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Long Range behavior of van der Waals forces

Ioannis Anapolitanos
(TU Stuttgart)
Analysis Seminar
Thursday, 14 November, 2013, at 16:15-17:15, in Aud. D3 (1531-215)
The van der Waals forces, which are forces between neutral atoms and molecules, play an important role in physics  (e.g. in phase transitions), material sciences and biology. These forces are of quantum nature and it is long being conjectured and experimentally verified that they have universal  behavior at large separations: they are attractive and decay as the inverse sixth power of the pairwise distance between  the atoms or molecules. 

The goal of this talk will be to prove the van der Waals law for a system of atoms, under some assumptions  which are verified for hydrogen atoms, and are physically expected for other systems of atoms as well.

 With an informal definition of the cohesive energy W(y), y = (y_1, ..., y_M)  between   M atoms as the difference between the lowest (ground state) energy, E(y), of the atoms  with their nuclei fixed at the positions y_1, ..., y_M and the sum, E_1+...E_M,  of lowest (ground state) energies of the non-interacting atoms, we show that for | y_i - y_j | large enough,  the cohesive energy W(y) is a sum over c_{ij}  |y_i-y_j|^{-6} up to an error, which is small at large inter particle distance.  Here c_{ij} are in principle computable positive constants depending on the nature of the atoms  i and j.

The talk is based on two papers, the first of which is a joint work with Israel Michael Sigal. 
Contact person: Jacob Schach Møller