Linear response theory mobility

Linear response theory, applied to the particle velocity, considered as a dynamic variable of the isolated particle-plus-bath system, allows to express the mobility in terms of the equilibrium velocity correlation function. Since the mobility p(co) is simply the generalized susceptibility %vx(o ), one has the Kubo formula... 

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... 

The photomicrographic measurements refer directly to polymer motion under the influence of an external force. However, measurements of migration velocity v as a function of applied electrical field E show that some of these electrophoretic measurements were made in a low-field linear regime, in which the electrophoretic mobility jx is independent of E. Linear response theory and the fluctuation-dissipation theorem are then applicable they provide that the modes of motion used by a polymer undergoing electrophoresis in the linear regime, and the modes of motion used by the same polymer as it diffuses, must be the same. This requirement on the equality of drag coefficients for driven and diffusive motion was first seen in Einstein s derivation of the Stokes-Einstein equation(16), namely thermal equilibrium requires that the drag coefficients / that determine the sedimentation rate v = mg/f and the diffusion coefficient D = kBT/f must be the same. 

An increase in the fraction of centres from 1D to 10" increases the transit time in a crystal from 1D to 10 seconds. This is consistent with the long time decays seen in imperfect samples [96, 97), This theory also indicates that the intrinsic carrier mobility is larger than 10 cm /Vs. The failure of linear response theory in a range of ID transport problems is of considerable general interest. 

The regression coefficients of descriptors denote the system (combination of mobile and stationary phases) response to these interactions. These coefficients can be measured, however the procedure is time consuming and inappropriate for practical purposes. According to the linear solvent strength theory (LSST) the retention of the analyte depends on the volume fraction (cp) of the organic modifier in binary mobile phase systems ... 

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