Fluctuation effects in disordered Peierls systems

We review the density of states and related quantities of quasi one-dimensional disordered Peierls systems in which fluctuation effects of a backscattering potential play a crucial role. The low-energy behavior of non-interacting fermions which are subject to a static random backscattering potential will be described by the fluctuating gap model (FGM). Recently, the FGM has also been used to explain the pseudogap phenomenon in high-$T_c$ superconductors. After an elementary introduction to the FGM in the context of commensurate and incommensurate Peierls chains, we develop a non-perturbative method which allows for a simultaneous calculation of the density of states (DOS) and the inverse localization length. First, we recover all known results in the limits of zero and infinite correlation lengths of the random potential. Then, we attack the problem of finite correlation lengths. While a complex order parameter, which describes incommensurate Peierls chains, leads to a suppression of the DOS, i.e. a pseudogap, the DOS exhibits a singularity at the Fermi energy if the order parameter is real and therefore refers to a commensurate system. We confirm these results by calculating the DOS and the inverse localization length for finite correlation lengths and Gaussian statistics of the backscattering potential with unprecedented accuracy numerically. Finally, we consider the case of classical phase fluctuations which apply to low temperatures where amplitude fluctuations are frozen out. In this physically important regime, which is also characterized by finite correlation lengths, we present analytic results for the DOS, the inverse localization length, the specific heat, and the Pauli susceptibility.Comment: 60 pages, 16 figure

Systems and methods for supplemental weather information presentation on a display

An embodiment of the supplemental weather display system presents supplemental weather information on a display in a craft. An exemplary embodiment receives the supplemental weather information from a remote source, determines a location of the supplemental weather information relative to the craft, receives weather information from an on-board radar system, and integrates the supplemental weather information with the weather information received from the on-board radar system

Cosmological backreaction of a quantized massless scalar field

We consider the backreaction problem of a quantized minimally coupled massless scalar field in cosmology. The adiabatically regularized stress-energy tensor in a general Friedmann-Robertson-Walker background is approximately evaluated by using the fact that subhorizon modes evolve adiabatically and superhorizon modes are frozen. The vacuum energy density is verified to obey a new first order differential equation depending on a dimensionless parameter of order unity, which calibrates subhorizon/superhorizon division. We check the validity of the approximation by calculating the corresponding vacuum energy densities in fixed backgrounds, which are shown to agree with the known results in de Sitter space and space-times undergoing power law expansions. We then apply our findings to slow-roll inflationary models. Although backreaction effects are found to be negligible during the near exponential expansion, the vacuum energy density generated during this period might be important at later stages since it decreases slower than radiation or dust.Comment: 20 pages, 2 figures, v2: comments and a reference added, to appear in JCA

Finite-temperature scalar fields and the cosmological constant in an Einstein universe

We study the back reaction effect of massless minimally coupled scalar field at finite temperatures in the background of Einstein universe. Substituting for the vacuum expectation value of the components of the energy-momentum tensor on the RHS of the Einstein equation, we deduce a relationship between the radius of the universe and its temperature. This relationship exhibit a maximum temperature, below the Planck scale, at which the system changes its behaviour drastically. The results are compared with the case of a conformally coupled field. An investigation into the values of the cosmological constant exhibit a remarkable difference between the conformally coupled case and the minimally coupled one.Comment: 7 pages, 2 figure