1,699 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
Localizations at infinity and essential spectrum of quantum Hamiltonians: I. General theory
We isolate a large class of self-adjoint operators H whose essential spectrum
is determined by their behavior at large x and we give a canonical
representation of their essential spectrum in terms of spectra of limits at
infinity of translations of H. The configuration space is an arbitrary abelian
locally compact not compact group.Comment: 63 pages. This is the published version with several correction
Demonstration of the difference Casimir force for samples with different charge carrier densities
A measurement of the Casimir force between a gold coated sphere and two Si
plates of different carrier densities is performed using a high vacuum based
atomic force microscope. The results are compared with the Lifshitz theory and
good agreement is found. Our experiment demonstrates that by changing the
carrier density of the semiconductor plate by several orders of magnitude it is
possible to modify the Casimir interaction. This result may find applications
in nanotechnology.Comment: 4 pages, 4 figures, to appear in Phys. Rev. Let
Control over Multi-Scale Self-Organization-Based Processes under the Extreme Tribological Conditions of Cutting through the Application of Complex Adaptive Surface-Engineered Systems
This paper features a comprehensive analysis of various multiscale selforganization processes that occur during cutting. A thorough study of entropy production during friction has uncovered several channels of its reduction that can be achieved by various selforganization processes. These processes are (1) self-organization during physical vapor deposition PVD coating deposition on the cutting tool substrates; (2) tribofilm formation caused by interactions with the environment during operation, which consist of the following compounds: thermal barriers; Magnéli phase tribo-oxides with metallic properties at elevated temperatures, tribo-oxides that transform into a liquid phase at operating temperatures, and mixed action tribo-oxides that serve as thermal barriers/lubricants, and (3) multiscale selforganization processes that occur on the surface of the tool during cutting, which include chip formation, the generation of adhesive layers, and the buildup edge formation. In-depth knowledge of these processes can be used to significantly increase the wear resistance of the coated cutting tools. This can be achieved by the application of the latest generation of complex adaptive surface-engineered systems represented by several state-of-the-art adaptive nano-multilayer PVD coatings, as well as high entropy alloy coatings (HEAC)
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
Nonlinear properties of left-handed metamaterials
We analyze nonlinear properties of microstructured materials with negative
refraction, the so-called left-handed metamaterials. We consider a
two-dimensional periodic structure created by arrays of wires and split-ring
resonators embedded into a nonlinear dielectric, and calculate the effective
nonlinear electric permittivity and magnetic permeability. We demonstrate that
the hysteresis-type dependence of the magnetic permeability on the field
intensity allows changing the material from left- to right-handed and back.
These effects can be treated as the second-order phase transitions in the
transmission properties induced by the variation of an external field.Comment: 4 pages, 3 figure
Robustness and Enhancement of Neural Synchronization by Activity-Dependent Coupling
We study the synchronization of two model neurons coupled through a synapse
having an activity-dependent strength. Our synapse follows the rules of
Spike-Timing Dependent Plasticity (STDP). We show that this plasticity of the
coupling between neurons produces enlarged frequency locking zones and results
in synchronization that is more rapid and much more robust against noise than
classical synchronization arising from connections with constant strength. We
also present a simple discrete map model that demonstrates the generality of
the phenomenon.Comment: 4 pages, accepted for publication in PR
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
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
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
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