The Electron Glass in a Switchable Mirror: Relaxation, Aging and Universality

The rare earth hydride YH$_{3-\delta}$ can be tuned through the metal-insulator transition both by changing $\delta$ and by illumination with ultraviolet light. The transition is dominated by strong electron-electron interactions, with transport in the insulator sensitive to both a Coulomb gap and persistent quantum fluctuations. Via a systematic variation of UV illumination time, photon flux, Coulomb gap depth, and temperature, we demonstrate that polycrystalline YH$_{3-\delta}$ serves as a model system for studying the properties of the interacting electron glass. Prominent among its features are logarithmic relaxation, aging, and universal scaling of the conductivity

Geometrical Models of the Phase Space Structures Governing Reaction Dynamics

Hamiltonian dynamical systems possessing equilibria of ${saddle} \times {centre} \times...\times {centre}$ stability type display \emph{reaction-type dynamics} for energies close to the energy of such equilibria; entrance and exit from certain regions of the phase space is only possible via narrow \emph{bottlenecks} created by the influence of the equilibrium points. In this paper we provide a thorough pedagogical description of the phase space structures that are responsible for controlling transport in these problems. Of central importance is the existence of a \emph{Normally Hyperbolic Invariant Manifold (NHIM)}, whose \emph{stable and unstable manifolds} have sufficient dimensionality to act as separatrices, partitioning energy surfaces into regions of qualitatively distinct behavior. This NHIM forms the natural (dynamical) equator of a (spherical) \emph{dividing surface} which locally divides an energy surface into two components (`reactants' and `products'), one on either side of the bottleneck. This dividing surface has all the desired properties sought for in \emph{transition state theory} where reaction rates are computed from the flux through a dividing surface. In fact, the dividing surface that we construct is crossed exactly once by reactive trajectories, and not crossed by nonreactive trajectories, and related to these properties, minimizes the flux upon variation of the dividing surface. We discuss three presentations of the energy surface and the phase space structures contained in it for 2-degree-of-freedom (DoF) systems in the threedimensional space $\R^3$, and two schematic models which capture many of the essential features of the dynamics for $n$-DoF systems. In addition, we elucidate the structure of the NHIM.Comment: 44 pages, 38 figures, PDFLaTe

Monte-Carlo Simulations of the Dynamical Behavior of the Coulomb Glass

We study the dynamical behavior of disordered many-particle systems with long-range Coulomb interactions by means of damage-spreading simulations. In this type of Monte-Carlo simulations one investigates the time evolution of the damage, i.e. the difference of the occupation numbers of two systems, subjected to the same thermal noise. We analyze the dependence of the damage on temperature and disorder strength. For zero disorder the spreading transition coincides with the equilibrium phase transition, whereas for finite disorder, we find evidence for a dynamical phase transition well below the transition temperature of the pure system.Comment: 10 pages RevTeX, 8 Postscript figure

Semiclassical time evolution of the density matrix and tunneling

The time dependent density matrix of a system with potential barrier is studied using path integrals. The characterization of the initial state, which is assumed to be restricted to one side of the barrier, and the time evolution of the density matrix lead to a three-fold path integral which is evaluated in the semiclassical limit. The semiclassical trajectories are found to move in the complex coordinate plane and barrier penetration only arises due to fluctuations. Both the form of the semiclassical paths and the relevant fluctuations change significantly as a function of temperature. The semiclassical analysis leads to a detailed picture of barrier penetration in the real time domain and the changeover from thermal activation to quantum tunneling. Deep tunneling is associated with quasi-zero modes in the fluctuation spectrum about the semiclassical orbits in the long time limit. The connection between this real time description of tunneling and the standard imaginary time instanton approach is established. Specific results are given for a double well potential and an Eckart barrier.Comment: 27 pages, 8 figures, to be published in Phys. Rev.

Explicit Solution of the Time Evolution of the Wigner Function

Previously, an explicit solution for the time evolution of the Wigner function was presented in terms of auxiliary phase space coordinates which obey simple equations that are analogous with, but not identical to, the classical equations of motion. They can be solved easily and their solutions can be utilized to construct the time evolution of the Wigner function. In this paper, the usefulness of this explicit solution is demonstrated by solving a numerical example in which the Wigner function has strong spatial and temporal variations as well as regions with negative values. It is found that the explicit solution gives a correct description of the time evolution of the Wigner function. We examine next the pseudoparticle approximation which uses classical trajectories to evolve the Wigner function. We find that the pseudoparticle approximation reproduces the general features of the time evolution, but there are deviations. We show how these deviations can be systematically reduced by including higher-order correction terms in powers of $\hbar^2$.Comment: 16 pages, in LaTex, invited talk presented at the Wigner Centennial Conference, Pecs, Hungary, July 8-12, 2002, to be published in the Journal of Optics B: Quantum and Classical Optics, June 200

Temperature dependence of the electron spin g factor in GaAs

The temperature dependence of the electron spin $g$ factor in GaAs is investigated experimentally and theoretically. Experimentally, the $g$ factor was measured using time-resolved Faraday rotation due to Larmor precession of electron spins in the temperature range between 4.5 K and 190 K. The experiment shows an almost linear increase of the $g$ value with the temperature. This result is in good agreement with other measurements based on photoluminescence quantum beats and time-resolved Kerr rotation up to room temperature. The experimental data are described theoretically taking into account a diminishing fundamental energy gap in GaAs due to lattice thermal dilatation and nonparabolicity of the conduction band calculated using a five-level kp model. At higher temperatures electrons populate higher Landau levels and the average $g$ factor is obtained from a summation over many levels. A very good description of the experimental data is obtained indicating that the observed increase of the spin $g$ factor with the temperature is predominantly due to band's nonparabolicity.Comment: 6 pages 4 figure

Delocalizing effect of the Hubbard repulsion for electrons on a two-dimensional disordered lattice

We study numerically the ground-state properties of the repulsive Hubbard model for spin-1/2 electrons on two-dimensional lattices with disordered on-site energies. The projector quantum Monte Carlo method is used to obtain very accurate values of the ground-state charge density distributions with $N_p$ and $N_p+1$ particles. The difference in these charge densities allows us to study the localization properties of an added particle. The results obtained at quarter-filling on finite clusters show that the Hubbard repulsion has a strong delocalizing effect on the electrons in disordered 2D lattices. However, numerical restrictions do not allow us to reach a definite conclusion about the existence of a metal-insulator transition in the thermodynamic limit in two-dimensions.Comment: revtex, 7 pages, 7 figure

Interacting electrons in a one-dimensional random array of scatterers - A Quantum Dynamics and Monte-Carlo study

The quantum dynamics of an ensemble of interacting electrons in an array of random scatterers is treated using a new numerical approach for the calculation of average values of quantum operators and time correlation functions in the Wigner representation. The Fourier transform of the product of matrix elements of the dynamic propagators obeys an integral Wigner-Liouville-type equation. Initial conditions for this equation are given by the Fourier transform of the Wiener path integral representation of the matrix elements of the propagators at the chosen initial times. This approach combines both molecular dynamics and Monte Carlo methods and computes numerical traces and spectra of the relevant dynamical quantities such as momentum-momentum correlation functions and spatial dispersions. Considering as an application a system with fixed scatterers, the results clearly demonstrate that the many-particle interaction between the electrons leads to an enhancement of the conductivity and spatial dispersion compared to the noninteracting case.Comment: 10 pages and 8 figures, to appear in PRB April 1