München 1997 – wissenschaftliches Programm

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MP: Theoretische und Mathematische Grundlagen der Physik

MP 9: Statistische Mechanik

MP 9.3: Fachvortrag

Donnerstag, 20. März 1997, 14:40–15:00, HS 117

Variational Master Field for Large-N Interacting Matrix Models – Free Random Variables on Trial — •M. Engelhardt¹ and S. Levit² — ¹Institut für theoretische Physik, Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen — ²Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel

Matrices are said to behave as free non-commuting random variables if the action which governs their dynamics constrains only their eigenvalues, i.e. depends on traces of powers of individual matrices. The authors use recently developed mathematical techniques in combination with a standard variational principle to formulate a new variational approach for matrix models. Approximate variational solutions of interacting large-N matrix models are found using the free random matrices as the variational space. Several classes of classical and quantum mechanical matrix models with different types of interactions are considered and the variational solutions compared with exact Monte Carlo and analytical results. Impressive agreement is found in a majority of cases.

Supported in part by DFG Re 856 / 1-3

[1] M.Engelhardt and S.Levit, hep-th/9609216