A theory of hyperfinite sets

We develop an axiomatic set theory -- the Theory of Hyperfinite Sets THS, which is based on the idea of existence of proper subclasses of big finite sets. We demonstrate how theorems of classical continuous mathematics can be transfered to THS, prove consistency of THS and present some applications.Comment: 28 page

Magnetoconductance of carbon nanotube p-n junctions

The magnetoconductance of p-n junctions formed in clean single wall carbon nanotubes is studied in the noninteracting electron approximation and perturbatively in electron-electron interaction, in the geometry where a magnetic field is along the tube axis. For long junctions the low temperature magnetoconductance is anomalously large: the relative change in the conductance becomes of order unity even when the flux through the tube is much smaller than the flux quantum. The magnetoconductance is negative for metallic tubes. For semiconducting and small gap tubes the magnetoconductance is nonmonotonic; positive at small and negative at large fields.Comment: 5 pages, 2 figure

Novel relativistic plasma excitations in a gated two-dimensional electron system

The microwave response of a two-dimensional electron system (2DES) covered by a conducting top gate is investigated in the relativistic regime for which the 2D conductivity $\sigma_{2 \rm{D}} > c/2\pi$. Weakly damped plasma waves are excited in the gated region of the 2DES. The frequency and amplitude of the resulting plasma excitations show a very unusual dependence on the magnetic field, conductivity, gate geometry and separation from the 2DES. We show that such relativistic plasmons survive for temperatures up to 300 K, allowing for new room-temperature microwave and terahertz applications.Comment: 9 pages, 7 figure

Re-entrant localization of single particle transport in disordered Andreev wires

We study effects of disorder on the low energy single particle transport in a normal wire surrounded by a superconductor. We show that the heat conductance includes the Andreev diffusion decreasing with increase in the mean free path $\ell$ and the diffusive drift produced by a small particle-hole asymmetry, which increases with increasing $\ell$. The conductance thus has a minimum as a function of $\ell$ which leads to a peculiar re-entrant localization as a function of the mean free path.Comment: 4 pages, 2 figure

Nonlinear Hysteretic Torsional Waves

We theoretically study and experimentally report the propagation of nonlinear hysteretic torsional pulses in a vertical granular chain made of cm-scale, self-hanged magnetic beads. As predicted by contact mechanics, the torsional coupling between two beads is found nonlinear hysteretic. This results in a nonlinear pulse distortion essentially different from the distortion predicted by classical nonlinearities, and in a complex dynamic response depending on the history of the wave particle angular velocity. Both are consistent with the predictions of purely hysteretic nonlinear elasticity and the Preisach-Mayergoyz hysteresis model, providing the opportunity to study the phenomenon of nonlinear dynamic hysteresis in the absence of other type of material nonlinearities. The proposed configuration reveals a plethora of interesting phenomena including giant amplitude-dependent attenuation, short term memory as well as dispersive properties. Thus, it could find interesting applications in nonlinear wave control devices such as strong amplitude-dependent filters

Tunneling into d-wave superconductors: Effects of interface spin-orbit coupling

Tunneling conductance of a clean normal metal/d-wave superconductor junction is studied by using the extended Blonder-Tinkham-Klapwijk formalism. We show that the conductance is significantly affected by the interface spin-orbit coupling of the Rashba type, which is inevitably present due to the asymmetry of the junction.Comment: 4 pages, 4 figure

Simple theory of extremely overdoped HTS

We demonstrate the existence of a simple physical picture of superconductivity for extremely overdoped CuO2 planes. It possesses all characteristic features of HTS, such as a high superconducting transition temperature, the $d_{x^2 - y^2}$ symmetry of order parameter, and the coexistence of a single electron Fermi surface and a pseudogap in the normal state. Values of pseudogap are calculated for different doping levels. An orbital paramagnetism of preformed pairs is predicted.Comment: 7 pages, 1 figur

Frobenius-Perron Resonances for Maps with a Mixed Phase Space

Resonances of the time evolution (Frobenius-Perron) operator P for phase space densities have recently been shown to play a key role for the interrelations of classical, semiclassical and quantum dynamics. Efficient methods to determine resonances are thus in demand, in particular for Hamiltonian systems displaying a mix of chaotic and regular behavior. We present a powerful method based on truncating P to a finite matrix which not only allows to identify resonances but also the associated phase space structures. It is demonstrated to work well for a prototypical dynamical system.Comment: 5 pages, 2 figures, 2nd version as published (minor changes