The Faraday effect revisited: General theory

This paper is the first in a series revisiting the Faraday effect, or more generally, the theory of electronic quantum transport/optical response in bulk media in the presence of a constant magnetic field. The independent electron approximation is assumed. At zero temperature and zero frequency, if the Fermi energy lies in a spectral gap, we rigorously prove the Widom-Streda formula. For free electrons, the transverse conductivity can be explicitly computed and coincides with the classical result. In the general case, using magnetic perturbation theory, the conductivity tensor is expanded in powers of the strength of the magnetic field $B$. Then the linear term in $B$ of this expansion is written down in terms of the zero magnetic field Green function and the zero field current operator. In the periodic case, the linear term in $B$ of the conductivity tensor is expressed in terms of zero magnetic field Bloch functions and energies. No derivatives with respect to the quasi-momentum appear and thereby all ambiguities are removed, in contrast to earlier work.Comment: Final version, accepted for publication in J. Math. Phy

DFT study of graphene antidot lattices: The roles of geometry relaxation and spin

Graphene sheets with regular perforations, dubbed as antidot lattices, have theoretically been predicted to have a number of interesting properties. Their recent experimental realization with lattice constants below 100 nanometers stresses the urgency of a thorough understanding of their electronic properties. In this work we perform calculations of the band structure for various hydrogen-passivated hole geometries using both spin-polarized density functional theory (DFT) and DFT based tight-binding (DFTB) and address the importance of relaxation of the structures using either method or a combination thereof. We find from DFT that all structures investigated have band gaps ranging from 0.2 eV to 1.5 eV. Band gap sizes and general trends are well captured by DFTB with band gaps agreeing within about 0.2 eV even for very small structures. A combination of the two methods is found to offer a good trade-off between computational cost and accuracy. Both methods predict non-degenerate midgap states for certain antidot hole symmetries. The inclusion of spin results in a spin-splitting of these states as well as magnetic moments obeying the Lieb theorem. The local spin texture of both magnetic and non-magnetic symmetries is addressed

Stipulation of Facts, \u3cem\u3eTVA v. Hill et al\u3c/em\u3e, Civil Action No. 3-76-48

Stipulation of facts agreed upon by the plaintiffs and defendants in the case of TVA v. Hill et al in the United States District Court for the Eastern District of Tennessee, Northern Division

An analysis of the relationships between subthreshold electrical properties and excitability in skeletal muscle

Skeletal muscle activation requires action potential (AP) initiation followed by its sarcolemmal propagation and tubular excitation to trigger Ca2+ release and contraction. Recent studies demonstrate that ion channels underlying the resting membrane conductance (GM) of fast-twitch mammalian muscle fibers are highly regulated during muscle activity. Thus, onset of activity reduces GM, whereas prolonged activity can markedly elevate GM. Although these observations implicate GM regulation in control of muscle excitability, classical theoretical studies in un-myelinated axons predict little influence of GM on membrane excitability. However, surface membrane morphologies differ markedly between un-myelinated axons and muscle fibers, predominantly because of the tubular (t)-system of muscle fibers. This study develops a linear circuit model of mammalian muscle fiber and uses this to assess the role of subthreshold electrical properties, including GM changes during muscle activity, for AP initiation, AP propagation, and t-system excitation. Experimental observations of frequency-dependent length constant and membrane-phase properties in fast-twitch rat fibers could only be replicated by models that included t-system luminal resistances. Having quantified these resistances, the resulting models showed enhanced conduction velocity of passive current flow also implicating elevated AP propagation velocity. Furthermore, the resistances filter passive currents such that higher frequency current components would determine sarcolemma AP conduction velocity, whereas lower frequency components excite t-system APs. Because GM modulation affects only the low-frequency membrane impedance, the GM changes in active muscle would predominantly affect neuromuscular transmission and low-frequency t-system excitation while exerting little influence on the high-frequency process of sarcolemmal AP propagation. This physiological role of GM regulation was increased by high Cl− permeability, as in muscle endplate regions, and by increased extracellular [K+], as observed in working muscle. Thus, reduced GM at the onset of exercise would enhance t-system excitation and neuromuscular transmission, whereas elevated GM after sustained activity would inhibit these processes and thereby accentuate muscle fatigue

Hydrodynamic guiding for addressing subsets of immobilized cells and molecules in microfluidic systems

BACKGROUND: The interest in microfluidics and surface patterning is increasing as the use of these technologies in diverse biomedical applications is substantiated. Controlled molecular and cellular surface patterning is a costly and time-consuming process. Methods for keeping multiple separate experimental conditions on a patterned area are, therefore, needed to amplify the amount of biological information that can be retrieved from a patterned surface area. We describe, in three examples of biomedical applications, how this can be achieved in an open microfluidic system, by hydrodynamically guiding sample fluid over biological molecules and living cells immobilized on a surface. RESULTS: A microfluidic format of a standard assay for cell-membrane integrity showed a fast and dose-dependent toxicity of saponin on mammalian cells. A model of the interactions of human mononuclear leukocytes and endothelial cells was established. By contrast to static adhesion assays, cell-cell adhesion in this dynamic model depended on cytokine-mediated activation of both endothelial and blood cells. The microfluidic system allowed the use of unprocessed blood as sample material, and a specific and fast immunoassay for measuring the concentration of C-reactive protein in whole blood was demonstrated. CONCLUSION: The use of hydrodynamic guiding made multiple and dynamic experimental conditions on a small surface area possible. The ability to change the direction of flow and produce two-dimensional grids can increase the number of reactions per surface area even further. The described microfluidic system is widely applicable, and can take advantage of surfaces produced by current and future techniques for patterning in the micro- and nanometer scale

Temperature dependence of the ``0.7'' 2(e^2)/h quasi plateau in strongly confined quantum point contacts

We present new results of the ``0.7'' 2(e^2)/h structure or quasi plateau in some of the most strongly confined point contacts so far reported. This strong confinement is obtained by a combination of shallow etching and metal gate deposition on modulation doped GaAs/GaAlAs heterostructures. The resulting subband separations are up to 20 meV, and as a consequence the quantized conductance can be followed at temperatures up to 30 K, an order of magnitude higher than in conventional split gate devices. We observe pronounced quasi plateaus at several of the lowest conductance steps all the way from their formation around 1 K to 30 K, where the entire conductance quantization is smeared out thermally. We study the deviation of the conductance from ideal integer quantization as a function of temperature, and we find an activated behavior, exp(-T_a/T), with a density dependent activation temperature T_a of the order of 2 K. We analyze our results in terms of a simple theoretical model involving scattering against plasmons in the constriction.Comment: RevTex (4 pages) including 2 postscript figures. To appear in Physica B, 199

TVA’s Brief in Reply to Plaintiffs’ Post-Trial Brief, \u3cem\u3eTVA v. Hill et al\u3c/em\u3e, Civil Action No. 3-76-48

Brief for the defendants in response to the plaintiffs\u27 post-trial brief in the case of TVA v. Hill et al in the United States District Court for the Eastern District of Tennessee, Northern Division

Post-Trial Brief of Tennessee Valley Authority, \u3cem\u3eTVA v. Hill et al\u3c/em\u3e, Civil Action No. 3-76-48

Post-trial brief for the defendants in the case of TVA v. Hill et al in the United States District Court for the Eastern District of Tennessee, Northern Division