K. W. Kehr’s research while affiliated with Forschungszentrum Jülich and other places

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Publications (105)


Mean first-passage times and hopping mobility of particles under bias in nonsymmetric potentials
  • Chapter

May 2007

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12 Reads

K. W. Kehr

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K. Mussawisade

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The hopping motion of particles on segments of linear chains is considered, where the transition rates correspond to nonsymmetric potentials. Attention is drawn to the directional dependence of the particle current, for various strengths of the applied bias field. The problem is mainly discussed in connection with the mean first-passage time of particles across the segment. Directional effects are absent in the regime of linear response; they appear for strong bias fields and nonsymmetric potentials which comprise different barriers and site energies. The results are compared with numerical simulations and an exact expression.


Diffusion of lattice gases in disordered lattices

April 2006

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7 Reads

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1 Citation

Lecture Notes in Physics

A survey of recent simulations and analytical work on collective diffusion of lattice gases in lattices with site-energy disorder is given. In one-dimensional disordered lattices, exact results have been obtained in the limit of small and large particle concentrations. Simulation results at intermediate concentrations show that the time-dependent site-occupancy correlations are not yet satisfactorily understood. In higher-dimensional disordered lattices, an effective-medium theory, which uses mean-field transition rates, gives an improvement over the phenomenological description and qualitative agreement with the simulations. The main effects derive from saturation of deep trapping sites. One conspicuous example is the existence of a coefficient of collective diffusion in a situation where no single-particle diffusion coefficient exists.


Diffusion of Particles on Lattices

January 2005

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53 Reads

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14 Citations

Diffusion processes take place almost everywhere in the material world; they are ubiquitous in condensed matter. Diffusion occurs in the different forms of condensed matter: in fluids, complex fluids, and solids. This chapter is concerned with the description of diffusion of particles in lattices. The theoretical description refers to diffusion in crystalline but also amorphous solids. Experimental facts on diffusion processes in solids are given in Chaps. 1-6, in particular. Empirical information gives the motivation and the basis for the theoretical description. Two important special cases of diffusion processes in crystalline solids are the tracer diffusion, where the displacement of marked atoms (radioactive isotopes) is determined, and interstitial diffusion, where atoms move on interstitial sites within the solid (see Chap. 1).


Absence of self-averaging in the complex admittance for transport through disordered media

April 2002

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14 Reads

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5 Citations

Physical Review B

Random walk models in one-dimensional disordered media with an oscillatory input current are investigated theoretically as generic models of the boundary perturbation experiment. It is shown that the complex admittance obtained in the experiment is not self-averaging when the jump rates wiw_i are random variables with the power-law distribution ρ(wi)wiα1(0<α1)\rho(w_i)\sim {w_i}^{\alpha-1} (0 < \alpha \leq 1). More precisely, the frequency-dependence of the disorder-averaged admittance <χ><\chi> disagrees with that of the admittance χ\chi of any sample. It implies that the Cole-Cole plot of <χ><\chi> shows a different shape from that of the Cole-Cole plots of χ\chi of each sample. The condition for absence of self-averaging is investigated with a toy model in terms of the extended central limit theorem. Higher dimensional media are also investigated and it is shown that the complex admittance for two-dimensional or three-dimensional media is also non-self-averaging. Comment: 38 pages, 18 figures, submitted to Phys. Rev. B. Section VII was revised completely with the new results for higher dimensional disordered media


FIG. 1. Fitting of the ͗ S n ͘ data derived from the Henyey and 
FIG. 2. Double logarithmic plot of ͗ S ͘ SIW / n 0.9 ͑ left ordinate axis ͒ and Ϫ ln ⌽ ( n , c )/ n 0.1 ͑ right ordinate axis ͒ as a function of the 
FIG. 3. Local exponent of x in Eq. ͑ 18 ͒ , as a function of x ϭ ␭ n 0.8 , derived numerically from the points in Fig. 2. 
Trapping and survival probability in two dimensions
  • Article
  • Full-text available

March 2001

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143 Reads

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21 Citations

Physical Review E

We investigate the survival probability Phi(n,c) of particles performing a random walk on a two-dimensional lattice that contains static traps, which are randomly distributed with a concentration c, as a function of the number of steps n. Phi(n,c) is analyzed in terms of a scaling ansatz, which allows us to locate quantitatively the crossover between the Rosenstock approximation (valid only at early times) and the asymptotic Donsker-Varadhan behavior (valid only at long times). While the existence of the crossover has been postulated before, its exact location has not been known. Our scaling hypothesis is based on the mean value of the quantity S(n), the number of sites visited in an n-step walk. We make use of the idea of self-interacting random walks, and a "slithering" snake algorithm, available in the literature, and we are thus able to obtain accurate survival probability data indirectly by Monte Carlo simulation techniques. The crossover can now be determined by our method, and it is found to depend on a combination of c and n. It occurs at small Phi(n,c) values, which is typically the case for large values of n.

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Absence of self-averaging in the complex admittance for transport through random media

December 2000

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22 Reads

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7 Citations

Physical Review B

A random walk model in a one dimensional disordered medium with an oscillatory input current is presented as a generic model of boundary perturbation methods to investigate properties of a transport process in a disordered medium. It is rigorously shown that an admittance which is equal to the Fourier-Laplace transform of the first-passage time distribution is non-self-averaging when the disorder is strong. The low frequency behavior of the disorder-averaged admittance, <χ>1ωμ<\chi > -1 \sim \omega^{\mu} where μ<1\mu < 1, does not coincide with the low frequency behavior of the admittance for any sample, χ1ω\chi - 1 \sim \omega. It implies that the Cole-Cole plot of <χ><\chi> appears at a different position from the Cole-Cole plots of χ\chi of any sample. These results are confirmed by Monte-Carlo simulations. Comment: 7 pages, 2 figures, published in Phys. Rev. B


Absence of self-averaging in the complex admittance for transport through random media

March 2000

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6 Reads

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9 Citations

A random walk model in a one-dimensional disordered medium with an oscillatory input current is presented as a generic model of boundary perturbation methods to investigate properties of a transport process in a disordered medium. It is rigorously shown that an admittance which is equal to the Fourier-Laplace transform of the first-passage time distribution is non-self-averaging when the disorder is strong. The low-frequency behavior of the disorder-averaged admittance, 〈χ〉-1∼ωμ, where μ<1, does not coincide with the low-frequency behavior of the admittance for any sample, χ-1∼ω. It implies that the Cole-Cole plot of 〈χ〉 appears at a different position from the Cole-Cole plots of χ of any sample. These results are confirmed by Monte Carlo simulations.


Hopping motion of lattice gases through nonsymmetric potentials under strong bias conditions

March 2000

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50 Reads

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9 Citations

Physical Review E

The hopping motion of lattice gases through potentials without mirror-reflection symmetry is investigated under various bias conditions. The model of two particles on a ring with four sites is solved explicitly; the resulting current in a sawtooth potential is discussed. The current of lattice gases in extended systems consisting of periodic repetitions of segments with sawtooth potentials is studied for different concentrations and values of the bias. Rectification effects are observed, similar to the single-particle case. A mean-field approximation for the current in the case of strong bias acting against the highest barriers in the system is made and compared with numerical simulations. The particle-vacancy symmetry of the model is discussed.


Toy model for molecular motors

February 1999

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20 Reads

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19 Citations

Physica A Statistical Mechanics and its Applications

A hopping model for molecular motors is presented consisting of a state with asymmetric hopping rates with period 2 and a state with uniform hopping rates. State changes lead to a stationary unidirectional current of a particle. The current is explicitly calculated as a function of the rate of state changes, including also an external bias field. The Einstein relation between the linear mobility of the particle and its diffusion coefficient is investigated. The power input into the system is derived, as well as the power output resulting from the work performed against the bias field. The efficiency of this model is found to be rather small.


Diffusion in a one-dimensional bosonic lattice gas

January 1999

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18 Reads

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16 Citations

Journal of Physics A Mathematical and General

A one-dimensional lattice-gas model with order preservation is considered where the occupation probabilities of sites correspond to Bose statistics as a consequence of the prescribed dynamics. The master equation for the particle-cluster dynamics at the sites is formulated. The corresponding continuum nonlinear diffusion equation is derived for the space- and time-dependent concentration fluctuations. The equation can be regarded, in the presence of a drift force, as the Burgers equation when terms irrelevant in the sense of renormalization-group ideas are neglected. Collective centre-of-mass and tagged-particle diffusion are investigated by numerical simulations and the results agree with the analytical derivations. Subdiffusive behaviour of the mean-square displacement of tagged particles and normal collective and centre-of-mass diffusion are observed when no bias is present. The dispersion of the centre-of-mass displacement exhibits superdiffusive behaviour in the case of mean drift of the particles. Discrepancies of about 20% between the numerically determined superdiffusion coefficients and the predictions of the mode-coupling theory are found and discussed.


Citations (61)


... We have seen that broadly speaking tunneling in the relativistic Schrödinger equation appears to follow the familiar pattern known from non-relativistic tunneling [35,36]. Most of the amplitude is reflected and only a wavepacket with a tiny amplitude is transmitted. ...

Reference:

Tunneling dynamics of the relativistic Schrödinger/Salpeter equation
Wave packet tunneling
  • Citing Article
  • December 1998

Annalen der Physik

... The fact that in pure AI the transverse relaxation rate remains unmeasurably small down to at least 0.1 K [15] suggests strongly that immediately below 60 K the D ~ § ~ T dependence characteristic of one-phonon processes [16] sets in. This would, at least qualitatively, account for the observation [17] that between 2 K and 25 K the /~+ trapping rate in dilute AIMn alloys is proportional to 7 -0.89 -+ 0.03. ...

Localization, diffusion and trapping of positive muons in al and dilute AlMn and AlLi compounds
  • Citing Article
  • January 1981

Hyperfine Interactions

K. W. Kehr

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D. Richter

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J. M. Welter

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[...]

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A. Yaouanc

... The structural organization of the ANN used in this study consists of input with 6 nodes corresponding to 6 input features (x j ), 2 hidden layers containing 10 nodes each with sigmoid and linear transfer function for 1 st and 2 nd hidden layers respectively, and output layer. Following the fitting mechanism of an ANN, the mathematical expression for the value on k th node (k=1, 2, .., 10) in 1 st hidden layer ( 1 ) is given by ...

Diffusion in Concentrated Lattice Gases. II. Particles with Attractive Nearest-Neighbor Interaction on Three-Dimensional Lattices
  • Citing Article
  • September 1982

Physical Review B

... In this paper, we consider a system where both tracers and crowders are allowed to diffuse. Diffusive transport in crowded environments has been extensively investigated using a diverse range of simulation techniques, analytic models, as well as experiments [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29]. The effect of mobile obstacles on Brownian diffusion was recently investigated by Berry and Chaté [30], demonstrating that the nature of obstacle diffusion determines whether tracer motion is diffusive or sub-diffusive. ...

Diffusion in concentrated lattice gases
  • Citing Article
  • February 1983

Journal of Statistical Physics

... The problem of the typical behaviour of a macroscopic quantity as compared to its average, has received considerable attention recently in the context of diffusion in disordered media (see Noskowicz and Goldhirsch (1988), Le Doussal (1989), Murthy and Kehr (1989), Kehr and Murthy (1990)). To motivate the basic issues involved we consider the following simple example. ...

Erratum: Mean first-passage time of random walks on a random lattice [Phys. Rev. A 40, 2082 (1989)]
  • Citing Article
  • January 1990

Physical review A, Atomic, molecular, and optical physics

... 1 For instance, such sudden shifts (or jump discontinuities) of magnetization plotted versus the magnetic field were already found in critical fields, in our earlier work [27] , where we studied the influence of lattice ordering on diffusion properties. ...

Diffusion in concentrated lattice gases. V. Particles with repulsive nearest-neighbor interaction on the face-centered-cubic lattice
  • Citing Article
  • August 1983

Physical review. B, Condensed matter

... Our model relies on the symmetric exclusion process: we consider an active tracer particle submitted to an external force, which evolves in a dynamical environment of mobile passive crowders on a lattice, whose dynamics is accounted for explicitly. This model thus belongs to the important class of exclusion processes, which are paradigmatic models of nonequilibrium statistical physics, and which received considerable attention, both in 1D [21,22], and in higher dimensions [23][24][25][26][27][28][29][30]. On top of providing an explicit description of the environment of the tracer, which allows us to characterize the response of the environment to the displacement of the tracer, this model is analytically tractable, gives accurate results in a wide range of parameters, and elucidates the conditions under which ANM is observed. ...

Diffusion in concentrated lattice gases. Self-diffusion of noninteracting particles in three-dimensional lattices
  • Citing Article
  • May 1981

Physical review. B, Condensed matter

... If the Flynn-Stoneham law of Fig. 2 remains valid at lower temperatures, D ~+(T) becomes so small that measurable deviations from R(t) = const, are expected below about 20 K in unirradiated A1. The fact that in pure AI the transverse relaxation rate remains unmeasurably small down to at least 0.1 K [15] suggests strongly that immediately below 60 K the D ~ § ~ T dependence characteristic of one-phonon processes [16] sets in. This would, at least qualitatively, account for the observation [17] that between 2 K and 25 K the /~+ trapping rate in dilute AIMn alloys is proportional to 7 -0.89 ...

Studies of μ+ Localization in Cu, Al, and Al Alloys in the Temperature Interval 0.03-100 K

Physical Review Letters

... Classical diffusion models have emerged as the cornerstone of transport models for decades in different facets of science and engineering. The classical diffusion models rely on the assumption of a Markovian process that is not necessarily present in natural systems [1][2][3][4][5]. Fluid flow in strongly homogeneous porous media obeys normal diffusion theory via the Darcy-type flux [6][7][8]. ...

Diffusion in a disordered medium
  • Citing Article
  • February 1982

Physical review. B, Condensed matter

... Several authors [22][23][24][25][26][27] have treated dispersive mobility theoretically but, as far as we know, low attention has been paid from the experimental point of view. This behaviour has been taken on account by several authors in order to describe the anomalous transport observed in some photosensitive materials, and has been extended succesfully to different areas such as fluid dymanics, geology, brownian movement, as well as to electric transport in insulating materials [27][28][29][30]. ...

Connection between dispersive transport and statistics of extreme events
  • Citing Article
  • May 1998

Physica A Statistical Mechanics and its Applications