Using path integrals for the propagation of light in a scattering dominated medium

Abstract

The high computational expense of simulating light through ray-tracing in large, sparsely instrumented particle detectors such as IceCube and Antares is a critical outstanding problem in particle physics. When the detector is sparsely instrumented, ray tracing is inefficient, as nearly all of these rays are either lost in the bulk of the detector due to absorption or simply fail to end on a detector. Particle astrophysics experiments face a similar problem when they simulate cosmic ray muon fluxes in their detectors. Many fields of science face calculations that involve constrained initial and final states, with stochastic processes between. Taking the case of ray-tracing of light as our example, this paper describes a new and highly computationally efficient approach to the problem. By specifying the problem as a path integral, the final state of these rays can be constrained to land on a light sensitive element. The path integral can then be efficiently sampled using Reversible Jump Markov Chain Monte-Carlo, yielding performance improvements of up to 1,000 times faster on a realistic test scenario.