Virial inversion and density functionals |
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Institution: | 1. Mathematisches Institut, Ludwig-Maximilians-Universität, 80333 München, Germany;2. Munich Center for Quantum Science and Technology (MCQST), Schellingstr. 4, 80799 München, Germany;3. Dipartimento di Ingegneria e Scienze dell''Informazione e Matematica, Università degli Studi dell''Aquila, 67100 L''Aquila, Italy;4. Department of Mathematics and Statistics, University of Reading, Reading RG6 6AX, UK |
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Abstract: | We prove a novel inversion theorem for functionals given as power series in infinite-dimensional spaces. This provides a rigorous framework to prove convergence of density functionals for inhomogeneous systems with applications in classical density function theory, liquid crystals, molecules with various shapes or other internal degrees of freedom. The key technical tool is the representation of the inverse via a fixed point equation and a combinatorial identity for trees, which allows us to obtain convergence estimates in situations where Banach inversion fails. |
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Keywords: | Cluster and virial expansions Density functional theory Holomorphic functions in Banach spaces |
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