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The evaluation of Feynman graphs for a (2+1)-dimensional nonrelativistic electron gas

โœ Scribed by R. Sinclair

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
656 KB
Volume
81
Category
Article
ISSN
0010-4655

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โœฆ Synopsis

Two-loop nonrelativistic Feynman graphs from many-body physics at zero temperature in 2 + 1 dimensions are evaluated using a combination of symbolic and numerical methods, reducing error, and allowing a greater choice of which numerical methods are in fact applied. The functions to be integrated numerically are nonzero over only small subintervals of their domain of integration. For reasons of efficiency, the code generated for the integration of such "sparse integrands" must provide not only function values, but also a description of the relevant subintervals.

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We study the effects of screening on the binding energy of positively and negatively charged impurities in the quasi-one-dimensional electron gas. We assume a parabolic confinement for the electron gas. Many-body effects beyond the random-phase approximation and the valley degeneracy are taken into