MacWilliams' Extension Theorem for Bi-Invariant Weights over Finite Principal Ideal Rings

A finite ring R and a weight w on R satisfy the Extension Property if every R-linear w-isometry between two R-linear codes in R^n extends to a monomial transformation of R^n that preserves w. MacWilliams proved that finite fields with the Hamming weight satisfy the Extension Property. It is known that finite Frobenius rings with either the Hamming weight or the homogeneous weight satisfy the Extension Property. Conversely, if a finite ring with the Hamming or homogeneous weight satisfies the Extension Property, then the ring is Frobenius. This paper addresses the question of a characterization of all bi-invariant weights on a finite ring that satisfy the Extension Property. Having solved this question in previous papers for all direct products of finite chain rings and for matrix rings, we have now arrived at a characterization of these weights for finite principal ideal rings, which form a large subclass of the finite Frobenius rings. We do not assume commutativity of the rings in question.Comment: 12 page

Profoundly reduced neovascularization capacity of bone marrow mononuclear cells derived from patients with chronic ischemic heart disease

Background— Cell therapy with bone marrow–derived stem/progenitor cells is a novel option for improving neovascularization and cardiac function in ischemic heart disease. Circulating endothelial progenitor cells in patients with coronary heart disease are impaired with respect to number and functional activity. However, whether this impairment also extends to bone marrow–derived mononuclear cells (BM-MNCs) in patients with chronic ischemic cardiomyopathy (ICMP) is unclea

A new quantum fluid at high magnetic fields in the marginal charge-density-wave system α\alpha-(BEDT-TTF)2M_2MHg(SCN)4_4 (where M=M=~K and Rb)

Single crystals of the organic charge-transfer salts $\alpha$-(BEDT-TTF)$_2M$Hg(SCN)$_4$ have been studied using Hall-potential measurements ($M=$K) and magnetization experiments ($M$ = K, Rb). The data show that two types of screening currents occur within the high-field, low-temperature CDW$_x$ phases of these salts in response to time-dependent magnetic fields. The first, which gives rise to the induced Hall potential, is a free current (${\bf j}_{\rm free}$), present at the surface of the sample. The time constant for the decay of these currents is much longer than that expected from the sample resistivity. The second component of the current appears to be magnetic (${\bf j}_{\rm mag}$), in that it is a microscopic, quasi-orbital effect; it is evenly distributed within the bulk of the sample upon saturation. To explain these data, we propose a simple model invoking a new type of quantum fluid comprising a CDW coexisting with a two-dimensional Fermi-surface pocket which describes the two types of current. The model and data are able to account for the body of previous experimental data which had generated apparently contradictory interpretations in terms of the quantum Hall effect or superconductivity.Comment: 13 pages, 11 figure

Quantization of the Hall conductivity well beyond the adiabatic limit in pulsed magnetic fields

We measure the Hall conductivity, $\sigma_{xy}$, 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 $\sigma_{xy}$ 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 $\sigma_{xy}$ quantization.Comment: 4 pages, 4 figures, submitted to PR

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

Recent high-magnetic-field studies of unusual groundstates in quasi-two-dimensional crystalline organic metals and superconductors

After a brief introduction to crystalline organic superconductors and metals, we shall describe two recently-observed exotic phases that occur only in high magnetic fields. The first involves measurements of the non-linear electrical resistance of single crystals of the charge-density-wave (CDW) system (Per)$_2$Au(mnt)$_2$ in static magnetic fields of up to 45 T and temperatures as low as 25 mK. The presence of a fully gapped CDW state with typical CDW electrodynamics at fields higher that the Pauli paramagnetic limit of 34 T suggests the existence of a modulated CDW phase analogous to the Fulde-Ferrell-Larkin-Ovchinnikov state. Secondly, measurements of the Hall potential of single crystals of $\alpha$-(BEDT-TTF)$_2$KHg(SCN)$_4$, made using a variant of the Corbino geometry in quasistatic magnetic fields, show persistent current effects that are similar to those observed in conventional superconductors. The longevity of the currents, large Hall angle, flux quantization and confinement of the reactive component of the Hall potential to the edge of the sample are all consistent with the realization of a new state of matter in CDW systems with significant orbital quantization effects in strong magnetic fields.Comment: SNS 2004 Conference presentatio

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

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 $t_z$, 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 $4 t_z \sim 8 ta b H /\phi_0$, where a and b are lattice constants, $\phi_0$ 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 $\beta-\alpha$ oscillation as well as the fundamental oscillations are suppressed by the interlayer hopping $t_z$, while the $\beta+\alpha$ oscillation gradually increases as $t_z$ increases and it has a maximum at $t_z/t\approx 0.025$. This interesting dependence on the dimensionality can be observed in the quasi-two-dimensional organic conductors with uniaxial pressure.Comment: 11 pages, 14 figure