Fractional rotational diffusion in potentials

C. Fractional Rotational Diffusion in a Bistable Potential with Nonequivalent Wells... 

Anomalous rotational diffusion in a potential may be treated by using the fractional equivalent of the diffusion equation in a potential [7], This diffusion equation allows one to include explicitly in Frohlich s model as generalized to fractional dynamics (i) the influence of the dissipative coupling to the heat bath on the Arrhenius (overbarrier) process and (ii) the influence of the fast (high-frequency) intrawell relaxation modes on the relaxation process. The fractional translational diffusion in a potential is discussed in detail in Refs. 7 and 31. Here, just as the fractional translational diffusion treated in Refs. 7 and 31, we consider fractional rotational subdiffusion (0rotation about fixed axis in a potential Vo(< >)- We suppose that a uniform field Fi (having been applied to the assembly of dipoles at a time t = oo so that equilibrium conditions prevail by the time t = 0) is switched off at t = 0. In addition, we suppose that the field is weak (i.e., pFj linear response condition). 

This potential has two potential minima on the sites at <(> = 0 and = n as well as two energy barriers located at < ) = jt/2 and <[) = 3n/2. This model has been treated in detail for normal diffusion in Refs. 8,61, and 62. Here we consider the fractional Fokker-Planck equation [Eq. (55)] for a fixed axis rotator with dipole moment p moving in a potential [Eq. (163)]. 

A certain fraction of the incident gas atoms are trapped in the attractive potential well, and once trapped they can move along the surface by diffusion. The adsorbed species may desorb from the surface if sufficient energy is imparted to it at a given surface site to overcome the attractive surface forces. The types of interactions that take place between a gas atom or molecule and the surface depend on the energy of the gaseous species (kinetic or translational energy, internal energy, rotation, vibration, or electronic excitation when appropriate), the temperature, and the atomic structure of the solid surface. 

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