Final Activity Report Summary - TRAMORE (Motion of Tracers in random Environments and the Einstein relation)
We studied the motion of tracer particles in random environments, realised either by random fields or by interacting particle systems with stochastic dynamics. When a tracer particle, initially performing a diffusive motion, is submitted to a uniform external field it starts drifting and reaches an asymptotic velocity. The Einstein Relation suggests that in the limit as the external field vanishes, the velocity becomes proportional to the field, the constant of proportionality being the self-diffusivity of the tracer.
The Einstein Relation is accepted by physicists as generally valid for reversible systems, and it bears important consequences in experimental physics (mobility is an easy quantity to measure experimentally and by the Einstein Relation it is an implicit way to measure the self-diffusivity of a particle). Einstein himself used this relation to estimate the Avogadro number. Until recently, rigorous proofs existed only in few models and were in general ad-hoc. During the last four years however, tools are being developed towards a unified approach.
We can now establish the validity of the Einstein Relation making only mild assumptions on the system other than time-reversibility. Time reversibility is known to play a central role for such a relation to hold. Examples are known where it fails without this assumption and we have constructed an example where the mobility matrix is not even symmetric.
The Einstein Relation is accepted by physicists as generally valid for reversible systems, and it bears important consequences in experimental physics (mobility is an easy quantity to measure experimentally and by the Einstein Relation it is an implicit way to measure the self-diffusivity of a particle). Einstein himself used this relation to estimate the Avogadro number. Until recently, rigorous proofs existed only in few models and were in general ad-hoc. During the last four years however, tools are being developed towards a unified approach.
We can now establish the validity of the Einstein Relation making only mild assumptions on the system other than time-reversibility. Time reversibility is known to play a central role for such a relation to hold. Examples are known where it fails without this assumption and we have constructed an example where the mobility matrix is not even symmetric.