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

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, $B_0=\Phi_0/al_{\text{el}}$, given by the transverse field strength at which one quantum of flux, $\Phi_0$, passes through a rectangle with sides set by the layer-spacing, $a$, and the elastic mean free path, $l_{\text{el}}$. 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 $f_{\beta} + f_{\alpha}$ and $f_{\beta} + 2f_{\alpha}$ 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

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

Theory of neutral and charged exciton scattering with electrons in semiconductor quantum wells

Electron scattering on both neutral ($X$) and charged ($X^-$) 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 $10^9 {\rm cm}^{-2}$ in a GaAs QW at $T=5K$, the $X^-$ linewidth due to electron scattering is roughly twice as large as that of the neutral exciton. This reflects both the $X^-$ larger interaction matrix elements compared with those of $X$, 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

Mott transition from a diluted exciton gas to a dense electron-hole plasma in a single V-shaped quantum wire

We report on the study of many-body interactions in a single high quality V-shaped quantum wire by means of continuous and time-resolved microphotoluminescence. The transition from a weakly interacting exciton gas when the carrier density n is less than 10^5 cm^-1 (i.e. n aX < 0.1, with aX the exciton Bohr radius), to a dense electron-hole plasma (n > 10^6 cm^-1, i.e. n aX > 1) is systematically followed in the system as the carrier density is increased. We show that this transition occurs gradually : the free carriers first coexist with excitons for n aX > 0.1, then the electron-hole plasma becomes degenerate at n aX = 0.8. We also show that the non-linear effects are strongly related to the kind of disorder and localization properties in the structure especially in the low density regime.Comment: 5 figure