1,811 research outputs found
Essential spectra and exponential estimates of eigenfunctions of lattice operators of quantum mechanics
This paper is devoted to estimates of the exponential decay of eigenfunctions
of difference operators on the lattice Z^n which are discrete analogs of the
Schr\"{o}dinger, Dirac and square-root Klein-Gordon operators. Our
investigation of the essential spectra and the exponential decay of
eigenfunctions of the discrete spectra is based on the calculus of so-called
pseudodifference operators (i.e., pseudodifferential operators on the group
Z^n) with analytic symbols and on the limit operators method. We obtain a
description of the location of the essential spectra and estimates of the
eigenfunctions of the discrete spectra of the main lattice operators of quantum
mechanics, namely: matrix Schr\"{o}dinger operators on Z^n, Dirac operators on
Z^3, and square root Klein-Gordon operators on Z^n
Liberty, Equality and Not Too Much Fraternity: An Experience in Practical Application of Liberal Education Teaching Techniques
The paper explores an experience in practical application of liberal education teaching techniques. We describe the most frequently used techniques and present sample classroom assignments based on this framework. We also discuss the opportunities and limitations provided by the use of these methods in a classroom setting.
Keywords: teaching techniques, liberal education, writing and analytical reading, humanities teaching
Comparison of the experimental data for the Casimir pressure with the Lifshitz theory at zero temperature
We perform detailed comparison of the experimental data of the experiment on
the determination of the Casimir pressure between two parallel Au plates with
the theoretical values computed using the Lifshitz formula at zero temperature.
Computations are done using the optical data for the complex index of
refraction of Au extrapolated to low frequencies by means of the Drude model
with both most often used and other suggested Drude parameters. It is shown
that the experimental data exclude the Lifshitz formula at zero temperature at
a 70% confidence level if the Drude model with most often used values of the
parameters is employed. If other values of the Drude parameters are used, the
Lifshitz formula at zero frequency is experimentally excluded at a 95%
confidence level. The Lifshitz formula at zero temperature combined with the
generalized plasma-like model with most often used value of the plasma
frequency is shown to be experimentally consistent. We propose a decisive
experiment which will shed additional light on the role of relaxation
properties of conduction electrons in the Casimir effect.Comment: 22 pages, 6 figures; Phys. Rev. B, to appea
Pattern formation without heating in an evaporative convection experiment
We present an evaporation experiment in a single fluid layer. When latent
heat associated to the evaporation is large enough, the heat flow through the
free surface of the layer generates temperature gradients that can destabilize
the conductive motionless state giving rise to convective cellular structures
without any external heating. The sequence of convective patterns obtained here
without heating, is similar to that obtained in B\'enard-Marangoni convection.
This work present the sequence of spatial bifurcations as a function of the
layer depth. The transition between square to hexagonal pattern, known from
non-evaporative experiments, is obtained here with a similar change in
wavelength.Comment: Submitted to Europhysics Letter
Possibility of measuring the thermal Casimir interaction between a plate and a cylinder attached to a micromachined oscillator
We investigate the possibility of measuring the thermal Casimir force and its
gradient in the configuration of a plate and a microfabricated cylinder
attached to a micromachined oscillator. The Lifshitz-type formulas in this
configuration are derived using the proximity force approximation. The accuracy
for the obtained expressions is determined from a comparison with exact results
available in ideal metal case. Computations of the thermal correction to both
the Casimir force and its gradient are performed in the framework of different
theoretical approaches proposed in the literature. The correction to the
Casimir force and its gradient due to lack of parallelism of the plate and
cylinder is determined using the nonmultiplicative approach. The error
introduced in the theory due to the finite length of the cylinder is estimated.
We propose that both static and dynamic experiments measuring the thermal
Casimir interaction between a cylinder and a plate using a micromachined
oscillator can shed additional light on the thermal Casimir force problem.
Specifically, it is shown that the static experiment is better adapted for the
measurement of thermal effects.Comment: 29 pages, 4 figures, 1 table; minor additions are made in accordance
to the version accepted for publication; to appear in Phys. Rev.
Essential spectra of difference operators on \sZ^n-periodic graphs
Let (\cX, \rho) be a discrete metric space. We suppose that the group
\sZ^n acts freely on and that the number of orbits of with respect to
this action is finite. Then we call a \sZ^n-periodic discrete metric
space. We examine the Fredholm property and essential spectra of band-dominated
operators on where is a \sZ^n-periodic discrete metric space.
Our approach is based on the theory of band-dominated operators on \sZ^n and
their limit operators.
In case is the set of vertices of a combinatorial graph, the graph
structure defines a Schr\"{o}dinger operator on in a natural way. We
illustrate our approach by determining the essential spectra of Schr\"{o}dinger
operators with slowly oscillating potential both on zig-zag and on hexagonal
graphs, the latter being related to nano-structures
Control of the Casimir force by the modification of dielectric properties with light
The experimental demonstration of the modification of the Casimir force
between a gold coated sphere and a single-crystal Si membrane by light pulses
is performed. The specially designed and fabricated Si membrane was irradiated
with 514 nm laser pulses of 5 ms width in high vacuum leading to a change of
the charge-carrier density. The difference in the Casimir force in the presence
and in the absence of laser radiation was measured by means of an atomic force
microscope as a function of separation at different powers of the absorbed
light. The total experimental error of the measured force differences at a
separation of 100 nm varies from 10 to 20% in different measurements. The
experimental results are compared with theoretical computations using the
Lifshitz theory at both zero and laboratory temperatures. The total theoretical
error determined mostly by the uncertainty in the concentration of charge
carriers when the light is incident is found to be about 14% at separations
less than 140 nm. The experimental data are consistent with the Lifshitz theory
at laboratory temperature, if the static dielectric permittivity of
high-resistivity Si in the absence of light is assumed to be finite. If the dc
conductivity of high-resistivity Si in the absence of light is included into
the model of dielectric response, the Lifshitz theory at nonzero temperature is
shown to be experimentally inconsistent at 95% confidence. The demonstrated
phenomenon of the modification of the Casimir force through a change of the
charge-carrier density is topical for applications of the Lifshitz theory to
real materials in fields ranging from nanotechnology and condensed matter
physics to the theory of fundamental interactions.Comment: 30 pages, 10 figures, 2 table
A Simple Theory of Condensation
A simple assumption of an emergence in gas of small atomic clusters
consisting of particles each, leads to a phase separation (first order
transition). It reveals itself by an emergence of ``forbidden'' density range
starting at a certain temperature. Defining this latter value as the critical
temperature predicts existence of an interval with anomalous heat capacity
behaviour . The value suggested in literature
yields the heat capacity exponent .Comment: 9 pages, 1 figur
Penta-Hepta Defect Motion in Hexagonal Patterns
Structure and dynamics of penta-hepta defects in hexagonal patterns is
studied in the framework of coupled amplitude equations for underlying plane
waves. Analytical solution for phase field of moving PHD is found in the far
field, which generalizes the static solution due to Pismen and Nepomnyashchy
(1993). The mobility tensor of PHD is calculated using combined analytical and
numerical approach. The results for the velocity of PHD climbing in slightly
non-optimal hexagonal patterns are compared with numerical simulations of
amplitude equations. Interaction of penta-hepta defects in optimal hexagonal
patterns is also considered.Comment: 4 pages, Postscript (submitted to PRL
Rigorous approach to the comparison between experiment and theory in Casimir force measurements
In most experiments on the Casimir force the comparison between measurement
data and theory was done using the concept of the root-mean-square deviation, a
procedure that has been criticized in literature. Here we propose a special
statistical analysis which should be performed separately for the experimental
data and for the results of the theoretical computations. In so doing, the
random, systematic, and total experimental errors are found as functions of
separation, taking into account the distribution laws for each error at 95%
confidence. Independently, all theoretical errors are combined to obtain the
total theoretical error at the same confidence. Finally, the confidence
interval for the differences between theoretical and experimental values is
obtained as a function of separation. This rigorous approach is applied to two
recent experiments on the Casimir effect.Comment: 10 pages, iopart.cls is used, to appear in J. Phys. A (special issue:
Proceedings of QFEXT05, Barcelona, Sept. 5-9, 2005
- …