I propose to develop a stochastic approach for the analysis of quantum systems that cannot be solved directly. This will involve the construction, theoretical analysis and numerical simulation of Langevin equations formulated from the Hamiltonian with few assumptions. In particular, I will use this approach to model mesoscopic transport phenomena in systems which exhibit electron-electron and electron-phonon interactions. I also expect there to be a significant cross over with the quantum state diffusion model for quantum mechanical measurement, which is relevant to the understanding of noise in quantum optics experiments. I anticipate that this model will also have consequences regarding the semiclassical theory of matrix element correlations in classically chaotic systems.
By investigating these ideas at the Universiti Paris-Sud, I would benefit from the experience of Montambaux in many body mesoscopic models, and would be in regular contact with a strong experimental mesoscopics group.