359 research outputs found
Spectral simplicity and asymptotic separation of variables
We describe a method for comparing the real analytic eigenbranches of two
families of quadratic forms that degenerate as t tends to zero. One of the
families is assumed to be amenable to `separation of variables' and the other
one not. With certain additional assumptions, we show that if the families are
asymptotic at first order as t tends to 0, then the generic spectral simplicity
of the separable family implies that the eigenbranches of the second family are
also generically one-dimensional. As an application, we prove that for the
generic triangle (simplex) in Euclidean space (constant curvature space form)
each eigenspace of the Laplacian is one-dimensional. We also show that for all
but countably many t, the geodesic triangle in the hyperbolic plane with
interior angles 0, t, and t, has simple spectrum.Comment: 53 pages, 2 figure
Fundamental solution method applied to time evolution of two energy level systems: exact and adiabatic limit results
A method of fundamental solutions has been used to investigate transitions in
two energy level systems with no level crossing in a real time. Compact
formulas for transition probabilities have been found in their exact form as
well as in their adiabatic limit. No interference effects resulting from many
level complex crossings as announced by Joye, Mileti and Pfister (Phys. Rev.
{\bf A44} 4280 (1991)) have been detected in either case. It is argued that
these results of this work are incorrect. However, some effects of Berry's
phases are confirmed.Comment: LaTeX2e, 23 pages, 8 EPS figures. Style correcte
The instability of Alexander-McTague crystals and its implication for nucleation
We show that the argument of Alexander and McTague, that the bcc crystalline
structure is favored in those crystallization processes where the first order
character is not too pronounced, is not correct. We find that any solution that
satisfies the Alexander-McTague condition is not stable. We investigate the
implication of this result for nucleation near the pseudo- spinodal in
near-meanfield systems.Comment: 20 pages, 0 figures, submitted to Physical Review
Semiclassical Solution of the Quantum Hydrodynamic Equation for Trapped Bose-condensed Gas in the l=0 Case
In this paper the quantum hydrodynamic equation describing the collective,
low energy excitations of a dilute atomic Bose gas in a given trapping
potential is investigated with the JWKB semiclassical method. In the case of
spherically symmetric harmonic confining potential a good agreement is shown
between the semiclassical and the exact energy eigenvalues as well as wave
functions. It is also demonstrated that for larger quantum numbers the
calculation of the semiclassical wave function is numerically more stable than
the exact polynomial with large alternating coefficients.Comment: 12 pages, 7 figure
Theory of Chiral Modulations and Fluctuations in Smectic-A Liquid Crystals Under an Electric Field
Chiral liquid crystals often exhibit periodic modulations in the molecular
director; in particular, thin films of the smectic-C* phase show a chiral
striped texture. Here, we investigate whether similar chiral modulations can
occur in the induced molecular tilt of the smectic-A phase under an applied
electric field. Using both continuum elastic theory and lattice simulations, we
find that the state of uniform induced tilt can become unstable when the system
approaches the smectic-A--smectic-C* transition, or when a high electric field
is applied. Beyond that instability point, the system develops chiral stripes
in the tilt, which induce corresponding ripples in the smectic layers. The
modulation persists up to an upper critical electric field and then disappears.
Furthermore, even in the uniform state, the system shows chiral fluctuations,
including both incipient chiral stripes and localized chiral vortices. We
compare these predictions with observed chiral modulations and fluctuations in
smectic-A liquid crystals.Comment: 11 pages, including 9 postscript figures, uses REVTeX 3.0 and
epsf.st
Stability of periodic domain structures in a two-dimensional dipolar model
We investigate the energetic ground states of a model two-phase system with
1/r^3 dipolar interactions in two dimensions. The model exhibits spontaneous
formation of two kinds of periodic domain structure. A striped domain structure
is stable near half filling, but as the area fraction is changed, a transition
to a hexagonal lattice of almost-circular droplets occurs. The stability of the
equilibrium striped domain structure against distortions of the boundary is
demonstrated, and the importance of hexagonal distortions of the droplets is
quantified. The relevance of the theory for physical surface systems with
elastic, electrostatic, or magnetostatic 1/r^3 interactions is discussed.Comment: Revtex (preprint style, 19 pages) + 4 postscript figures. A version
in two-column article style with embedded figures is available at
http://electron.rutgers.edu/~dhv/preprints/index.html#ng_do
X-Ray Scattering Measurements of the Transient Structure of a Driven Charge-Density-Wave
We report time-resolved x-ray scattering measurements of the transient
structural response of the sliding {\bf Q} charge-density-wave (CDW) in
NbSe to a reversal of the driving electric field. The observed time scale
characterizing this response at 70K varies from 15 msec for driving
fields near threshold to 2 msec for fields well above threshold. The
position and time-dependent strain of the CDW is analyzed in terms of a
phenomenological equation of motion for the phase of the CDW order parameter.
The value of the damping constant, eV
seconds \AA, is in excellent agreement with the value
determined from transport measurements. As the driving field approaches
threshold from above, the line shape becomes bimodal, suggesting that the CDW
does not depin throughout the entire sample at one well-defined voltage.Comment: revtex 3.0, 7 figure
Low-dose expression of a human apolipoprotein E transgene in macrophages restores cholesterol efflux capacity of apolipoprotein E-deficient mouse plasma
Apolipoprotein E- (apoE) deficient (E-/-) mice develop severe hyperlipidemia and diffuse atherosclerosis. Low-dose expression of a human apoE3 transgene in macrophages of apoE-deficient mice (E-/-hTgE+/0), which results in about 5% of wild-type apoE plasma levels, did not correct hyperlipidemia but significantly reduced the extent of atherosclerotic lesions. To investigate the contribution of apoE to reverse cholesterol transport, we compared plasmas of wild-type (E+/+), E-/-, and E-/-hTgE+/0 mice for the appearance of apoE-containing lipoproteins by electrophoresis and their capacity to take up and esterify 3H-labeled cholesterol from radiolabeled fibroblasts or J774 macrophages. Wild-type plasma displayed lipoproteins containing apoE that were the size of high density lipoprotein and that had either electrophoretic alpha or gamma mobilities. Similar particles were also present in E-/-hTgE+/0 plasma. Depending on incubation time, E-/- plasma released 48-74% less 3H-labeled cholesterol from fibroblasts than E+/+ plasma, whereas cholesterol efflux into E-/-hTgE+/0 plasma was only 11-25% lower than into E+/+ plasma. E-/-hTgE+/0 plasma also released 10% more 3H-labeled cholesterol from radiolabeled J774 macrophages than E-/- plasma. E+/+ and E-/-hTgE+/0 plasma each esterified significantly more cell-derived 3H-labeled cholesterol than E-/- plasma. Moreover, E-/- plasma accumulated much smaller proportions of fibroblast-derived 3H-labeled cholesterol in fractions with electrophoretic gamma and alpha mobility than E+/+ and E-/-hTgE+/0 plasma. Thus, low-dose expression of apoE in macrophages nearly restored the cholesterol efflux capacity of apoE-deficient plasma through the formation of apoE-containing particles, which efficiently take up cell-derived cholesterol, and through the increase of cholesterol esterification activity. Thus, macrophage-derived apoE may protect against atherosclerosis by increasing cholesterol efflux from arterial wall cells
Inflationary Perturbations: the Cosmological Schwinger Effect
This pedagogical review aims at presenting the fundamental aspects of the
theory of inflationary cosmological perturbations of quantum-mechanical origin.
The analogy with the well-known Schwinger effect is discussed in detail and a
systematic comparison of the two physical phenomena is carried out. In
particular, it is demonstrated that the two underlying formalisms differ only
up to an irrelevant canonical transformation. Hence, the basic physical
mechanisms at play are similar in both cases and can be reduced to the
quantization of a parametric oscillator leading to particle creation due to the
interaction with a classical source: pair production in vacuum is therefore
equivalent to the appearance of a growing mode for the cosmological
fluctuations. The only difference lies in the nature of the source: an electric
field in the case of the Schwinger effect and the gravitational field in the
case of inflationary perturbations. Although, in the laboratory, it is
notoriously difficult to produce an electric field such that pairs extracted
from the vacuum can be detected, the gravitational field in the early universe
can be strong enough to lead to observable effects that ultimately reveal
themselves as temperature fluctuations in the Cosmic Microwave Background.
Finally, the question of how quantum cosmological perturbations can be
considered as classical is discussed at the end of the article.Comment: 49 pages, 6 figures, to appear in a LNP volume "Inflationary
Cosmology
Homogenized dynamics of stochastic partial differential equations with dynamical boundary conditions
A microscopic heterogeneous system under random influence is considered. The
randomness enters the system at physical boundary of small scale obstacles as
well as at the interior of the physical medium. This system is modeled by a
stochastic partial differential equation defined on a domain perforated with
small holes (obstacles or heterogeneities), together with random dynamical
boundary conditions on the boundaries of these small holes.
A homogenized macroscopic model for this microscopic heterogeneous stochastic
system is derived. This homogenized effective model is a new stochastic partial
differential equation defined on a unified domain without small holes, with
static boundary condition only. In fact, the random dynamical boundary
conditions are homogenized out, but the impact of random forces on the small
holes' boundaries is quantified as an extra stochastic term in the homogenized
stochastic partial differential equation. Moreover, the validity of the
homogenized model is justified by showing that the solutions of the microscopic
model converge to those of the effective macroscopic model in probability
distribution, as the size of small holes diminishes to zero.Comment: Communications in Mathematical Physics, to appear, 200
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