138 research outputs found
An Algorithm for constructing Hjelmslev planes
Projective Hjelmslev planes and Affine Hjelmselv planes are generalisations
of projective planes and affine planes. We present an algorithm for
constructing a projective Hjelmslev planes and affine Hjelsmelv planes using
projective planes, affine planes and orthogonal arrays. We show that all
2-uniform projective Hjelmslev planes, and all 2-uniform affine Hjelsmelv
planes can be constructed in this way. As a corollary it is shown that all
2-uniform Affine Hjelmselv planes are sub-geometries of 2-uniform projective
Hjelmselv planes.Comment: 15 pages. Algebraic Design Theory and Hadamard matrices, 2014,
Springer Proceedings in Mathematics & Statistics 13
Quantization of the Hall conductivity well beyond the adiabatic limit in pulsed magnetic fields
We measure the Hall conductivity, , on a Corbino geometry sample
of a high-mobility AlGaAs/GaAs heterostructure in a pulsed magnetic field. At a
bath temperature about 80 mK, we observe well expressed plateaux in
at integer filling factors. In the pulsed magnetic field, the
Laughlin condition of the phase coherence of the electron wave functions is
strongly violated and, hence, is not crucial for quantization.Comment: 4 pages, 4 figures, submitted to PR
The transverse magnetoresistance of the two-dimensional chiral metal
We consider the two-dimensional chiral metal, which exists at the surface of
a layered, three-dimensional sample exhibiting the integer quantum Hall effect.
We calculate its magnetoresistance in response to a component of magnetic field
perpendicular to the sample surface, in the low temperature, but macroscopic,
regime where inelastic scattering may be neglected. The magnetoresistance is
positive, following a Drude form with a field scale,
, given by the transverse field strength at which
one quantum of flux, , passes through a rectangle with sides set by the
layer-spacing, , and the elastic mean free path, .
Experimental measurement of this magnetoresistance may therefore provide a
direct determination of the elastic mean free path in the chiral metal.Comment: submitted to Phys Rev
Enhancement of de Haas-van Alphen Oscillation due to Spin in the Magnetic Breakdown System
The effects of the Zeeman term on the de Haas-van Alphen oscillation is
studied in the magnetic breakdown system. We find that the amplitude of the
oscillation with the frequencies of and are enhanced by the Zeeman term, while they are expected to be
reduced in the semiclassical theory. A possible interpretation of the
experiments in organic conductors is discussed.Comment: 4 pages,4 figures. Submitted to Journal of Physical Society of Japa
Effect of quantum confinement on exciton-phonon interactions
We investigate the homogeneous linewidth of localized type-I excitons in
type-II GaAs/AlAs superlattices. These localizing centers represent the
intermediate case between quasi-two-dimensional (Q2D) and
quasi-zero-dimensional localizations. The temperature dependence of the
homogeneous linewidth is obtained with high precision from
micro-photoluminescence spectra. We confirm the reduced interaction of the
excitons with their environment with decreasing dimensionality except for the
coupling to LO-phonons. The low-temperature limit for the linewidth of these
localized excitons is five times smaller than that of Q2D excitons. The
coefficient of exciton-acoustic-phonon interaction is 5 ~ 6 times smaller than
that of Q2D excitons. An enhancement of the average exciton-LO-phonon
interaction by localization is found in our sample. But this interaction is
very sensitive to the detailed structure of the localizing centers.Comment: 6 pages, 4 figure
Critical State Behaviour in a Low Dimensional Metal Induced by Strong Magnetic Fields
We present the results of magnetotransport and magnetic torque measurements
on the alpha-(BEDT-TTF)2KHg(SCN)4 charge-transfer salt within the high magnetic
field phase, in magnetic fields extending to 33 T and temperatures as low as 27
mK. While the high magnetic field phase (at fields greater than ~ 23 T) is
expected, on theoretical grounds, to be either a modulated charge-density wave
phase or a charge/spin-density wave hybrid, the resistivity undergoes a
dramatic drop below ~ 3 K within the high magnetic field phase, falling in an
approximately exponential fashion at low temperatures, while the magnetic
torque exhibits pronounced hysteresis effects. This hysteresis, which occurs
over a broad range of fields, is both strongly temperature-dependent and has
several of the behavioural characteristics predicted by critical-state models
used to describe the pinning of vortices in type II superconductors in strong
magnetic fields. Thus, rather than exhibiting the usual behaviour expected for
a density wave ground state, both the transport and the magnetic properties of
alpha-(BEDT-TTF)2KHg(SCN)4, at high magnetic fields, closely resembles those of
a type II superconductor
Good Random Matrices over Finite Fields
The random matrix uniformly distributed over the set of all m-by-n matrices
over a finite field plays an important role in many branches of information
theory. In this paper a generalization of this random matrix, called k-good
random matrices, is studied. It is shown that a k-good random m-by-n matrix
with a distribution of minimum support size is uniformly distributed over a
maximum-rank-distance (MRD) code of minimum rank distance min{m,n}-k+1, and
vice versa. Further examples of k-good random matrices are derived from
homogeneous weights on matrix modules. Several applications of k-good random
matrices are given, establishing links with some well-known combinatorial
problems. Finally, the related combinatorial concept of a k-dense set of m-by-n
matrices is studied, identifying such sets as blocking sets with respect to
(m-k)-dimensional flats in a certain m-by-n matrix geometry and determining
their minimum size in special cases.Comment: 25 pages, publishe
Partial spreads and vector space partitions
Constant-dimension codes with the maximum possible minimum distance have been
studied under the name of partial spreads in Finite Geometry for several
decades. Not surprisingly, for this subclass typically the sharpest bounds on
the maximal code size are known. The seminal works of Beutelspacher and Drake
\& Freeman on partial spreads date back to 1975, and 1979, respectively. From
then until recently, there was almost no progress besides some computer-based
constructions and classifications. It turns out that vector space partitions
provide the appropriate theoretical framework and can be used to improve the
long-standing bounds in quite a few cases. Here, we provide a historic account
on partial spreads and an interpretation of the classical results from a modern
perspective. To this end, we introduce all required methods from the theory of
vector space partitions and Finite Geometry in a tutorial style. We guide the
reader to the current frontiers of research in that field, including a detailed
description of the recent improvements.Comment: 30 pages, 1 tabl
de Haas-van Alphen Effect in the Two-Dimensional and the Quasi-Two-Dimensional Systems
We study the de Haas-van Alphen (dHvA) oscillation in two-dimensional and
quasi-two-dimensional systems. We give a general formula of the dHvA
oscillation in two-dimensional multi-band systems. By using this formula, the
dHvA oscillation and its temperature-dependence for the two-band system are
shown. By introducing the interlayer hopping , we examine the crossover
from the two-dimension, where the oscillation of the chemical potential plays
an important role in the magnetization oscillation, to the three-dimension,
where the oscillation of the chemical potential can be neglected as is well
know as the Lifshitz and Kosevich formula. The crossover is seen at , where a and b are lattice constants, is the flux
quantum and 8t is the width of the total energy band. We also study the dHvA
oscillation in quasi-two-dimensional magnetic breakdown systems. The quantum
interference oscillations such as oscillation as well as the
fundamental oscillations are suppressed by the interlayer hopping , while
the oscillation gradually increases as increases and it
has a maximum at . This interesting dependence on the
dimensionality can be observed in the quasi-two-dimensional organic conductors
with uniaxial pressure.Comment: 11 pages, 14 figure
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