Homogeneous Paraexciton Dynamics at Ultralow Temperatures by Numerical Simulations

Abstract

This paper presents a theoretical investigation of the relaxation behavior of paraexcitons including exciton–phonon and exciton–exciton collisions as relaxation processes. Paraexcitons have been modeled as a homogeneous gas within cuprous oxide. Special care has been given to the evolution of the distribution function with low and high density of the paraexciton gas and the cooling process. The total working procedure has been described by the Boltzmann equation which is solved numerically using MATLAB. The analysis of the relaxation behavior has been done for the temperatures between 0.1 and 3 K. The numerical calculations show that for very low lattice temperatures (T ≪ 1 K), the process of thermalization is slow, and at 0.1 K, the paraexcitons might not reach the lattice temperature within their finite lifetime. For all the temperatures in the investigated range, when the paraexciton density is significantly higher than the critical density, a high peak of paraexciton occupation number at or near zero energy indicates the occurrence of Bose–Einstein condensation. Therefore, the calculations indicate that the condensation may take place.