176 research outputs found
Nonclassical Kinetics in Constrained Geometries: Initial Distribution Effects
We present a detailed study of the effects of the initial distribution on the
kinetic evolution of the irreversible reaction A+B -> 0 in one dimension. Our
analytic as well as numerical work is based on a reaction-diffusion model of
this reaction. We focus on the role of initial density fluctuations in the
creation of the macroscopic patterns that lead to the well-known kinetic
anomalies in this system. In particular, we discuss the role of the long
wavelength components of the initial fluctuations in determining the long-time
behavior of the system. We note that the frequently studied random initial
distribution is but one of a variety of possible distributions leading to
interesting anomalous behavior. Our discussion includes an initial distribution
with correlated A-B pairs and one in which the initial distribution forms a
fractal pattern. The former is an example of a distribution whose long
wavelength components are suppressed, while the latter exemplifies one whose
long wavelength components are enhanced, relative to those of the random
distribution.Comment: To appear in International Journal of Bifurcation and Chaos Vol. 8
No.
Comment on ``Phase and Phase Diffusion of a Split Bose-Einstein Condensate''
Recently Javanainen and Wilkens [Phys. Rev. Lett. 78, 4675 (1997)] have
analysed an experiment in which an interacting Bose condensate, after being
allowed to form in a single potential well, is "cut" by splitting the well
adiabatically with a very high potential barrier, and estimate the rate at
which, following the cut, the two halves of the condensate lose the "memory" of
their relative phase. We argue that, by neglecting the effect of interactions
in the initial state before the separation, they have overestimated the rate of
phase randomization by a numerical factor which grows with the interaction
strength and with the slowness of the separation process.Comment: 2 pages, no figures, to appear in Phys. Rev. Let
Feshbach-type resonances for two-particle scattering in graphene
Two-particle scattering in graphene is a multichannel problem, where the
energies of the identical or opposite-helicity channels lie in disjoint energy
segments. Due to the absence of Galilean invariance, these segments depend on
the total momentum . The dispersion relations for the two opposite-helicity
scattering channels are analogous to those of two one-dimensional tight-binding
lattices with opposite dispersion relations, which are known to easily bind
states at their edges. When an -wave separable interaction potential is
assumed, those bound states reveal themselves as three Feshbach resonances in
the identical-helicity channel. In the limit , one of the
resonances survives and the opposite-helicity scattering amplitudes vanish.Comment: 8 pages, 2 figure
Violation of Cauchy-Schwarz inequalities by spontaneous Hawking radiation in resonant boson structures
The violation of a classical Cauchy-Schwarz (CS) inequality is identified as
an unequivocal signature of spontaneous Hawking radiation in sonic black holes.
This violation can be particularly large near the peaks in the radiation
spectrum emitted from a resonant boson structure forming a sonic horizon. As a
function of the frequency-dependent Hawking radiation intensity, we analyze the
degree of CS violation and the maximum violation temperature for a double
barrier structure separating two regions of subsonic and supersonic condensate
flow. We also consider the case where the resonant sonic horizon is produced by
a space-dependent contact interaction. In some cases, CS violation can be
observed by direct atom counting in a time-of-flight experiment. We show that
near the conventional zero-frequency radiation peak, the decisive CS violation
cannot occur.Comment: 10 pages, 6 figure
Oscillatory decay of a two-component Bose-Einstein condensate
We study the decay of a two-component Bose-Einstein condensate with negative
effective interaction energy. With a decreasing atom number due to losses, the
atom-atom interaction becomes less important and the system undergoes a
transition from a bistable Josephson regime to the monostable Rabi regime,
displaying oscillations in phase and number. We study the equations of motion
and derive an analytical expression for the oscillation amplitude. A quantum
trajectory simulation reveals that the classical description fails for low
emission rates, as expected from analytical considerations. Observation of the
proposed effect will provide evidence for negative effective interaction.Comment: 4 pages, 3 figue
Many-body effects in doped graphene on a piezoelectric substrate
We investigate the many-body properties of graphene on top of a piezoelectric
substrate, focusing on the interaction between the graphene electrons and the
piezoelectric acoustic phonons. We calculate the electron and phonon
self-energies as well as the electron mobility limited by the substrate
phonons. We emphasize the importance of the proper screening of the
electron-phonon vertex and discuss the various limiting behaviors as a function
of electron energy, temperature, and doping level. The effect on the graphene
electrons of the piezoelectric acoustic phonons is compared with that of the
intrinsic deformation acoustic phonons of graphene. Substrate phonons tend to
dominate over intrinsic ones for low doping levels at high and low
temperatures.Comment: 13 pages, 8 figure
Andreev reflection in bosonic condensates
We study the bosonic analog of Andreev reflection at a normal-superfluid
interface where the superfluid is a boson condensate. We model the normal
region as a zone where nonlinear effects can be neglected. Against the
background of a decaying condensate, we identify a novel contribution to the
current of reflected atoms. The group velocity of this Andreev reflected
component differs from that of the normally reflected one. For a
three-dimensional planar or two-dimensional linear interface Andreev reflection
is neither specular nor conjugate.Comment: 5 pages, 3 figures. Text revise
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