Spectrum of certain nonself-adjoint operators and solutions of langevin equations with complex drift.

As part of a program to evaluate expectations in complex distributions by long-term averages of solutions to Langevin equations with complex drift, a simple one-dimensional example is examined in some detail. The validity and rate of convergence of this scheme depends on the spectrum of an associated nonself-adjoint Hamiltonian which is found numerically. In the regime where the stochastic evaluation should be accurate numerical solution of the Langevin equation shows this to be the case.