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We discuss a new numerical method for the determination of excited states ofa quantum system using a generalization of the Feynman-Kac formula. The methodrelies on introducing an ensemble of non-interacting identical systems with afermionic statistics imposed on the systems as a whole, and on determining theground state of this fermionic ensemble by taking the large time limit of theEuclidean kernel. Due to the exclusion principle, the ground state of an$n$-system ensemble is realized by the set of individual systems occupyingsuccessively the $n$ lowest states, all of which can therefore be sampled inthis way. To demonstrate how the method works, we consider a one-dimensionaloscillator and a chain of harmonically coupled particles.Comment: 14 pages, Latex + 4 eps figure

Using a fermionic ensemble of systems to determine excited states