Courant Institute and Physics Department, New York University

Mercredi, 2 novembre 2011,

11 h 00 Bibliothèque 4e étage,

tour 12 - 13, site Jussieu

Complex problems of interest are not going to be solved exactly. Besides, what we really want are results at decent resolution that we know how to sequentially improve. Inequalities, bounding the level of uncertainty, are arguably the theoretical tools of choice, unfamiliar though they may be.

Systems of many indistinguishable particles can generally be cast in a form involving in principle known few-particle intractions,and available information via expectations of few-particle observables. Our objective is to carry out analysis of such systems in terms of these expectations alone, and successive restriction by inequalities is the tool of choice.

We start with the ground state of a classical lattice gas analyzed via low order distributions, and proceed quickly to that of fermion systems via reduced density matrices. Traditional inequalities take advantage of the field picture of a fluid. We show how focussing as well on individual particles is a powerful adjunct and use it to derive a known integral equation approximation for classical fluids in thermal equilibrium. We conclude by extending the analysis to fermion fluids, of course with open questions remaining.