Diffusion in a random medium: A renormalization group approach

We investigate through a continuous random diffusion equation the long-distance properties of the general non-symmetric hopping model. The lower and upper critical dimensionalities are d = 1 and d = 2 respectively. A renormalization group analysis shows that the velocity and the diffusion constant obey scaling laws with non-classical exponents, which are computed to first order in ε = 2 ? d. Similar scaling laws, based on heuristic arguments, are conjectured for the AC conductivity.     

A Simplified “Ratchet” Model of Molecular Motors

A limiting case of one of the ratchet models of Ajdari, Prost, et al. is analyzed. An explicit solution is obtained for the probability distribution as a function of the time for any initial distribution with all the transients included. In the long-time limit the drift velocity and diffusion coefficient are obtained in terms of the microscopic transition rates that are the parameters in the model. In spite of its extreme simplicity, with realistic values of its kinetic parameters the model yields values of the drift velocity and effective force that are of the right magnitude for a molecular motor. The model proves to be a simple special case of Derrida's periodic one-dimensional hopping model, for which he found a solution in the long-time limit.     

Front Propagation Dynamics with Exponentially-Distributed Hopping

We study reaction-diffusion systems where diffusion is by jumps whose sizes are distributed exponentially. We first study the Fisher-like problem of propagation of a front into an unstable state, as typified by the A+B → 2A reaction. We find that the effect of fluctuations is especially pronounced at small hopping rates. Fluctuations are treated heuristically via a density cutoff in the reaction rate. We then consider the case of propagating up a reaction rate gradient. The effect of fluctuations here is pronounced, with the front velocity increasing without limit with increasing bulk particle density. The rate of increase is faster than in the case of a reaction-gradient with nearest-neighbor hopping. We derive analytic expressions for the front velocity dependence on bulk particle density. Computer simulations are performed to confirm the analytical results.     

Limit Properties of One Dimensional Periodic Hopping Model

在细致平衡的基础上,通过形式运算得到了平均速度及有效扩散常数在模型的内部状态数量趋向无穷大时的极限显示表达式．这一结果将有助于进一步了解一维跳跃模型的性质.     

A model of hopping and band DC photoconduction in doped crystals

Expressions for the screening length and the ambipolar diffusion length are derived, for the first time, for the case where hopping conduction and band conduction coexist in semiconductors with hydrogen-like impurities. A method is proposed for calculating the diffusion coefficient of electrons (holes) hopping between impurity atoms from data on the Hall effect, in the case where the hopping and band conductivities are equal. An interpretation is given of available experimental data on hopping photoconduction between acceptors (Ga) and donors (As) in p-Ge at T=4.2 K doped by a transmutation method. It is shown that the relative magnitude of the mobilities of electrons hopping between donors and holes hopping between acceptors can be found from the hopping photoconductivity measured as a function of the intensity of band-to-band optical carrier excitation.     

On the theory of surface diffusion: kinetic versus lattice gas approach

The present paper extends the results of a recent analytic kinetic theory of particle-on-substrate diffusion. The approach treats explicitly the molecule–surface interaction and takes into account inter-molecular interaction within the hard particle approximation. The physics influencing the diffusion pre-exponential factor and mechanisms determining the density dependence of collective diffusivity are discussed. The kinetic results are compared with those of the traditional lattice gas hopping models. Analytical expressions for jump rates in the low density limit are derived, and the density dependence of effective jump rates at finite occupancy is discussed. It is shown how the traditional hopping model oversimplifies the picture of diffusion by neglecting the collision part of the hopping process.     

Spin relaxation and magnetic properties of benzo-1,2,3-trithiolium radical cations

Magnetic and dynamics properties of paramagnetic centers in various trithiolium cations were characterized by static magnetic susceptibility measurements and EPR spectroscopy. Magnetically correlated units consisting of at least pairs of spins with ferromagnetic exchange coupling were found in some trithioles. The rates of intramolecular spin diffusion and intermolecular spin hopping were estimated separately. The rates and the anisotropy (v/v=20–300) of spin dynamics were shown to depend on the molecular structure.     

Derivation of diffusion coefficient of a Brownian particle in tilted periodic potential from the coordinate moments

In this research, diffusion of an overdamped Brownian particle in the tilted periodic potential is investigated. Using the one-dimensional hopping model, the formulations of the mean velocity VN and effective diffusion coefficient DN of the Brownian particle have been obtained [B. Derrida, J. Stat. Phys. 31 (1983) 433]. Based on the relation between the effective diffusion coefficient and the moments of the mean first passage time, the formulation of effective diffusion coefficient Deff of the Brownian particle also has been obtained [P. Reimann, et al., Phys. Rev. E 65 (2002) 031104]. In this research, we'll give another analytical expression of the effective diffusion coefficient Deff from the moments of the particle's coordinate.     

Diffusion-limited annihilation in inhomogeneous environments

We study diffusion-limited (on-site) pair annihilation A + A → 0 and (on-site) fusion A + A → A which we show to be equivalent for arbitrary space-dependent diffusion and reaction rates. For one-dimensional lattices with nearest neighbour hopping we find that in the limit of infinite reaction rate the time-dependent n-point density correlations for many-particle initial states are determined by the correlation functions of a dual diffusion-limited annihilation process with at most 2n particles initially. Furthermore, by reformulating general properties of annihilating random walks in one dimension in terms of fermionic anticommutation relations we derive an exact representation for these correlation functions in terms of conditional probabilities for a single particle performing a random walk with dual hopping rates. This allows for the exact and explicit calculation of a wide range of universal and non-universal types of behaviour for the decay of the density and density correlations.     

Diffusion of oxygen on tungsten (110)

The surface diffusion of oxygen on W(110) was studied in the temperature range 760–880°C and for coverages up to one monolayer. Coverage-distance plots after diffusion runs were determined via corresponding work function profiles measured by a newly developed, laterally resolving vibrating capacitor method. The coverage profiles were evaluated in terms of a concentration dependent diffusion coefficient (DC) using the Boltzmann-Matano analysis. The temperature dependence of the DC can be described by a constant activation energy of 27 ± 2 kcal/mole in the coverage range 0.4 < θ < 0.9. The concentration dependence of the DC shows a maximum near θ = 0.45and a decrease beyond θ = 0.6. This behavior is correlated with observed LEED structures and interpreted by a rather abrupt change of the chemical potential near θ = 0.5 and a decreasing hopping probability for higher coverages.     

Variable range hopping mechanism in band-tail states of feldspars: A time-resolved IRSL study

Time-resolved infra-red stimulated luminescence (TR-IRSL) technique enables an understanding of the dynamics of trapped electrons after IR excitation in the band-tail states of feldspar. This work intends to study the underlying physical mechanism of IRSL production. TR-IRSL studies were carried out on four feldspar mineral specimens of variable chemical composition and structural state. Assuming the IR excited trapped electrons make random walks in the band-tail states and recombine by tunnelling dynamically, hopping time is derived from the OFF time data of TR-IRSL. This analysis indicates that the hopping time decreases with stimulation temperature. Using Einstein diffusion equation, hopping probability is computed and is shown to obey the equation describing variable range hopping mechanism of Mott kind. Mott's parameters (hopping length and hopping energy) are then derived. Hopping length decreases with stimulation temperature whereas hopping energy increases with temperature. The average hopping length and energy are in the range of 11–18 Å and 45–55 meV respectively and the diffusion constant is estimated to be in the range of 10^?10–10^?9 cm² s^?1 for all the feldspar samples.     

Random walk on a disordered directed Bethe lattice

The random walk of a particle on a directed Bethe lattice of constant coordinanceZ is examined in the case of random hopping rates. As a result, the higher the coordinance, the narrower the regions of anomalous drift and diffusion. The annealed and quenched mean square dispersions are calculated in all dynamical phases. In opposition to the one-dimensional (Z=2) case, the annealed and quenched mean quadratic dispersions are shown to be identical in all phases.We shall employ indifferently the expressions Bethe lattice or infinite Cayley tree to denote an infinite ramified lattice of constant coordinanceZ.^{(4, 5)}     

Surface diffusion of Cr adatoms on Au(111) by quantum tunneling

The low-temperature surface diffusion of isolated Cr adatoms on Au(111) has been determined using nonperturbing x rays. Changes in the x-ray magnetic circular dichroism spectral line shape together with Monte Carlo calculations demonstrate that adatom nucleation proceeds via quantum tunneling diffusion rather than over-barrier hopping for temperatures <40K. The jump rates are shown to be as much as 35 orders of magnitude higher than that expected for thermal over-barrier hopping at 10 K.     

Diffusion in a 2D bond percolation model. A Monte Carlo simulation

A Monte Carlo computer simulation of a simple stochastic hopping model is presented. The velocity autocorrelation function and the diffusion coefficient are analyzed and compared with the results obtained by using kinetic theory. The theory and the simulation agree within the statistical error.     

Effect of hopping rate and jump length of hopping electrons on the conductivity and dielectric properties of Co–Cd ferrite

The cobalt cadmium ferrite has an n-type conductivity. As the Cd addition (x) increases, the hopping rate increases and so the conductivity increases up to x=0.5. A sudden decrease in the hopping rate occurs above x=0.5 due to the decrease of Co²⁺ ions on octahedral sites. Above x=0.7, the hopping rate increases again and the conductivity increases. As the hopping length increases the conductivity decreases, i.e. conductivity is inversely proportional to hopping length, but is directly proportional to the hopping rate of electrons. As the ferrous ions increase on octahedral sites, the conductivity increases and the jumping length decreases leading to the increase of dielectric constant.     

Diffusion blocking at low particle concentration

The rate equations describing classical particle hopping in periodic lattices are integrated to obtain exact, self-consistent expressions for the occupancy correlation functions at low atomic concentration. The long-wavelength, small-frequency behaviour is analyzed analytically. Exact results for labelled particle diffusion are obtained which properly include the correlation and atomic blocking effects.     

Quantum diffusion of a light particle in the Meissner phase of a superconductor

The influence of a superconducting fermionic environment on quantum diffusion is investigated. Within the framework of a two-state model hopping rates are calculated both for the biased and unbiased case. As for the latter, the jump frequency shows towards lower temperatures an exponential increase caused by the dyingout of quasiparticle excitations. The calculated rates show a much stronger sensitivity on bias than in the normal state. For small bias (compared to the energy gap) they behave non-monotonically: below a certain temperature an exponential decrease is found which leads to a localization of the particle. For large bias the hopping rates are not substantially changed by the onset of superconductivity.     

A theory of exciton dynamics with a percolation threshold

Mode-coupling methods are used to obtain an integral equation for the exciton diffusion constant in isotopically mixed crystals. Numerical solutions are obtained for nearest neighbor hopping in one- and two-dimensional square lattices. These solutions exhibit percolation thresholds.Supported by NSF Grant CHE78-09704.     

Enhancement of hole drift velocity in amorphous As2Se3 by iodine doping

The addition of ～ 0.6 at.% iodine to approximately stoichiometric a-As₂Se₃ enhances the hole drift velocity by more than a decade but does not affect its field, thickness and temperature dependence or the degree of disorder. It is speculated that iodine reduces the ratio of trapping to hopping states in the trap-controlled hopping process which recently has been proposed for a-As₂Se₃.