Commutative deformations of general relativity: nonlocality, causality, and dark matter

Hopf algebra methods are applied to study Drinfeld twists of (3+1)-diffeomorphisms and deformed general relativity on \emph{commutative} manifolds. A classical nonlocality length scale is produced above which microcausality emerges. Matter fields are utilized to generate self-consistent Abelian Drinfeld twists in a background independent manner and their continuous and discrete symmetries are examined. There is negligible experimental effect on the standard model of particles. While baryonic twist producing matter would begin to behave acausally for rest masses above $\sim1-10$ TeV, other possibilities are viable dark matter candidates or a right handed neutrino. First order deformed Maxwell equations are derived and yield immeasurably small cosmological dispersion and produce a propagation horizon only for photons at or above Planck energies. This model incorporates dark matter without any appeal to extra dimensions, supersymmetry, strings, grand unified theories, mirror worlds, or modifications of Newtonian dynamics.Comment: 47 pages including references, 0 figures, 0 tables Various typos/omissions correcte

Scattering Matrix Theory For Nonlinear Transport

We report a scattering matrix theory for dynamic and nonlinear transport in coherent mesoscopic conductors. In general this theory allows predictions of low frequency linear dynamic conductance, as well as weakly nonlinear DC conductance. It satisfies the conditions of gauge invariance and electric current conservation, and can be put into a form suitable for numerical computation. Using this theory we examine the third order weakly nonlinear DC conductance of a tunneling diode

Phase-sensitive quantum effects in Andreev conductance of the SNS system of metals with macroscopic phase breaking length

The dissipative component of electron transport through the doubly connected SNS Andreev interferometer indium (S)-aluminium (N)-indium (S) has been studied. Within helium temperature range, the conductance of the individual sections of the interferometer exhibits phase-sensitive oscillations of quantum-interference nature. In the non-domain (normal) state of indium narrowing adjacent to NS interface, the nonresonance oscillations have been observed, with the period inversely proportional to the area of the interferometer orifice. In the domain intermediate state of the narrowing, the magneto-temperature resistive oscillations appeared, with the period determined by the coherence length in the magnetic field equal to the critical one. The oscillating component of resonance form has been observed in the conductance of the macroscopic N-aluminium part of the system. The phase of the oscillations appears to be shifted by $\pi$ compared to that of nonresonance oscillations. We offer an explanation in terms of the contribution into Josephson current from the coherent quasiparticles with energies of order of the Thouless energy. The behavior of dissipative transport with temperature has been studied in a clean normal metal in the vicinity of a single point NS contact.Comment: 9 pages, 7 figures, to be published in Low Temp. Phys., v. 29, No. 12, 200

Phase Dependent Thermopower in Andreev Interferometers

We report measurements of the thermopower S of mesoscopic Andreev interferometers, which are hybrid loops with one arm fabricated from a superconductor (Al), and one arm from a normal metal (Au). S depends on the phase of electrons in the interferometer, oscillating as a function of magnetic flux with a period of one flux quantum (= h/2e). The magnitude of S increases as the temperature T is lowered, reaching a maximum around T = 0.14 K, and decreases at lower temperatures. The symmetry of S oscillations with respect to magnetic flux depends on the topology of the sample.Comment: 4 pages, 4 figure

Diffusive conductors as Andreev interferometers

We present a novel mechanism of phase-dependent electric transport in diffusive normal metal-superconductor structures. We provide a detailed theoretical and numerical analysis of recent unexplained experiments essentially explaining them.Comment: Self extracting file, 7 pages latex and 4 postscript figures. The paper is also available at http://www.tn.tudelft.nl/tn/thspap.html In this revision we resolved some printing problems concerning figures 2 and

Phase-dependent magnetoconductance fluctuations in a chaotic Josephson junction

Motivated by recent experiments by Den Hartog et al., we present a random-matrix theory for the magnetoconductance fluctuations of a chaotic quantum dot which is coupled by point contacts to two superconductors and one or two normal metals. There are aperiodic conductance fluctuations as a function of the magnetic field through the quantum dot and $2\pi$-periodic fluctuations as a function of the phase difference $\phi$ of the superconductors. If the coupling to the superconductors is weak compared to the coupling to the normal metals, the $\phi$-dependence of the conductance is harmonic, as observed in the experiment. In the opposite regime, the conductance becomes a random $2\pi$-periodic function of $\phi$, in agreement with the theory of Altshuler and Spivak. The theoretical method employs an extension of the circular ensemble which can describe the magnetic field dependence of the scattering matrix.Comment: 4 pages, RevTeX, 3 figure

Density of States in Superconductor - Normal Metal - Superconductor Junctions

We consider the chi_0 dependence of the density of states inside the normal metal of a superconductor - normal metal - superconductor (SNS) junction.Here chi_0 is the phase difference of two superconductors of the junction. It is shown that in the absence of electron-electron interaction the energy dependence of the density of states has a gap which decreases as chi_0 increases and closes at chi_0= pi. Both the analytical expressions for the chi_0 dependence of the density of states and the results of numerical simulations are presented.Comment: 7 pages with 4 included epsf figures, published version with small change

Weakly Nonlinear AC Response: Theory and Application

We report a microscopic and general theoretical formalism for electrical response which is appropriate for both DC and AC weakly nonlinear quantum transport. The formalism emphasizes the electron-electron interaction and maintains current conservation and gauge invariance. It makes a formal connection between linear response and scattering matrix theory at the weakly nonlinear level. We derive the dynamic conductance and predict the nonlinear-nonequilibrium charge distribution. The definition of a nonlinear capacitance leads to a remarkable scaling relation which can be measured to give microscopic information about a conductor

Current partition: Nonequilibrium Green's function Approach

We present a solution to the problem of AC current partition in a multi-probe mesoscopic conductor within the nonequilibrium Green's function formalism. This allows the derivation of dynamic conductance which is appropriate for nonequilibrium situations and which satisfies the current conservation and gauge invariance requirements. This formalism presents a significant generalization to previous theory: (i) there is no limit in the frequency, and (ii) it allows detailed treatments of interactions in the mesoscopic region. The formalism is applied to calculate dynamic conductance of tunneling structures with and without assuming wideband limit.Comment: 4 pages, 3 figure