A new quantum model for Ohmic dissipation

Wilkinson, Michael (2001). A new quantum model for Ohmic dissipation. Journal of Physics: Condensed Matter, 13 pp. 8087–8103.

DOI: https://doi.org/10.1088/0953-8984/13/35/315

Abstract

This paper discusses a model for dissipation in electrical conductors, in which a time-dependent flux X(t) is threaded through a loop. The rate of dissipation is proportional to a constant D_E characterising the diffusion of single particle energies and Ohmic dissipation occurs when D_E is proportional to $\dot$ X^2. The diffusion constant D_E is investigated for a random matrix model and compared with the predictions of the Kubo-Greenwood formula. The results agree with the Kubo-Greenwwod formula in a physically significant regime where other models do not show agreement. Numerical experiments also identified another regime of this model which exhibits Ohmic dissipation, with a conductance which does not agree with the Kubo-Greenwood formula.