15 research outputs found
Nonlinear relaxation field in charged systems under high electric fields
The influence of an external electric field on the current in charged systems
is investigated. The results from the classical hierarchy of density matrices
are compared with the results from the quantum kinetic theory. The kinetic
theory yields a systematic treatment of the nonlinear current beyond linear
response. To this end the dynamically screened and field-dependent
Lenard-Balescu equation is integrated analytically and the nonlinear relaxation
field is calculated. The classical linear response result known as Debye -
Onsager relaxation effect is only obtained if asymmetric screening is assumed.
Considering the kinetic equation of one specie the other species have to be
screened dynamically while the screening with the same specie itself has to be
performed statically. Different other approximations are discussed and
compared.Comment: language correction
Conductivity in quasi two-dimensional systems
The conductivity in quasi two-dimensional systems is calculated using the
quantum kinetic equation. Linearizing the Lenard-Balescu collision integral
with the extension to include external field dependences allows one to
calculate the conductivity with diagrams beyond the GW approximation including
maximally crossed lines. Consequently the weak localization correction as an
interference effect appears here from the field dependence of the collision
integral (the latter dependence sometimes called intra-collisional field
effect). It is shown that this weak localization correction has the same origin
as the Debye-Onsager relaxation effect in plasma physics. The approximation is
applied to a system of quasi two-dimensional electrons in hetero-junctions
which interact with charged and neutral impurities and the low temperature
correction to the conductivity is calculated analytically. It turns out that
the dynamical screening due to charged impurities leads to a linear temperature
dependence, while the scattering from neutral impurities leads to the usual
Fermi-liquid behavior. By considering an appropriate mass action law to
determine the ratio of charged to neutral impurities we can describe the
experimental metal-insulator transition at low temperatures as a Mott-Hubbard
transition.Comment: 7 pages 7 pages appendix 11 figure
Active Brownian Motion Models and Applications to Ratchets
We give an overview over recent studies on the model of Active Brownian
Motion (ABM) coupled to reservoirs providing free energy which may be converted
into kinetic energy of motion. First, we present an introduction to a general
concept of active Brownian particles which are capable to take up energy from
the source and transform part of it in order to perform various activities. In
the second part of our presentation we consider applications of ABM to ratchet
systems with different forms of differentiable potentials. Both analytical and
numerical evaluations are discussed for three cases of sinusoidal,
staircase-like and Mateos ratchet potentials, also with the additional loads
modeled by tilted potential structure. In addition, stochastic character of the
kinetics is investigated by considering perturbation by Gaussian white noise
which is shown to be responsible for driving the directionality of the
asymptotic flux in the ratchet. This \textit{stochastically driven
directionality} effect is visualized as a strong nonmonotonic dependence of the
statistics of the right versus left trajectories of motion leading to a net
current of particles. Possible applications of the ratchet systems to molecular
motors are also briefly discussedComment: 12 pages, 17 figure
Asymmetric Bethe-Salpeter equation for pairing and condensation
The Martin-Schwinger hierarchy of correlations are reexamined and the
three-particle correlations are investigated under various partial summations.
Besides the known approximations of screened, ladder and maximally crossed
diagrams the pair-pair correlations are considered. It is shown that the
recently proposed asymmetric Bethe-Salpeter equation to avoid unphysical
repeated collisions is derived as a result of the hierarchical dependencies of
correlations. Exceeding the parquet approximation we show that an asymmetry
appears in the selfconsistent propagators. This form is superior over the
symmetric selfconsistent one since it provides the Nambu-Gorkov equations and
gap equation for fermions and the Beliaev equations for bosons while from the
symmetric form no gap equation results. The selfenergy diagrams which account
for the subtraction of unphysical repeated collisions are derived from the
pair-pair correlation in the three-particle Greenfunction. It is suggested to
distinguish between two types of selfconsistency, the channel-dressed
propagators and the completely dressed propagators, with the help of which the
asymmetric expansion completes the Ward identity and is -derivable.Comment: 12 pages. 26 figure
Active Brownian Particles. From Individual to Collective Stochastic Dynamics
We review theoretical models of individual motility as well as collective
dynamics and pattern formation of active particles. We focus on simple models
of active dynamics with a particular emphasis on nonlinear and stochastic
dynamics of such self-propelled entities in the framework of statistical
mechanics. Examples of such active units in complex physico-chemical and
biological systems are chemically powered nano-rods, localized patterns in
reaction-diffusion system, motile cells or macroscopic animals. Based on the
description of individual motion of point-like active particles by stochastic
differential equations, we discuss different velocity-dependent friction
functions, the impact of various types of fluctuations and calculate
characteristic observables such as stationary velocity distributions or
diffusion coefficients. Finally, we consider not only the free and confined
individual active dynamics but also different types of interaction between
active particles. The resulting collective dynamical behavior of large
assemblies and aggregates of active units is discussed and an overview over
some recent results on spatiotemporal pattern formation in such systems is
given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte
Statistical dynamics of dislocation systems: The influence of dislocation-dislocation correlations.
During plastic deformation of crystalline materials, the collective dynamics of interacting dislocations gives rise to various patterning phenomena. A crucial and still open question is whether the long range dislocation-dislocation interactions which do not have an intrinsic range can lead to spatial patterns which may exhibit well-defined characteristic scales. It is demonstrated for a general model of two-dimensional dislocation systems that spontaneously emerging dislocation pair correlations introduce a length scale which is proportional to the mean dislocation spacing. General properties of the pair correlation functions are derived, and explicit calculations are performed for a simple special case, viz pair correlations in single-glide dislocation dynamics. It is shown that in this case the dislocation system exhibits a patterning instability leading to the formation of walls normal to the glide plane. The results are discussed in terms of their general implications for dislocation patterning