Relationship between a Non-Markovian Process and Fokker-Planck Equation

We demonstrate the equivalence of a non-Markovian evolution equation with a linear memory-coupling and a Fokker-Planck equation (FPE). In case the feedback term offers a direct and permanent coupling of the current probability density to an initial distribution, the corresponding FPE offers a non-trivial drift term depending itself on the diffusion parameter. As the consequence the deterministic part of the underlying Langevin equation is likewise determined by the noise strength of the stochastic part. This memory induced stochastic behavior is discussed for different, but representative initial distributions. The analytical calculations are supported by numerical results. © 2006 Elsevier B.V. All rights reserved.The authors (S.T. and K.Z.) acknowledge support by the DFG (SFB 418) as well as by DAAD (S. Tatur)

Strong exciton-plasmon coupling in semiconducting carbon nanotubes

We study theoretically the interactions of excitonic states with surface electromagnetic modes of small-diameter (~1 nm) semiconducting single-walled carbon nanotubes. We show that these interactions can result in strong exciton-surface-plasmon coupling. The exciton absorption line shape exhibits Rabi splitting ~0.1 eV as the exciton energy is tuned to the nearest interband surface plasmon resonance of the nanotube. We also show that the quantum confined Stark effect may be used as a tool to control the exciton binding energy and the nanotube band gap in carbon nanotubes in order, e.g., to bring the exciton total energy in resonance with the nearest interband plasmon mode. The exciton-plasmon Rabi splitting we predict here for an individual carbon nanotube is close in its magnitude to that previously reported for hybrid plasmonic nanostructures artificially fabricated of organic semiconductors on metallic films. We expect this effect to open up paths to new tunable optoelectronic device applications of semiconducting carbon nanotubes.Comment: 22 pages, 8 figures, accepted for PR