Ph D in physics - Path integral computations of transport properties in solids

About 40 years ago, the path integral formulation of quantum mechanics due to Feynman was turned into a very efficient scheme for simula7ng numerically quantum systems at finite temperature. In this scheme, every quantum par7cle is represented as a ring polymercomposed of P “beads” connected by “springs” of stiffness 2π√P/(βh). The mappingbecomes exact in the limit of a large number of beads. The system of ring polymers can besimulated using classical Monte Carlo or Molecular dynamics methods, and the sampling of its phase space gives a relatively straighJorward access to all thermodynamic properties ofthe quantum system at finite temperature.

The determina7on of transport properties (e.g. diffusion, heat or electrical conductivity) ismuch more tricky. Indeed, transport coefficients are determined by time dependentcorrelation functions, which are not directly accessible within the mapping described above.

However, correlation functions can be obtained in imaginary time using the path integralmethod. The imaginary time correlation function can then be transformed to real time,however this transformation requires computations with a very good accuracy.

The “Heatflow” project supported by ANR involves three scientists based in Grenoble (Jean-Louis Barrat, Markus Holzmann, Stefano Mossa) and will attempt to carry out this program for calculating heat conductivity of solids. Although it is well known that quantum effects are important for thermal properties even at intermediate temperature, no exact scheme ipresently available to compute them for insulating solids. Such an exact scheme would allow one to investigate long standing problems such as the thermal anomalies of amorphous solids at low temperature, and be of technological importance for example for thermoelectric materials.

Within this project, the PHD student will work together with a postdoc and the three senior sciantists on the development of path integral computations on simple model solids, and its application to th ecomputation of heat conductivity in crystals and disordered systems.