COLÓQUIO JORGE ANDRÉ SWIECA (IF-IME)
"Partial Differential Equation Approach to Solve (or Give Insight to) Problems in Statistical Mechanics"
Prof. Dr. Domingos Humberto Urbano Marchetti (IF-USP)
11 de maio, segunda-feira, Auditório Novo 1, IFUSP, às 13h30
Abstract: In this talk, the pressure of a gas of particles with a uniformly repulsive pair interaction in a finite container is shown to satisfy a "viscous" Hamilton-Jacobi (H-J) equation whose solution in power series is recursively given by the variation of constants formula. We investigate the solution of the H-J and of its Legendre transform equation by the Cauchy-Majorant method and provide a lower bound to the radius of convergence on the virial series of the gas which goes beyond the threshold established by Lagranges inversion formula. Hamilton-Jacobi inequality can be applied to dominate the RG flow equation for a d-dimensional hard-core lattice gas interacting through an attractive Yukawa-Kac potential up to the mean field limit, answering a problem proposed by Kac, Uhlenbeck and Hemmer.
