seminar FisMat

FisMat Seminar, Junio 22, 2022, 11:30

Speaker: Walter Alberto de Siqueira Pedra

Title: Equilibrium States of Many-Body (Fermion) Systems with Long-Range Interactions

Place: Pontificia Universidad Católica, Facultad de Matemáticas, Campus San Joaquin, Sala 1

We present our results on infinite volume equilibrium states of many-fermion systems on the lattice with mean-field interactions (“Non-cooperative Equilibria of Fermi Systems with Long-Range Interactions”, Memoirs of the AMS, 2013) in relation to our recent contributions on Kac limits for equilibrium states (“From Short-Range to Mean-Field Models in Quantum Lattices”, arXiv:2203.01021): We recently proved that under very general conditions such long-range limits of equilibria of short-range models are equilibria of some naturally associated mean-field model. This is reminiscent of well-known works of Penrose and Lebowitz (1966, classical case), and Lieb (1971, quantum), on the Kac limit of the pressure in the thermodynamic limit.