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Application to Multi-Mode Systems

Bryan J. Dalton, John Jeffers, Stephen Mark Barnett

Published Nov 13, 2014• 0 citations
Publisher

Abstract

Abstract This chapter presents two examples of applying phase space methods in systems where large numbers of modes may be involved, such as in fermion cases with large particle numbers. Functional Fokker–Planck equations (FFPEs) are derived directly using the field operator correspondence rules. The boson application is to colliding bosons in a trap potential, such as for Bose–Einstein condensates. FFPEs and Ito stochastic field equations (SFEs) are derived for both positive P and Wigner distribution functional cases, and expressions obtained for quantum correlation functions. The fermion application is to colliding spin-1/2 fermions in a trap potential, such as an optical lattice. FFPEs and Ito SFEs are derived for the unnormalised B distribution functional. Solutions to the Ito SFE are presented for the untrapped and optical-lattice cases. For the untrapped case with two fermions, evaluation of short-time Fock state coherences and populations gives the same result as obtained in a previous chapter.

DOI
10.1093/acprof:oso/9780199562749.003.0015

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