Exact reformulation of the bosonic many-body problem in terms of stochastic wave functions: convergence issues

Details Exact reformulation of the bosonic many-body problem in terms of stochastic wave functions: convergence issues Exact reformulation of the bosonic many-body problem in terms of stochastic wave functions: convergence issues

2002-09-05

arxiv.org/abs/cond-mat/0209135v1

Laser Physics 13, 509-516 (2003)

Physics

Condensed Matter

Soft Condensed Matter

Proceedings of the Laser Physics Workshop held in Bratislava, July 2002. Submitted to Laser Physics

Scientific paper

10.1007/s00023-003-0961-7

There exist methods to reformulate in an exact way the many-body problem of interacting bosons in terms of the stochastic evolution of single particle wave functions. For one such reformulation, the so-called simple Fock scheme, we present an elementary derivation, much simpler than the original one. Furthermore, we show that two other schemes, based on coherent states of the matter field rather than on Fock states, lead to an infinite statistical uncertainty in the continuous time limit. The simple Fock scheme is therefore, up to now, the only one that was proved to lead to a convergent Monte Carlo simulation scheme at all times.

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