chapter  6
Jump Diffusion
Pages 14

While the above-mentioned formalism is quite appropriate for gaseous and liquid states, we need an alternate approach for fluctuation phenomena in solids. A solid consists of a discrete array of atoms localized at lattice sites. At finite temperatures, the atoms perform vibratory motions around their equilibrium lattice positions which, at moderate temperatures, may be viewed as harmonic. However, at random time instants and aided by background fluctuations, an atom can jump into an available vacancy or jump into an empty spot at an interstitial site. Indeed, interstitial jumps in an empty lattice can be viewed as an uncorrelated random walk (Section 1.3).