Application of Graphics Processing Units (GPUs) to the Study of Non-linear Dynamics of the Exciton Bose-Einstein Condensate in a Semiconductor Quantum Well

In this paper, we explore the use of Graphics Processing Units (GPUs) to solve numerically the nonlinear Gross-Pitaevskii equation with an external potential. Our implementation uses NVIDIA's Compute Unified Device Architecture (CUDA) programming paradigm and demonstrates a speedup of 190x on an NVIDIA Tesla C2050 (Fermi) GPU compared to an optimized software implementation on a single-core of an Intel Xeon 5500-series processor. We apply the developed technique to the study of Bose-Einstein condensation (BEC) of excitons in semiconductor nanostructures. The technique is also applicable to the studies of atomic condensates, quantized vortices in quantum fluids, propagation of light pulses in optical wave guides, and ocean wave dynamics.