 pages including 14 PostScript figure
Finite-Range Gravity and Its Role in Gravitational Waves, Black Holes and Cosmology
Theoretical considerations of fundamental physics, as well as certain
cosmological observations, persistently point out to permissibility, and maybe
necessity, of macroscopic modifications of the Einstein general relativity. The
field-theoretical formulation of general relativity helped us to identify the
phenomenological seeds of such modifications. They take place in the form of
very specific mass-terms, which appear in addition to the field-theoretical
analog of the usual Hilbert-Einstein Lagrangian. We interpret the added terms
as masses of the spin-2 and spin-0 gravitons. The arising finite-range gravity
is a fully consistent theory, which smoothly approaches general relativity in
the massless limit, that is, when both masses tend to zero and the range of
gravity tends to infinity. We show that all local weak-field predictions of the
theory are in perfect agreement with the available experimental data. However,
some other conclusions of the non-linear massive theory are in a striking
contrast with those of general relativity. We show in detail how the
arbitrarily small mass-terms eliminate the black hole event horizon and replace
a permanent power-law expansion of a homogeneous isotropic universe with an
oscillatory behaviour. One variant of the theory allows the cosmological scale
factor to exhibit an `accelerated expansion'instead of slowing down to a
regular maximum of expansion. We show in detail why the traditional,
Fierz-Pauli, massive gravity is in conflict not only with the static-field
experiments but also with the available indirect gravitational-wave
observations. At the same time, we demonstrate the incorrectness of the widely
held belief that the non-Fierz-Pauli theories possess `negative energies' and
`instabilities'.Comment: 56 pages including 11 figures; significant modifications; in
particular, we demonstrate the incorrectness of the widely held belief that
the non-Fierz-Pauli theories should suffer from negative energies and
instabilities; to appear in Int. J. Mod. Phys.
Anomalous diffusion in the dynamics of complex processes
Anomalous diffusion, process in which the mean-squared displacement of system
states is a non-linear function of time, is usually identified in real
stochastic processes by comparing experimental and theoretical displacements at
relatively small time intervals. This paper proposes an interpolation
expression for the identification of anomalous diffusion in complex signals for
the cases when the dynamics of the system under study reaches a steady state
(large time intervals). This interpolation expression uses the chaotic
difference moment (transient structural function) of the second order as an
average characteristic of displacements. A general procedure for identifying
anomalous diffusion and calculating its parameters in real stochastic signals,
which includes the removal of the regular (low-frequency) components from the
source signal and the fitting of the chaotic part of the experimental
difference moment of the second order to the interpolation expression, is
presented. The procedure was applied to the analysis of the dynamics of
magnetoencephalograms, blinking fluorescence of quantum dots, and X-ray
emission from accreting objects. For all three applications, the interpolation
was able to adequately describe the chaotic part of the experimental difference
moment, which implies that anomalous diffusion manifests itself in these
natural signals. The results of this study make it possible to broaden the
range of complex natural processes in which anomalous diffusion can be
identified. The relation between the interpolation expression and a diffusion
model, which is derived in the paper, allows one to simulate the chaotic
processes in the open complex systems with anomalous diffusion.Comment: 47 pages, 15 figures; Submitted to Physical Review
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