Physics – Condensed Matter
Scientific paper
1996-01-19
Phys. Rev. E 53, 4467 (1996)
Physics
Condensed Matter
13 pages, REVTEX, no figures. Added: Erratum on orthogonality relations Eq. (4.16)
Scientific paper
10.1103/PhysRevE.53.4467
For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical particles, we exploit the fact that this method separates the problem of the potential, dealt with by the Feynman-Kac functional, from the process which gives sample paths of a non-interacting system. For motion in 1 dimension, we emphasize that the permutation symmetry of the identical particles completely determines the domain of Brownian motion and the appropriate boundary conditions: absorption for fermions, reflection for bosons. Further analysis of the sample paths for motion in 3 dimensions allows us to decompose these paths into a superposition of 1-dimensional sample paths. This reduction expresses the propagator (and consequently the energy and other thermodynamical quantities) in terms of well-behaved 1-dimensional fermion and boson diffusion processes and the Feynman-Kac functional.
Brosens F.
Devreese J. T.
Lemmens L. F.
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