Dielectric susceptibility of the Coulomb-glass

We derive a microscopic expression for the dielectric susceptibility $\chi$ 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 $\chi$ is a function of the thermal fluctuations of the dipole moment of the system. We calculate $\chi$ numerically for three-dimensional Coulomb glasses as a function of temperature and frequency

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

Off-equilibrium dynamics of the two-dimensional Coulomb glass

The dynamics of the 2D Coulomb glass model is investigated by kinetic Monte Carlo simulation. An exponential divergence of the relaxation time signals a zero-temperature freezing transition. At low temperatures the dynamics of the system is glassy. The local charge correlations and the response to perturbations of the local potential show aging. The dynamics of formation of the Coulomb gap is slow and the density of states at the Fermi level decays in time as a power law. The relevance of these findings for recent transport experiments in Anderson-insulating films is pointed out.Comment: 7 pages, 7 figure

Coherent State Path Integrals in the Weyl Representation

We construct a representation of the coherent state path integral using the Weyl symbol of the Hamiltonian operator. This representation is very different from the usual path integral forms suggested by Klauder and Skagerstan in \cite{Klau85}, which involve the normal or the antinormal ordering of the Hamiltonian. These different representations, although equivalent quantum mechanically, lead to different semiclassical limits. We show that the semiclassical limit of the coherent state propagator in Weyl representation is involves classical trajectories that are independent on the coherent states width. This propagator is also free from the phase corrections found in \cite{Bar01} for the two Klauder forms and provides an explicit connection between the Wigner and the Husimi representations of the evolution operator.Comment: 23 page

Electronic correlation effects and the Coulomb gap at finite temperature

We have investigated the effect of the long-range Coulomb interaction on the one-particle excitation spectrum of n-type Germanium, using tunneling spectroscopy on mechanically controllable break junctions. The tunnel conductance was measured as a function of energy and temperature. At low temperatures, the spectra reveal a minimum at zero bias voltage due to the Coulomb gap. In the temperature range above 1 K the Coulomb gap is filled by thermal excitations. This behavior is reflected in the temperature dependence of the variable-range hopping resitivity measured on the same samples: Up to a few degrees Kelvin the Efros-Shkovskii ln$R \propto T^{-1/2}$ law is obeyed, whereas at higher temperatures deviations from this law are observed, indicating a cross-over to Mott's ln$R \propto T^{-1/4}$ law. The mechanism of this cross-over is different from that considered previously in the literature.Comment: 3 pages, 3 figure

An Exact Formula for the Average Run Length to False Alarm of the Generalized Shiryaev-Roberts Procedure for Change-Point Detection under Exponential Observations

We derive analytically an exact closed-form formula for the standard minimax Average Run Length (ARL) to false alarm delivered by the Generalized Shiryaev-Roberts (GSR) change-point detection procedure devised to detect a shift in the baseline mean of a sequence of independent exponentially distributed observations. Specifically, the formula is found through direct solution of the respective integral (renewal) equation, and is a general result in that the GSR procedure's headstart is not restricted to a bounded range, nor is there a "ceiling" value for the detection threshold. Apart from the theoretical significance (in change-point detection, exact closed-form performance formulae are typically either difficult or impossible to get, especially for the GSR procedure), the obtained formula is also useful to a practitioner: in cases of practical interest, the formula is a function linear in both the detection threshold and the headstart, and, therefore, the ARL to false alarm of the GSR procedure can be easily computed.Comment: 9 pages; Accepted for publication in Proceedings of the 12-th German-Polish Workshop on Stochastic Models, Statistics and Their Application

Semiclassical Propagation of Wavepackets with Real and Complex Trajectories

We consider a semiclassical approximation for the time evolution of an originally gaussian wave packet in terms of complex trajectories. We also derive additional approximations replacing the complex trajectories by real ones. These yield three different semiclassical formulae involving different real trajectories. One of these formulae is Heller's thawed gaussian approximation. The other approximations are non-gaussian and may involve several trajectories determined by mixed initial-final conditions. These different formulae are tested for the cases of scattering by a hard wall, scattering by an attractive gaussian potential, and bound motion in a quartic oscillator. The formula with complex trajectories gives good results in all cases. The non-gaussian approximations with real trajectories work well in some cases, whereas the thawed gaussian works only in very simple situations.Comment: revised text, 24 pages, 6 figure

Non-Markovian Configurational Diffusion and Reaction Coordinates for Protein Folding

The non-Markovian nature of polymer motions is accounted for in folding kinetics, using frequency-dependent friction. Folding, like many other problems in the physics of disordered systems, involves barrier crossing on a correlated energy landscape. A variational transition state theory (VTST) that reduces to the usual Bryngelson-Wolynes Kramers approach when the non-Markovian aspects are neglected is used to obtain the rate, without making any assumptions regarding the size of the barrier, or the memory time of the friction. The transformation to collective variables dependent on the dynamics of the system allows the theory to address the controversial issue of what are ``good'' reaction coordinates for folding.Comment: 9 pages RevTeX, 3 eps-figures included, submitted to PR

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

Hopping Conduction in Uniaxially Stressed Si:B near the Insulator-Metal Transition

Using uniaxial stress to tune the critical density near that of the sample, we have studied in detail the low-temperature conductivity of p-type Si:B in the insulating phase very near the metal-insulator transition. For all values of temperature and stress, the conductivity collapses onto a single universal scaling curve. For large values of the argument, the scaling function is well fit by the exponentially activated form associated with variable range hopping when electron-electron interactions cause a soft Coulomb gap in the density of states at the Fermi energy. The temperature dependence of the prefactor, corresponding to the T-dependence of the critical curve, has been determined reliably for this system, and is proportional to the square-root of T. We show explicitly that nevlecting the prefactor leads to substantial errors in the determination of the scaling parameters and the critical exponents derived from them. The conductivity is not consistent with Mott variable-range hopping in the critical region nor does it obey this form for any range of the parameters. Instead, for smaller argument of the scaling function, the conductivity of Si:B is well fit by an exponential form with exponent 0.31 related to the critical exponents of the system at the metal- insulator transition.Comment: 13 pages, 6 figure