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arXiv:nucl-th/0502054

In-matter three-body problem

Alexander N. Kvinikhidze, Boris Blankleider

Published Feb 18, 2005• 0 citations
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Abstract

We formulate three-dimensional equations for the finite temperature in-matter three-body problem. Our approach takes into account the full infinite series for the effective pair-interaction kernel, so that all possible two-body sub-processes allowed by the underlying Hamiltonian are retained.
DOI
10.48550/arxiv.nucl-th/0502054

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The non-commutativity of the position and momentum operators is formulated as an effective potential in classical phase space and expanded as a series of successive many-body terms, with the pair term being dominant. A non-linear partial differential equation in temperature and space is given for this. The linear solution is obtained explicitly, which is valid at high and intermediate temperatures, or at low densities. An algorithm for solving the full non-linear problem is given. Symmetrization effects accounting for particle statistics are also written as a series of effective many-body potentials, of which the pair term is dominant at terrestrial densities. Casting these quantum functions as pair-wise additive, temperature-dependent, effective potentials enables the established techniques of classical statistical mechanics to be applied to quantum systems. The quantum Ornstein-Zernike equation is given as an example.