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

Magnetic field induced transition in a wide parabolic well superimposed with superlattice

We study a $Al_{x}Ga_{x-1}As$ parabolic quantum wells (PQW) with $GaAs/Al_{x}Ga_{x-1}As$ square superlattice. The magnetotransport in PQW with intentionally disordered short-period superlattice reveals a surprising transition from electrons distribution over whole parabolic well to independent-layer states with unequal density. The transition occurs in the perpendicular magnetic field at Landau filling factor $\nu\approx3$ and is signaled by the appearance of the strong and developing fractional quantum Hall (FQH) states and by the enhanced slope of the Hall resistance. We attribute the transition to the possible electron localization in the x-y plane inside the lateral wells, and formation of the FQH states in the central well of the superlattice, driven by electron-electron interaction.Comment: 5 pages, 4 figure

Muon-spin-rotation study of the magnetic structure in the tetragonal antiferromagnetic state of weakly underdoped Ba1−x _{1-x} Kx _{x} Fe2 _{2} As2 _{2}

With muon spin rotation ($\mu$SR) we studied the transition between the orthorhombic antiferromagnetic (o-AF) and the tetragonal antiferromagnetic (t-AF) states of a weakly underdoped Ba$_{1-x}$K$_{x}$Fe$_{2}$As$_{2}$ single crystal. We observed some characteristic changes of the magnitude and the orientation of the magnetic field at the muon site which, due to the fairly high point symmetry of the latter, allow us to identify the magnetic structure of the t-AF state. It is the so-called, inhomogeneous double-$\mathbf{Q}$ magnetic structure with $c$-axis oriented moments which has a vanishing magnetic moment on half of the Fe sites.Comment: 5 pages, 4 figures. Supplementary Material: 8 figure

Asymptotic behaviours of the heat kernel in covariant perturbation theory

The trace of the heat kernel is expanded in a basis of nonlocal curvature invariants of $N$th order. The coefficients of this expansion (the nonlocal form factors) are calculated to third order in the curvature inclusive. The early-time and late-time asymptotic behaviours of the trace of the heat kernel are presented with this accuracy. The late-time behaviour gives the criterion of analyticity of the effective action in quantum field theory. The latter point is exemplified by deriving the effective action in two dimensions.Comment: 22 pages, REVTeX, Alberta Thy 45-9