On Three Levels

This volume contains the proceedings of a five-day NATO Advanced Research Workshop "On Three Levels, the mathematical physics of micro-, meso-, and macro phenomena," conducted from July 19 to 23 in Leuven, Belgium. The main purpose of the workshop was to bring together and to confront where relevant, classical and quantum approaches in the rigorous study of the relation between the various levels of physical description. The reader will find here discussions on a variety of topics involving a broad range of scales. For the micro-level, contributions are presented on models of reaction-diffusion pro cesses, quantum groups and quantum spin systems. The reports on quantum disorder, the quantum Hall effect, semi-classical approaches of wave mechanics and the random Schrodinger equation can be situated on the meso-level. Discussions on macroscopic quantum effects and large scale fluctuations are dealing with the macroscopic level of description. These three levels are however not independent and emphasis is put on relating these scales of description. This is especially the case for the contributions on kinetic and hydrodynamicallimits, the discussions on large deviations and the strong and weak coupling limits. The advisory board was composed of J.L. Lebowitz, J.T. Lewis and E.H. Lieb. The organizing committee was formed by Ph.A. Martin, G.L. Sewell, E.R. Speer and A.

Proceedings of a NATO ARW held in Leuven, Belgium, July 19-23, 1993

Quantum kinetic equations.- Microscopic derivation of hydrodynamics with phase transition in a plasma model.- Ferromagnetism in itinerant electron systems: rigorous examples from flat-band Hubbard models.- Homogeneity in the ground state of the two-dimensional Falicov-Kimball model.- Diffusive limit of the asymmetric simple exclusion: The Navier-Stokes correction.- Weak coupling limit: Feynman diagrams.- Limit laws for recurrence times in expanding maps of an interval.- Stochastic geometric aspects of some quantum spin chains.- The two species totally asymmetric simple exclusion process.- How to reconstruct a heat bath.- Interacting particle systems on non-commutative spaces.- Non-self-averaging effects in sums of random variables, spin glasses, random maps and random walks.- Quantum adiabatic evolution.- Semi-classical inelastic S-matrix for one-dimensional N-states systems.- Gibbsian versus non-Gibbsian measures: some results and some questions in renormalization group theory and stochastic dynamics.- Stabilities and instabilities in classical lattice gas models without periodic ground states.- One-dimensional anomaly of the Fermi surface.- Quantum fluctuation limit: Examples from solid state physics.- Large deviations and the thermodynamic formalism: A new proof of the equivalence of ensembles.- Finitely correlated pure states.- Stationary states of Hamiltonian systems with noise.- Stochastic regularization of coherent-state path integrals and quantum Hall effect.- An ADE- O classification of minimal incompressible quantum Hall fluids.- Simple random walks: New developments.- Symmmetry breaking and long range order in Heisenberg antiferromagnets.- Integrable s = 1/2 quantum spin chains with short-range exchange.- Who is afraid of Griffiths' singularities?.- Microspectral properties of crystals and their band structure.- Stochastically forced Burgers equation.- Glauber evolution for Kac potentials. Analysis of critical fluctuations: convergence to a nonlinear stochastic PDE.- Local structure of interfaces in a Kawasaki + Glauber particle model.- Quantum chaos, fractal spectra and atomic stabilization.- Statistical properties of random banded matrices: Analytical results.- On the Wulff construction as a problem of equivalence of statistical ensembles.- Scaling profiles of a spreading drop from Langevin or Monte-Carlo dynamics.- Rigorous calculation of collective excitations in a mean field model.- The fluid-dynamical limit for the BBGKY hierarchy of a discrete velocity model.- Isospectral deformation of discrete random Laplacians.- Scattering and the role of operators in Bohmian mechanics.- Towards the Euclidean formulation of quantum statistical mechanics.- Large deviations in the spherical model.- Entropy density and the split property.- Perturbations of quantum canonical relations and Q-independence.- The spectrum of the spin-boson model.- Some results on the projected two-dimensional Ising model.- The second virial coefficient for quantum-mechanical sticky spheres.- Bethe-Ansatz solution of a modified SU(3)-XXZ model.- The quantum mean field state as a limit of canonical states: Maxwell-Boltzmann statistics.- Multifractal properties of discrete stochastic mappings.- Gibbs states of the Chern-Simons charged particle system in the mean-field type limit.- Rigorous Bethe Ansatz for the nonlinear Schrodinger model.- Flat nonregular states on Weyl algebras.- Second virial coefficient for one-dimensional systems.- Self-adjointness and the existence of deterministic trajectories in quantum theory.- An application of the Maes-Shlosman constructive criteria.- Brownian trapping with grouped traps.- Local thermodynamic equilibrium and continuous media: A programme.- Stochastic model of a quantum diffusion-reaction process.- Crystalisation of itinerant electrons.- Molecular chain: dynamical variables, quantization and statistical mechanics.- Quasiparticle's spin and fractional statistics in the fractional quantum Hall effect.- Participants.