Virial inversion and density functionals. (English) Zbl 1509.82009
Summary: 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.
MSC:
| 82B05 | Classical equilibrium statistical mechanics (general) |
| 82D15 | Statistical mechanics of liquids |
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
| 82M36 | Computational density functional analysis in statistical mechanics |
| 47J07 | Abstract inverse mapping and implicit function theorems involving nonlinear operators |
| 05C05 | Trees |
Keywords:
cluster and virial expansions; density functional theory; holomorphic functions in Banach spacesReferences:
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