LEMMENS4) (a), J. T. DEVBEESE~) (b), and E". BROSENS (a) Using a canonical transformation the Hamiltonian of a gas of interacting polarons is studied. After elimination of the phonons the reduced Hamiltonian describes a system of charged particles interacting through a n effective interparticle potential. The Hartree-Fock ground state of the reduced system is analysed.Mit einer kanonischen Transformation wird der Hamiltonian eines Gases wechselwirkender Polaronen untersucht. Nach der Eliminierung der Phononen beschreibt der reduzierte Hamiltonian ein System von geladenen Teilchen, die iiber ein effektives lnterteilchenpotential wechselwirken. Der Hartree-Fock-Qrundzustand des reduzierten Systems wird analysiert. l) Universiteitsplein 1,
A generalization of symmetrized density matrices in combination with the technique of generating functions allows one to calculate the partition function of identical particles in a parabolic confining well. Harmonic two-body interactions ͑repulsive or attractive͒ are taken into account. Also the influence of a homogeneous magnetic field, introducing anisotropy in the model, is examined. Although the theory is developed for fermions and bosons, special attention is paid to the thermodynamic properties of bosons and their condensation.
Two basic correlation functions are calculated for a model of N harmonically interacting identical particles in a parabolic potential well. The density and the pair correlation function of the model are investigated for the boson case. The dependence of these static response properties on the complete range of the temperature and of the number of particles is obtained. The calculation technique is based on the path integral approach of symmetrized density matrices for identical particles in a parabolic confining well. ͓S1063-651X͑97͒14306-9͔
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.
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