We investigate the effects of interactions and disorder in open quantum systems.

Past Projects:
(1) Using a mean-field master equation approach we calculate the effects of disorder and interactions on the relaxation of interacting Two-level systems (dipolar spin-glass) near equilibrium. We found that interactions increase the relaxation rate contrary to the Electron-glass system.

(2) We derived an effective action that describes the effects of disordered Fermi liquid on the conductance of the Electron-glass system coupled to phonons. We found competing effects between the renormalization of the density of states which tends to increase the conductivity and the polaronic effect which decreases it. The total effect in a wide regime of parameters was a reduction in the conductivity as observed in experiments.

(3) We investigate the effects of corrections beyond the static (Hartree) mean-field solution on the conductance of the electron glass system. Using the $\Psi$ functional approach (a generalization of the Luttinger–Ward functional) we calculate systematically the self-energy corrections to the propagators of the model. The different contributions are (1) renormalization of the density of states, (2) renormalization of the phonon polaronic effect, (3) renormalization electron-hole interactions (ladder resummation) (4) The electronic polaronic effect.
Contributions #1 - #3 seem to contribute to the increase of the transition rate while contribution #4 might decrease or increase decreases it.
It is then left to estimate qualitatively if the overall effect increases or decreases the conductivity.

Thesis link:
http://dx.doi.org/10.13140/RG.2.2.26895.92320

Secondary project:
Localization-Delocalization and Damped-Overdamped transitions of the Spin-boson model at finite temperature.