Time-Splitting Numerical Simulator of Nonstandard GPEs and Applications

We aim to develop and release a time-splitting numerical simulator of noisy driven-dissipative Gross-Pitaevskii equations (GPE), for use in general non-Hermitian problems. Our solver correctly addresses crucial method differences that other available GPE solvers neglect, when incorporating complex potential/coefficient and added noise term components for nonstandard GPEs, such as when considering the time-dependency of the solution density. This solver has applications to any area of research which would benefit from simulations of nonstandard GPEs, which include any of the following traits: complex Laplacian term coefficients, complex potentials, complex nonlinear term coefficients, coupled components, added noise terms. Examples include simulating dynamics involving (critical) exceptional point physics and modeling (noisy) interacting condensates, which are systems proposed as a basis for unconventional computing systems. Although previous research on hybrid polariton Bose-Einstein condensate computing systems has shown promising analytical results of an advantage over traditional computing systems, because of the approximations/limitations of the methods utilized in those approaches, those results should be verified through numerical analysis.