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SUMMARY:Virial inversion and microscopic derivation of density functionals
  - Dimitrios Tsagkarogiannis (University of L'Aquila)
DTSTART:20190619T133000Z
DTEND:20190619T141000Z
UID:TALK126529@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:We present a rigorous derivation of the free energy functional
  for<br>inhomogeneous systems\, i.e. with a density that depends on the po
 sition\,<br>orientation or other internal degrees of freedom. It can be vi
 ewed as an<br>extension of the virial inversion (developed for homogeneous
  systems) to<br>uncountably many species. The key technical tool is a comb
 inatorial identity for<br>a special type of trees which allows us to imple
 ment the inversion step as well<br>as to prove its convergence. Applicatio
 ns include classical density functional<br>theory\, Onsager&#39\;s functio
 nal for liquid crystals\, hard spheres of different sizes<br>and shapes. F
 urthermore\, the method can be generalized in order to provide<br>converge
 nce for other expansions commonly used in the liquid state theory.<br>The 
 validity is always in the gas regime\, but with the new method we improve<
 br>the original radius of convergence for the hard spheres as proved by Le
 bowitz<br>and Penrose and subsequent works. This is joint work with Sabine
  Jansen and<br>Tobias Kuna.<br>
LOCATION:Seminar Room 2\, Newton Institute
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