123 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
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
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
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
Theory of neutral and charged exciton scattering with electrons in semiconductor quantum wells
Electron scattering on both neutral () and charged () excitons in
quantum wells is studied theoretically. A microscopic model is presented,
taking into account both elastic and dissociating scattering. The model is
based on calculating the exciton-electron direct and exchange interaction
matrix elements, from which we derive the exciton scattering rates. We find
that for an electron density of in a GaAs QW at ,
the linewidth due to electron scattering is roughly twice as large as
that of the neutral exciton. This reflects both the larger interaction
matrix elements compared with those of , and their different dependence on
the transferred momentum. Calculated reflection spectra can then be obtained by
considering the three electronic excitations of the system, namely, the
heavy-hole and light-hole 1S neutral excitons, and the heavy-hole 1S charged
exciton, with the appropriate oscillator strengths.Comment: 18 pages, 12 figure
Transient four-wave mixing in T-shaped GaAs quantum wires
The binding energy of excitons and biexcitons and the exciton dephasing in T-shaped GaAs quantum wires is investigated by transient four-wave mixing. The T-shaped structure is fabricated by cleaved-edge overgrowth, and its geometry is engineered to optimize the one-dimensional confinement. In this wire of 6.6×24 nm2 size, we find a one-dimensional confinement of more than 20 meV, an inhomogeneous broadening of 3.4 meV, an exciton binding energy of 12 meV, and a biexciton binding energy of 2.0 meV. A dispersion of the homogeneous linewidth within the inhomogeneous broadening due to phonon-assisted relaxation is observed. The exciton acoustic-phonon-scattering coefficient of 6.1±0.5 μeV/K is larger than in comparable quantum-well structures
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