The basis of nonlocal curvature invariants in quantum gravity theory

A complete basis of nonlocal invariants in quantum gravity theory is built to third order in spacetime curvature and matter-field strengths. The nonlocal identities are obtained which reduce this basis for manifolds with dimensionality $2\omega<6$. The present results are used in heat-kernel theory, theory of gauge fields and serve as a basis for the model-independent approach to quantum gravity and, in particular, for the study of nonlocal vacuum effects in the gravitational collapse problem.Comment: 28 pages, REVTeX, Alberta Thy 14-9

Crossover between distinct mechanisms of microwave photoresistance in bilayer systems

We report on temperature-dependent magnetoresistance measurements in balanced double quantum wells exposed to microwave irradiation for various frequencies. We have found that the resistance oscillations are described by the microwave-induced modification of electron distribution function limited by inelastic scattering (inelastic mechanism), up to a temperature of T*~4 K. With increasing temperature, a strong deviation of the oscillation amplitudes from the behavior predicted by this mechanism is observed, presumably indicating a crossover to another mechanism of microwave photoresistance, with similar frequency dependence. Our analysis shows that this deviation cannot be fully understood in terms of contribution from the mechanisms discussed in theory.Comment: 7 pages, 4 figure

Classification of limit varieties of J\mathscr J-trivial monoids

A variety of algebras is called limit if it is non-finitely based but all its proper subvarieties are finitely based. We present a new pair of limit varieties of monoids and show that together with the five limit varieties of monoids previously discovered by Jackson, Zhang and Luo and the first-named author, there are exactly seven limit varieties of $\mathscr J$-trivial monoids.Comment: 26 page

Nonlinear transport and oscillating magnetoresistance in double quantum wells

We study the evolution of low-temperature magnetoresistance in double quantum wells in the region below 1 Tesla as the applied current density increases. A flip of the magneto-intersubband oscillation peaks, which occurs as a result of the current-induced inversion of the quantum component of resistivity, is observed. We also see splitting of these peaks as another manifestation of nonlinear behavior, specific for the two-subband electron systems. The experimental results are quantitatively explained by the theory based on the kinetic equation for the isotropic non-equilibrium part of electron distribution function. The inelastic scattering time is determined from the dependence of the inversion magnetic field on the current.Comment: 20 pages, 10 figure