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

Cold and Ultracold Molecules: Science, Technology, and Applications

This article presents a review of the current state of the art in the research field of cold and ultracold molecules. It serves as an introduction to the Special Issue of the New Journal of Physics on Cold and Ultracold Molecules and describes new prospects for fundamental research and technological development. Cold and ultracold molecules may revolutionize physical chemistry and few body physics, provide techniques for probing new states of quantum matter, allow for precision measurements of both fundamental and applied interest, and enable quantum simulations of condensed-matter phenomena. Ultracold molecules offer promising applications such as new platforms for quantum computing, precise control of molecular dynamics, nanolithography, and Bose-enhanced chemistry. The discussion is based on recent experimental and theoretical work and concludes with a summary of anticipated future directions and open questions in this rapidly expanding research field.Comment: 82 pages, 9 figures, review article to appear in New Journal of Physics Special Issue on Cold and Ultracold Molecule