K L Sebastian
Articles written in Journal of Chemical Sciences
Volume 99 Issue 1-2 August 1987 pp 53-60
Using a path integral approach, we propose a method for the calculation of sticking probability of atoms on solid surfaces. The method makes use of a sticking trajectory for the calculation. The formalism is illustrated by applying it to the collision of an atom with a solid, the solid being modelled as a collection of bosons, the interaction term in the Hamiltonian being linear in the boson coordinates.
Volume 129 Issue 7 July 2017 pp 929-937 REGULAR ARTICLE
Many experiments are now available where it has been shown that the probability distribution function (pdf) for the position of a Brownian particle diffusing in a heterogeneous medium is not Gaussian. However, in spite of this non-Gaussianity, the mean square displacement (MSD) still remains Fickian, i.e.,
⟨x²⟩ ∝ T . One possible explanation of this non-Gaussian yet Brownian behavior is that the diffusivity of the particle itself is “diffusing”. Chubynsky and Slater (Phys. Rev. Lett. 113 098302 2014) proposed a model of “diffusing diffusivity” which they were able to solve analytically at small time scales, but simulations were performed for intermediate to large time scales.We present here a class of diffusing diffusivity models and show that the problem of calculating pdf for the position of diffusing particle is equivalent to calculating the survival probability of a particle undergoing Brownian motion in the presence of a sink.We give exact analytical results for all time scales and show that the pdf is non-Gaussian at short times which crosses over to a Gaussian at longtimes. The MSD is also shown to vary linearly with time at all times. We find that our results reproduce the numerical results of Chubynsky and Slater quite well.
Volume 134, 2022
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