The Role of Inequalities in Many-Body System Analysis
Jerome K Percus
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.