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Sum rules and exact relations for quantal Coulomb systems
Author(s) -
Adamyan V.M.,
Tkachenko I.M.
Publication year - 2003
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.200310020
Subject(s) - complex plane , function (biology) , holomorphic function , coulomb , simple (philosophy) , analytic function , plane (geometry) , physics , class (philosophy) , mathematical analysis , mathematics , quantum mechanics , computer science , electron , philosophy , geometry , epistemology , evolutionary biology , artificial intelligence , biology
A complex response function describing a reaction of a multi‐particle system to a weak alternating external field is the boundary value of a Nevanlinna class function (i.e. a holomorphic function with non‐negative imaginary part in the upper half‐plane). Attempts of direct calculations of response functions based on standard approximations of the kinetic theory for real Coulomb condensed systems often result in considerable discrepancies with experiments and computer simulations. At the same time a relatively simple approach using only the exact values of leading asymptotic terms of the response function permits to restrict essentially a subset of Nevanlinna class functions containing this response function, and in this way to obtain sufficient data to explain and predict experimental results. Mathematical details of this approach are demonstrated on an example with the response function being the (external) dynamic electrical conductivity of cold dense hydrogen‐like plasmas. In particular, the exact values of the leading terms of asymptotic expansions of the conductivity are calculated. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)