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Stochastic extension of mean field theories

par Mai Seve-Dinh - 12 octobre 2014

Toutes les versions de cet article : English , français

PhD advisors : Eric Suraud & Phuong Mai Dinh

The quantum description of dissipative mechanisms in finite quantum systems is a long standing question in physics. The problem was originally pointed out by N. Bohr in the late thirties, taking as an illustration the case of a nucleus hit by a neutron, which progressively heats up the system. Since then, the question was addressed in particular in nuclear physics a few decades ago, with the results that mostly classical and/or semi-classical approaches were developed. No convincing fully quantum approach could be developed, which means that a bunch of dynamical scenarios (where quantum effects still play a role in spite of dissipative trends) cannot be addressed. Since a few years there is a strong experimental motivation on such questions, now in the case of nanostructures and molecules irradiated by possibly intense lasers. This motivated an increasing number of theoretical investigations, mostly on the basis of the well developed Time Dependent Density Functional Theory (TDDFT), which, in its standard formulations, provides a robust effective mean field description of many low-energy dynamical scenarios. Still, by construction as mean fields, these TDDFT approaches fail to account for dissipative effects leading to the (observed) electronic pattern. There is thus a crucial need for a formal and practical route to account for dissipative/thermalization features on top of quantum mean field.

We propose in this project a formalism allowing us to describe the collisional correlations responsible for thermalization effects in quantum finite systems, with applications in nanostructures and molecules. The approach is built as a stochastic extension of TDDFT in its standard effective mean field version. Correlations are treated in time dependent perturbation theory and loss of coherence is assumed at some time intervals. This allows a stochastic reduction of the correlated dynamics in terms of a stochastic ensemble of pure time dependent mean-field states. This theory was formulated long ago for density matrices but has never been applied in practical cases because of its computational involvement. With a proper reformulation of the theory in terms of wave functions, applications are now conceivable and first tests have been successfully led in a simplified 1D model. This opens up the road to a thorough investigation of the theory both from the formal and practical points of view. At formal side there remains open questions of conservation laws and on how to export the theory at moderate excitations where the stochastic reduction calls for too large samplings so that a reformulation is mandatory in terms of a mixed state rather than the previous ensemble of pure states. At practical side, the new theory needs to be tested in realistic examples and benchmarked against model cases where exact solutions can be provided. The work will consist in getting familiar with the theory and participating in either formal or numerical aspects on some specific open questions.

[1] E. Suraud, P.G. Reinhard, New J. Phys. 16 (2014) 063066

[2] N. Slama, P.-G. Reinhard, E. Suraud, Ann. Phys. (NY) 355 (2015) 182

[3] L. Lacombe, P.G. Reinhard, E. Suraud, P. M. Dinh, Ann. Phys. (NY) 373 (2016) 216

Contact : Eric Suraud and Phuong Mai Dinh