Analytical Results on Disorder effects on Polaritons and Barrier Crossing Problems

Abstract

Disorder plays a significant role in the study of numerous fields of research in chemistry. Whether it is a more that 80 years old classic problem like Kramers’ escape rate or the current interest in polaritons, disorder needs to be accounted in realistic modelling of systems. Recently, modifying chemistry by using setups like Fabry-Perot cavity has been attracting attention of chemists experimentally and theoretically. Theoretical models analytically solved so far do not account for the disorder in system. We analytically solve for the most used Tavis-Cumming Hamiltonian but with disorder. We report the effects of disorder on observables like the energies of polaritonic states, the line-shape of the spectra to name a few. Another problem for which we provide analytical results is the barrier crossing problem for a particle experiencing non-Gaussian noise. For such a system, the primary observation we report is that the rate of escape depends on the full shape of the potential energy and not just on the barrier height.