1,100 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
Cyclic Statistics In Three Dimensions
While 2-dimensional quantum systems are known to exhibit non-permutation,
braid group statistics, it is widely expected that quantum statistics in
3-dimensions is solely determined by representations of the permutation group.
This expectation is false for certain 3-dimensional systems, as was shown by
the authors of ref. [1,2,3]. In this work we demonstrate the existence of
``cyclic'', or , {\it non-permutation group} statistics for a system of n
> 2 identical, unknotted rings embedded in . We make crucial use of a
theorem due to Goldsmith in conjunction with the so called Fuchs-Rabinovitch
relations for the automorphisms of the free product group on n elements.Comment: 13 pages, 1 figure, LaTex, minor page reformattin
Anomalous phase shift in a Josephson junction via an antiferromagnetic interlayer
The anomalous ground state phase shift in S/AF/S Josephson junctions in the
presence of the Rashba SO-coupling is predicted and numerically investigated.
It is found to be a consequence of the uncompensated magnetic moment at the
S/AF interfaces. The anomalous phase shift exhibits a strong dependence on the
value of the SO-coupling and the sublattice magnetization with the simultaneous
existence of stable and metastable branches. It depends strongly on the
orientation of the Neel vector with respect to the S/AF interfaces via the
dependence on the orientation of the interface uncompensated magnetic moment,
what opens a way to control the Neel vector by supercurrent in Josephson
systems.Comment: published versio
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
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
Thermodynamic aspects of materials' hardness: prediction of novel superhard high-pressure phases
In the present work we have proposed the method that allows one to easily
estimate hardness and bulk modulus of known or hypothetical solid phases from
the data on Gibbs energy of atomization of the elements and corresponding
covalent radii. It has been shown that hardness and bulk moduli of compounds
strongly correlate with their thermodynamic and structural properties. The
proposed method may be used for a large number of compounds with various types
of chemical bonding and structures; moreover, the temperature dependence of
hardness may be calculated, that has been performed for diamond and cubic boron
nitride. The correctness of this approach has been shown for the recently
synthesized superhard diamond-like BC5. It has been predicted that the
hypothetical forms of B2O3, diamond-like boron, BCx and COx, which could be
synthesized at high pressures and temperatures, should have extreme hardness
Synchronous Behavior of Two Coupled Electronic Neurons
We report on experimental studies of synchronization phenomena in a pair of
analog electronic neurons (ENs). The ENs were designed to reproduce the
observed membrane voltage oscillations of isolated biological neurons from the
stomatogastric ganglion of the California spiny lobster Panulirus interruptus.
The ENs are simple analog circuits which integrate four dimensional
differential equations representing fast and slow subcellular mechanisms that
produce the characteristic regular/chaotic spiking-bursting behavior of these
cells. In this paper we study their dynamical behavior as we couple them in the
same configurations as we have done for their counterpart biological neurons.
The interconnections we use for these neural oscillators are both direct
electrical connections and excitatory and inhibitory chemical connections: each
realized by analog circuitry and suggested by biological examples. We provide
here quantitative evidence that the ENs and the biological neurons behave
similarly when coupled in the same manner. They each display well defined
bifurcations in their mutual synchronization and regularization. We report
briefly on an experiment on coupled biological neurons and four dimensional ENs
which provides further ground for testing the validity of our numerical and
electronic models of individual neural behavior. Our experiments as a whole
present interesting new examples of regularization and synchronization in
coupled nonlinear oscillators.Comment: 26 pages, 10 figure
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