2,000 research outputs found
Hopping models and ac universality
Some general relations for hopping models are established. We proceed to
discuss the universality of the ac conductivity which arises in the extreme
disorder limit of the random barrier model. It is shown that the relevant
dimension entering into the diffusion cluster approximation (DCA) is the
harmonic (fracton) dimension of the diffusion cluster. The temperature scaling
of the dimensionless frequency entering into the DCA is discussed. Finally,
some open questions about ac universality are mentioned.Comment: 6 page
History-dependent relaxation and the energy scale of correlation in the Electron-Glass
We present an experimental study of the energy-relaxation in
Anderson-insulating indium-oxide films excited far from equilibrium. In
particular, we focus on the effects of history on the relaxation of the excess
conductance dG. The natural relaxation law of dG is logarithmic, namely
dG=-log(t). This may be observed over more than five decades following, for
example, cool-quenching the sample from high temperatures. On the other hand,
when the system is excited from a state S_{o} in which it has not fully reached
equilibrium to a state S_{n}, the ensuing relaxation law is logarithmic only
over time t shorter than the time t_{w} it spent in S_{o}. For times t>t_{w}
dG(t) show systematic deviation from the logarithmic dependence. It was
previously shown that when the energy imparted to the system in the excitation
process is small, this leads to dG=P(t/t_{w}) (simple-aging). Here we test the
conjecture that `simple-aging' is related to a symmetry in the relaxation
dynamics in S_{o} and S_{n}. This is done by using a new experimental procedure
that is more sensitive to deviations in the relaxation dynamics. It is shown
that simple-aging may still be obeyed (albeit with a modified P(t/t_{w})) even
when the symmetry of relaxation in S_{o} and S_{n} is perturbed by a certain
degree. The implications of these findings to the question of aging, and the
energy scale associated with correlations are discussed
Persistent X-Ray Photoconductivity and Percolation of Metallic Clusters in Charge-Ordered Manganites
Charge-ordered manganites of composition exhibit persistent photoconductivity upon
exposure to x-rays. This is not always accompanied by a significant increase in
the {\it number} of conduction electrons as predicted by conventional models of
persistent photoconductivity. An analysis of the x-ray diffraction patterns and
current-voltage characteristics shows that x-ray illumination results in a
microscopically phase separated state in which charge-ordered insulating
regions provide barriers against charge transport between metallic clusters.
The dominant effect of x-ray illumination is to enhance the electron {\it
mobility} by lowering or removing these barriers. A mechanism based on magnetic
degrees of freedom is proposed.Comment: 8 pages, 4 figure
Dielectric susceptibility of the Coulomb-glass
We derive a microscopic expression for the dielectric susceptibility
of a Coulomb glass, which corresponds to the definition used in classical
electrodynamics, the derivative of the polarization with respect to the
electric field. The fluctuation-dissipation theorem tells us that is a
function of the thermal fluctuations of the dipole moment of the system. We
calculate numerically for three-dimensional Coulomb glasses as a
function of temperature and frequency
On dispersive energy transport and relaxation in the hopping regime
A new method for investigating relaxation phenomena for charge carriers
hopping between localized tail states has been developed. It allows us to
consider both charge and energy {\it dispersive} transport. The method is based
on the idea of quasi-elasticity: the typical energy loss during a hop is much
less than all other characteristic energies. We have investigated two models
with different density of states energy dependencies with our method. In
general, we have found that the motion of a packet in energy space is affected
by two competing tendencies. First, there is a packet broadening, i.e. the
dispersive energy transport. Second, there is a narrowing of the packet, if the
density of states is depleting with decreasing energy. It is the interplay of
these two tendencies that determines the overall evolution. If the density of
states is constant, only broadening exists. In this case a packet in energy
space evolves into Gaussian one, moving with constant drift velocity and mean
square deviation increasing linearly in time. If the density of states depletes
exponentially with decreasing energy, the motion of the packet tremendously
slows down with time. For large times the mean square deviation of the packet
becomes constant, so that the motion of the packet is ``soliton-like''.Comment: 26 pages, RevTeX, 10 EPS figures, submitted to Phys. Rev.
Glassy behavior of electrons near metal-insulator transitions
The emergence of glassy behavior of electrons is investigated for systems
close to the disorder and/or interaction-driven metal-insulator transitions.
Our results indicate that Anderson localization effects strongly stabilize such
glassy behavior, while Mott localization tends to suppress it. We predict the
emergence of an intermediate metallic glassy phase separating the insulator
from the normal metal. This effect is expected to be most pronounced for
sufficiently disordered systems, in agreement with recent experimental
observations.Comment: Final version as published in Physical Review Letter
Universal Crossover between Efros-Shklovskii and Mott Variable-Range-Hopping Regimes
A universal scaling function, describing the crossover between the Mott and
the Efros-Shklovskii hopping regimes, is derived, using the percolation picture
of transport in strongly localized systems. This function is agrees very well
with experimental data. Quantitative comparison with experiment allows for the
possible determination of the role played by polarons in the transport.Comment: 7 pages + 1 figure, Revte
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
Geometrical Models of the Phase Space Structures Governing Reaction Dynamics
Hamiltonian dynamical systems possessing equilibria of 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 , and two schematic models which capture many of
the essential features of the dynamics for -DoF systems. In addition, we
elucidate the structure of the NHIM.Comment: 44 pages, 38 figures, PDFLaTe
Stochastic Transition States: Reaction Geometry amidst Noise
Classical transition state theory (TST) is the cornerstone of reaction rate
theory. It postulates a partition of phase space into reactant and product
regions, which are separated by a dividing surface that reactive trajectories
must cross. In order not to overestimate the reaction rate, the dynamics must
be free of recrossings of the dividing surface. This no-recrossing rule is
difficult (and sometimes impossible) to enforce, however, when a chemical
reaction takes place in a fluctuating environment such as a liquid.
High-accuracy approximations to the rate are well known when the solvent forces
are treated using stochastic representations, though again, exact no-recrossing
surfaces have not been available. To generalize the exact limit of TST to
reactive systems driven by noise, we introduce a time-dependent dividing
surface that is stochastically moving in phase space such that it is crossed
once and only once by each transition path
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