Einstein relation susceptibilities

Interestingly, each one of the two FDTs can be formulated in two equivalent ways, depending on whether one is primarily interested in writing a Kubo formula for a generalized susceptibility %(co) [namely, in the present case, p(m) or y(o))], or an expression for its dissipative part [namely, the Einstein relation... 

Let us now come back to the specific problem of the diffusion of a particle in an out-of-equilibrium environment. In a quasi-stationary regime, the particle velocity obeys the generalized Langevin equation (22). The generalized susceptibilities of interest are the particle mobility p(co) = Xvxi03) and the generalized friction coefficient y(co) = — (l/mm)x ( ) [the latter formula deriving from the relation (170) between y(f) and Xj> (f))- The results of linear response theory as applied to the particle velocity, namely the Kubo formula (156) and the Einstein relation (159), are not valid out-of-equilibrium. The same... 

ECP (Effective Core Potential) 171 Effective pair potential 68 EHMO (Extended Huckel Molecular Orbital Model) 130 Eigenvalue 17 Eigenvector 17 Einstein relation 253 Electric dipole moment 100, 265, 282 Electric field gradient 278 Electric moments 184 Electric quadrupole moment 268, 269 Electric second moment 268 Electric susceptibility 256 Electron affinity 147 Electron correlation 186, 273 Electron density 100, 218, 222 Electron relaxation 118 Electron spin 91, 95, 99, 277, 305 Electronic Schrodinger equation 74 Electrostatic field 14 Electrostatic field gradient 271... 

The Einstein relation is a special case of a more general result known as the fluctuation-dissipation theorem (FDT). The FDT relates the strength of the random thermal fluctuations (here D) to the corresponding susceptibility to external perturbations (here in such a way that ensures that the probability distribution converges to the proper equilibriiun result at stea state. 

Note that Equation [51] represents formally the tensorial relationship, while Equation [52] expresses this relation by the (Cartesian) components of P and E and some coefficients whereas Equation [53] states this relation by using Einstein s summation convention. Here, the coefficients are the components of the electric susceptibility tensor which is a tensor of rank 2. The tensor % is an example of what is usually called a property tensor or matter tensor. Strictly speaking, property tensors describe physical properties of the static crystal which belong to the totally symmetric irreducible representation of the relevant point group. Properties, however, that depend on vibrations of the crystal lattice are described by tensors which belong to the different irreducible representations. The corresponding tensors are then often designated as tensorial covariants. 

The electrophoretic mobility of the cell increases greatly with age, but this variation could not be related to variations in the amount of sialic acid at the surface (see review by Balazs and Jacobson, 1966). During the cell cycle, a definite increase of neuraminidase-susceptible sialic acid was observed by Rosenberg and Einstein (1972) in human lymphoid cells, whereas Kraemer (1967) could not observe this change in osteosarcoma cells. 

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