We study the transport properties of classical Hamiltonian models describing the motion of an unconfined particle coupled to vibrational degrees of freedom in thermal equilibrium at zero or positive temperature. We identify and discuss conditions under which, in such systems, the particle has a well-defined diffusion constant and mobility. We will in particular point out some marked differences with the situation where the particle is confined and described with a Caldeira-Leggett model. We will more specifically report on results obtained in a classical version of the Holstein molecular crystal model, speculate on their relevance in the corresponding quantum system and describe a number of open problems.
P. Lafitte et al., "Normal Transport at Positive Temperatures in Classical Hamiltonian Open Systems," Adventures in Mathematical Physics, American Mathematical Society, Jan 2007.
Keywords and Phrases
Hamiltonian Models; Thermal Equilibrium; Transport Properties
Book - Chapter
© 2007 American Mathematical Society, All rights reserved.