Monte-Carlo algorithm for sampling the thermodynamic properties of the 1D Bose gas at finite temperature

Project level: Honours, Summer

The stochastic Gross-Pitaevskii formalism can sample the grand-canonical ensemble for the interacting Bose gas by assuming the ergodic hypothesis that time evolution fairly samples the phase space of the system. However, solving a differential equation in time to sample a thermal density matrix is somewhat inefficient.  This project aims to develop a Monte-Carlo algorithm making use of the SGPE approximation that will be much more efficient, and allow for the calculation of some non-local correlation functions that are beyond the reach of current techniques.