16,988 research outputs found
Treating some solid state problems with the Dirac equation
The ambiguity involved in the definition of effective-mass Hamiltonians for
nonrelativistic models is resolved using the Dirac equation. The multistep
approximation is extended for relativistic cases allowing the treatment of
arbitrary potential and effective-mass profiles without ordering problems. On
the other hand, if the Schrodinger equation is supposed to be used, our
relativistic approach demonstrate that both results are coincidents if the
BenDaniel and Duke prescription for the kinetic-energy operator is implemented.
Applications for semiconductor heterostructures are discussed.Comment: 06 pages, 5 figure
Special subgroups of regular semigroups
This work was partially supported by the Portuguese Foundation for Science and Technology through the grant UID/MAT/00297/2013 (CMA).Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.PostprintPeer reviewe
Significance of Ghost Orbit Bifurcations in Semiclassical Spectra
Gutzwiller's trace formula for the semiclassical density of states in a
chaotic system diverges near bifurcations of periodic orbits, where it must be
replaced with uniform approximations. It is well known that, when applying
these approximations, complex predecessors of orbits created in the bifurcation
("ghost orbits") can produce pronounced signatures in the semiclassical spectra
in the vicinity of the bifurcation. It is the purpose of this paper to
demonstrate that these ghost orbits themselves can undergo bifurcations,
resulting in complex, nongeneric bifurcation scenarios. We do so by studying an
example taken from the Diamagnetic Kepler Problem, viz. the period quadrupling
of the balloon orbit. By application of normal form theory we construct an
analytic description of the complete bifurcation scenario, which is then used
to calculate the pertinent uniform approximation. The ghost orbit bifurcation
turns out to produce signatures in the semiclassical spectrum in much the same
way as a bifurcation of real orbits would.Comment: 20 pages, 6 figures, LATEX (IOP style), submitted to J. Phys.
Decoherence of Semiclassical Wigner Functions
The Lindblad equation governs general markovian evolution of the density
operator in an open quantum system. An expression for the rate of change of the
Wigner function as a sum of integrals is one of the forms of the Weyl
representation for this equation. The semiclassical description of the Wigner
function in terms of chords, each with its classically defined amplitude and
phase, is thus inserted in the integrals, which leads to an explicit
differential equation for the Wigner function. All the Lindblad operators are
assumed to be represented by smooth phase space functions corresponding to
classical variables. In the case that these are real, representing hermitian
operators, the semiclassical Lindblad equation can be integrated. There results
a simple extension of the unitary evolution of the semiclassical Wigner
function, which does not affect the phase of each chord contribution, while
dampening its amplitude. This decreases exponentially, as governed by the time
integral of the square difference of the Lindblad functions along the classical
trajectories of both tips of each chord. The decay of the amplitudes is shown
to imply diffusion in energy for initial states that are nearly pure.
Projecting the Wigner function onto an orthogonal position or momentum basis,
the dampening of long chords emerges as the exponential decay of off-diagonal
elements of the density matrix.Comment: 23 pg, 2 fi
Duality between quantum and classical dynamics for integrable billiards
We establish a duality between the quantum wave vector spectrum and the
eigenmodes of the classical Liouvillian dynamics for integrable billiards.
Signatures of the classical eigenmodes appear as peaks in the correlation
function of the quantum wave vector spectrum. A semiclassical derivation and
numerical calculations are presented in support of the results. These classical
eigenmodes can be observed in physical experiments through the auto-correlation
of the transmission coefficient of waves in quantum billiards. Exact classical
trace formulas of the resolvent are derived for the rectangle, equilateral
triangle, and circle billiards. We also establish a correspondence between the
classical periodic orbit length spectrum and the quantum spectrum for
integrable polygonal billiards.Comment: 12 pages, 4 figure
Congruences associated with inverse transversals
An inverse transversal of a regular semigroup is an inverse subsemigroup of that contains a unique inverse of every element of . Here we consider the congruences on such a semigroup, considered as an algebra of type (2, 1). The structure of such semigroups being known, with 'building bricks' the inverse subsemigroup and the sub-bands , we investigate how congruences on are related to congruences on these building bricks
Application of two-parameter dynamical replica theory to retrieval dynamics of associative memory with non-monotonic neurons
The two-parameter dynamical replica theory (2-DRT) is applied to investigate
retrieval properties of non-monotonic associative memory, a model which lacks
thermodynamic potential functions. 2-DRT reproduces dynamical properties of the
model quite well, including the capacity and basin of attraction.
Superretrieval state is also discussed in the framework of 2-DRT. The local
stability condition of the superretrieval state is given, which provides a
better estimate of the region in which superretrieval is observed
experimentally than the self-consistent signal-to-noise analysis (SCSNA) does.Comment: 16 pages, 19 postscript figure
The Optical System for the Large Size Telescope of the Cherenkov Telescope Array
The Large Size Telescope (LST) of the Cherenkov Telescope Array (CTA) is
designed to achieve a threshold energy of 20 GeV. The LST optics is composed of
one parabolic primary mirror 23 m in diameter and 28 m focal length. The
reflector dish is segmented in 198 hexagonal, 1.51 m flat to flat mirrors. The
total effective reflective area, taking into account the shadow of the
mechanical structure, is about 368 m. The mirrors have a sandwich structure
consisting of a glass sheet of 2.7 mm thickness, aluminum honeycomb of 60 mm
thickness, and another glass sheet on the rear, and have a total weight about
47 kg. The mirror surface is produced using a sputtering deposition technique
to apply a 5-layer coating, and the mirrors reach a reflectivity of 94%
at peak. The mirror facets are actively aligned during operations by an active
mirror control system, using actuators, CMOS cameras and a reference laser.
Each mirror facet carries a CMOS camera, which measures the position of the
light spot of the optical axis reference laser on the target of the telescope
camera. The two actuators and the universal joint of each mirror facet are
respectively fixed to three neighboring joints of the dish space frame, via
specially designed interface plate.Comment: In Proceedings of the 34th International Cosmic Ray Conference
(ICRC2015), The Hague, The Netherlands. All CTA contributions at
arXiv:1508.0589
Modified TAP equations for the SK spin glass
The stability of the TAP mean field equations is reanalyzed with the
conclusion that the exclusive reason for the breakdown at the spin glass
instability is an inconsistency for the value of the local susceptibility. A
new alternative approach leads to modified equations which are in complete
agreement with the original ones above the instability. Essentially altered
results below the instability are presented and the consequences for the
dynamical mean field equations are discussed.Comment: 7 pages, 2 figures, final revised version to appear in Europhys. Let
Pair of Heavy-Exotic-Quarks at LHC
We study the production and signatures of heavy exotic quarks pairs at LHC in
the framework of the vector singlet model (VSM), vector doublet model (VDM) and
fermion-mirror-fermion (FMF) model. The pair production cross sections for the
electroweak and strong sector are computed.Comment: 7 pages, 6 figures. accept at Int. Jour. of Mod. Phy
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