Showing papers on "Einstein relation published in 2009"

Towards a Nonequilibrium Thermodynamics: A Self-Contained Macroscopic Description of Driven Diffusive Systems

Abstract: In this paper we present a self-contained macroscopic description of diffusive systems interacting with boundary reservoirs and under the action of external fields. The approach is based on simple postulates which are suggested by a wide class of microscopic stochastic models where they are satisfied. The description however does not refer in any way to an underlying microscopic dynamics: the only input required are transport coefficients as functions of thermodynamic variables, which are experimentally accessible. The basic postulates are local equilibrium which allows a hydrodynamic description of the evolution, the Einstein relation among the transport coefficients, and a variational principle defining the out of equilibrium free energy. Associated to the variational principle there is a Hamilton-Jacobi equation satisfied by the free energy, very useful for concrete calculations. Correlations over a macroscopic scale are, in our scheme, a generic property of nonequilibrium states. Correlation functions of any order can be calculated from the free energy functional which is generically a non local functional of thermodynamic variables. Special attention is given to the notion of equilibrium state from the standpoint of nonequilibrium.

Stochastic trailing string and Langevin dynamics from AdS/CFT

Abstract: Using the gauge/string duality, we derive a set of Langevin equations describing the dynamics of a relativistic heavy quark moving with constant average speed through the strongly-coupled = 4 SYM plasma at finite temperature. We show that the stochasticity arises at the string world-sheet horizon, and thus is causally disconnected from the black hole horizon in the space-time metric. This hints at the non-thermal nature of the fluctuations, as further supported by the fact that the noise term and the drag force in the Langevin equations do not obey the Einstein relation. We propose a physical picture for the dynamics of the heavy quark in which dissipation and fluctuations are interpreted as medium-induced radiation and the associated quantum-mechanical fluctuations. This picture provides the right parametric estimates for the drag force and the (longitudinal and transverse) momentum broadening coefficients.

Anomalous current in periodic Lorentz gases with infinite horizon

Abstract: Electric current is studied in a two-dimensional periodic Lorentz gas in the presence of a weak homogeneous electric field. When the horizon is finite, that is, free flights between collisions are bounded, the resulting current is proportional to the voltage difference , that is, , where is the diffusion matrix of a Lorentz particle moving freely without an electric field (see a mathematical proof in [1]). This formula agrees with Ohm's classical law and the Einstein relation. Here the more difficult model with an infinite horizon is investigated. It is found that infinite corridors between scatterers allow the particles (electrons) to move faster, resulting in an abnormal current (causing 'superconductivity'). More precisely, the current is now given by , where is the 'superdiffusion' matrix of a Lorentz particle moving freely without an electric field. This means that Ohm's law fails in this regime, but the Einstein relation (suitably interpreted) still holds. New results are also obtained for the infinite-horizon Lorentz gas without external fields, complementing recent studies by Szasz and Varju [2]. Bibliography: 31 titles.

Diffusion of a sphere in a dilute solution of polymer coils

Abstract: We calculate the short time and the long time diffusion coefficients of a spherical tracer particle in a polymer solution in the low density limit by solving the Smoluchowski equation for a two-particle system and applying a generalized Einstein relation (fluctuation dissipation theorem). The tracer particle as well as the polymer coils are idealized as hard spheres with a no-slip boundary condition for the solvent but the hydrodynamic radius of the polymer coils is allowed to be smaller than the direct-interaction radius. We take hydrodynamic interactions up to 11th order in the particle distance into account. For the limit of small polymers, the expected generalized Stokes–Einstein relation is found. The long time diffusion coefficient also roughly obeys the generalized Stokes–Einstein relation for larger polymers whereas the short time coefficient does not. We find good qualitative and quantitative agreement to experiments.

Estimating diffusivity along a reaction coordinate in the high friction limit: Insights on pulse times in laser-induced nucleation

Abstract: In the high friction limit of Kramers’ theory, the diffusion coefficient for motion along the reaction coordinate is a crucial parameter in determining reaction rates from mean first passage times. The Einstein relation between mean squared displacement, time, and diffusivity is inaccurate at short times because of ballistic motion and inaccurate at long times because trajectories drift away from maxima in the potential of mean force. Starting from the Smoluchowski equation for a downward parabolic barrier, we show how drift induced by the potential of mean force can be included in estimating the diffusivity. A modified relation between mean squared displacement, time, and diffusivity now also includes a dependence on the barrier curvature. The new relation provides the diffusivity at the top of the barrier from a linear regression that is analogous to the procedure commonly used with Einstein's relation. The new approach has particular advantages over previous approaches when evaluations of the reaction coordinate are costly or when the reaction coordinate cannot be differentiated to compute restraining forces or velocities. We use the new method to study the dynamics of barrier crossing in a Potts lattice gas model of nucleation from solution. Our analysis shows that some current hypotheses about laser-induced nucleation mechanisms lead to a nonzero threshold laser pulse duration below which a laser pulse will not affect nucleation. We therefore propose experiments that might be used to test these hypotheses.

All-Electrical Measurement of the Density of States in (Ga,Mn)As

Abstract: We report on electrical measurements of the effective density of states in the ferromagnetic semiconductor material (Ga,Mn)As. By analyzing the conductivity correction to an enhanced electron-electron interaction the electrical diffusion constant was extracted for (Ga,Mn)As samples of different dimensionality. Using the Einstein relation allows us to deduce the effective density of states of (Ga,Mn)As at the Fermi energy.

A note on conductivity and charge diffusion in holographic flavor systems

Abstract: We analyze the charge diffusion and conductivity in a Dp/Dq holographic setup that is dual to a supersymmetric Yang-Mills theory in p+1 dimensions with Nf << Nc flavor degrees of freedom at finite temperature and nonvanishing U(1) baryon number chemical potential. We provide a new derivation of the results that generalize the membrane paradigm to the present context. We perform a numerical analysis in the particular case of the D3/D7 flavor system. The results obtained support the validity of the Einstein relation at finite chemical potential.

Density dynamics from current auto-correlations at finite time- and length-scales

Abstract: We consider the increase of the spatial variance of some inhomogeneous, non-equilibrium density (particles, energy, etc.) in a periodic quantum system of condensed-matter type. This is done for a certain class of initial quantum states which is supported by static linear response and typicality arguments. We directly relate the broadening to some current auto-correlation function at finite times. Our result is not limited to diffusive behavior, however, in that case it yields a generalized Einstein relation. These findings facilitate the approximation of diffusion constants/conductivities on the basis of current auto-correlation functions at finite times for finite systems. Pursuing this, we quantitatively confirm the magnetization diffusion constant in a spin chain which was recently found from non-equilibrium bath scenarios.

Density dynamics from current auto-correlations at finite time- and length-scales

Abstract: We consider the increase of the spatial variance of some inhomogeneous, non-equilibrium density (particles, energy, etc.) in a periodic quantum system of condensed matter-type. This is done for a certain class of initial quantum states which is supported by static linear response and typicality arguments. We directly relate the broadening to some current auto-correlation function at finite times. Our result is not limited to diffusive behavior, however, in that case it yields a generalized Einstein relation. These findings facilitate the approximation of diffusion constants/conductivities on the basis of current auto-correlation functions at finite times for finite systems. Pursuing this, we quantitatively confirm the magnetization diffusion constant in a spin chain which was recently found from non-equilibrium bath scenarios.

Conductivity and Diffusion Constant in Lifshitz Backgrounds

Abstract: We study the DC conductivity and the diffusion constant for asymptotically Lifshitz black branes in $(d+2)$- dimensions with arbitrary dynamical exponent $z$. For a solvable example with $z=2, d=4$, we calculate the real-time correlation functions, from which we can read off the corresponding conductivity and diffusion constant. For black branes with arbitrary $z$ and $d$, we work out the conductivity and obtain the diffusion constant by making use of the Einstein relation. All the results agree with those obtained via the membrane paradigm.

Einstein relation in hopping transport of organic semiconductors

Abstract: The ratio between mobility and diffusion parameters (Einstein relation) in organic semiconductors has been a debating issue in the recent years. In this paper we developed an analytical model based on hopping transport theory and the Gaussian density of states. The validity of Einstein relation in organic semiconductors is discussed. It is shown that the classic Einstein relation is invalid for organic semiconductors, even for the carrier concentration for experimental purpose.

Einstein relation and effective temperature for systems with quenched disorder.

Abstract: According to the Einstein relation the ratio between independent measurements of fluctuations (e.g., diffusivity) and the response to a weak external field (e.g., mobility) is equal to the thermal temperature when the system is kept close to thermal equilibrium. For strongly disordered systems, which are not self-averaging this ratio is a random variable and hence in this sense the Einstein relation is not valid. Thus effective temperatures found using the fluctuation dissipation ratio are at least in some cases stochastic variables. This scenario is tested with the quenched trap model. An average over an ensemble of systems yields an averaged effective temperature, which is compared with results obtained from the mean-field continuous-time random-walk model.

Potential-Dependent Generalized Einstein Relation in Disordered Organic Semiconductors

Abstract: The generalized Einstein relation (GER) is extended to consider the potential energy of carriers in an electric field (PDGER). It can be equivalently seen as the GER having position-dependent Fermi energy, and implies the organic semiconductor is in non-equilibrium under an electric field. The distribution of the carrier density with position is solved for two polymer layers. The numerical results are used to evaluate the PDGER. It is shown that the ratio of diffusion coefficient to mobility, μ/D, increases with Fermi energy and decreases with carrier density. The PDGER gives non-traditional values for the two polymer layers; the value of μ/D is small near the surface, and slightly increases as the position departs from the surface.

Einstein Relation in n-Channel Inversion Layers of Nonlinear Optical, Optoelectronic and Related Materials: Simplified Theory, Relative Comparison and Suggestion for an Experimental Determination

Abstract: In this paper, we study the Einstein relation for the diffusivity to mobility ratio (DMR) in n-channel inversion layers of non-linear optical materials on the basis of a newly formulated electron dispersion relation by considering their special properties within the frame work of k.p formalism. The results for the n-channel inversion layers of III-V, ternary and quaternary materials form a special case of our generalized analysis. The DMR for n-channel inversion layers of II-VI, IV-VI and stressed materials has been investigated by formulating the respective 2D electron dispersion laws. It has been found, taking n-channel inversion layers of CdGeAs2, Cd(3)AS(2), InAs, InSb, Hg1-xCdxTe, In1-xGaxAsyP1-y lattice matched to InP, CdS, PbTe, PbSnTe, Pb1-xSnxSe and stressed InSb as examples, that the DMR increases with the increasing surface electric field with different numerical values and the nature of the variations are totally band structure dependent. The well-known expression of the DMR for wide gap materials has been obtained as a special case under certain limiting conditions and this compatibility is an indirect test for our generalized formalism. Besides, an experimental method of determining the 2D DMR for n-channel inversion layers having arbitrary dispersion laws has been suggested.

Molecular dynamics simulation of diffusion coefficients of small molecules in amorphous PET

Abstract: Diffusion of molecules with molecular weights ranging from 32 to 339 in amorphous polyethylene terephthalate(PET) was examined by using molecular dynamics simulation.The diffusion coefficients were calculated based on Einstein relation and the influence of simulation time and density on diffusion coefficients was discussed.The results showed that for a higher temperature a shorter simulation time was needed in order that the linear area in mean square displacement (MSD) curves could be observed while for a lower temperature a longer simulation time was needed.Diffusion coefficients decreased with increasing density of the polymer and a higher density required a longer simulation time.Comparison of the calculated diffusion coefficients with experimental values found in the literature indicated that the calculated and experimental values were in the same order of magnitude.It suggested that the polymer model was acceptable and could describe correctly the diffusion process of small molecules in PET.This work can provide an approximate method of calculating diffusion coefficient,which is the key parameter in the migration model.

Einstein relation in carbon nanotubes and quantum wires of nonlinear optical and optoelectronic materials

Abstract: We study the Einstein relation for the diffusivity-to-mobility ratio (DMR) in carbon nanotubes (CNTs) and quantum wires (QWs) of nonlinear optical and optoelectronic materials. The respective DMR in QWs exhibits increasing quantum steps with increasing electron statistics. In CNTs, the DMR exhibits periodic oscillations with increasing carrier degeneracy and the nature is radically different as compared with the corresponding DMR of QWs since they emphasize the different signatures of the two entirely different one dimensional nanostructured systems. In addition, we have suggested an experimental method of determining the DMR for CNTs and QWs having arbitrary dispersion laws.

Non-Equilibrium relation between mobility and diffusivity of interacting Brownian particles under shear

Abstract: We investigate the relation between mobility and diffusivity for Brownian particles under steady shear near the glass transition, using mode coupling approximations. For the two directions perpendicular to the shear direction, the particle motion is diffusive at long times and the mobility reaches a finite constant. Nevertheless, the Einstein relation holds only for the short-time in-cage motion and is violated for long times. In order to get the relation between diffusivity and mobility, we perform the limit of small wavevector for the relations derived previously [Phys. Rev. Lett. 102 (2009), 135701], without further approximation. We find good agreement to simulation results. Furthermore, we split the extra term in the mobility in an exact way into three terms. Two of them are expressed in terms of mean squared displacements. The third is given in terms of the (less handy) force-force correlation function.

On the Einstein Relation in holographic systems at finite baryon density

Abstract: We study the conductivity, susceptibility and diffusion of a strongly coupled quark gluon plasma from the holographic perspective. We calculate general expressions for these quantities in the presence of finite baryon density and show that in this context, for the D3/D7 intersection the Einstein relation holds, providing another non-trivial check of the holographic correspondence at finite temperature.

Monte Carlo Algorithm for Mobility Calculations in Thin Body Field Effect Transistors: Role of Degeneracy and Intersubband Scattering

Abstract: We generalize the Monte Carlo algorithm originally designed for small signal analysis of the three-dimensional electron gas to quasi-two-dimensional electron systems. The method allows inclusion of arbitrary scattering mechanisms and general band structure. Contrary to standard Monte Carlo methods to simulate transport, this algorithm takes naturally into account the fermionic nature of electrons via the Pauli exclusion principle. The method is based on the solution of the linearized Boltzmann equation and is exact in the limit of negligible driving fields. The theoretically derived Monte Carlo algorithm has a clear physical interpretation. The diffusion tensor is calculated as an integral of the velocity autocorrelation function. The mobility tensor is related to the diffusion tensor via the Einstein relation for degenerate statistics. We demonstrate the importance of degeneracy effects by evaluating the low-field mobility in contemporary field-effect transistors with a thin silicon body. We show that degeneracy effects are essential for the correct interpretation of experimental mobility data for field effect transistors in single- and double-gate operation mode. In double-gate structures with (100) crystal orientation of the silicon film degeneracy effects lead to an increased occupation of the higher subbands. This opens an additional channel for elastic scattering. Increased intersubband scattering compensates the volume inversion induced effect on the mobility enhancement and leads to an overall decrease in the mobility per channel in double-gate structures.

Nonequilibrium Linear Response for Markov Dynamics, II: Inertial Dynamics

Abstract: We continue our study of the linear response of a nonequilibrium system. This Part II concentrates on models of open and driven inertial dynamics but the structure and the interpretation of the result remain unchanged: the response can be expressed as a sum of two temporal correlations in the unperturbed system, one entropic, the other frenetic. The decomposition arises from the (anti)symmetry under time-reversal on the level of the nonequilibrium action. The response formula involves a statistical averaging over explicitly known observables but, in contrast with the equilibrium situation, they depend on the model dynamics in terms of an excess in dynamical activity. As an example, the Einstein relation between mobility and diffusion constant is modified by a correlation term between the position and the momentum of the particle.