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Absence of diffusion in the Anderson tight binding model for large disorder or low energy
We prove that the Green's function of the Anderson tight binding Hamiltonian decays exponentially fast at long distances on ℤv, with probability 1. We must assume that either the disorder is large orExpand
Spectral Analysis for Systems of Atoms and Molecules Coupled to the Quantized Radiation Field
Abstract:We consider systems of static nuclei and electrons – atoms and molecules – coupled to the quantized radiation field. The interactions between electrons and the soft modes of the quantizedExpand
Infrared bounds, phase transitions and continuous symmetry breaking
We present a new method for rigorously proving the existence of phase transitions. In particular, we prove that phase transitions occur in (φ·φ)32 quantum field theories and classical, isotropicExpand
Operator algebras and conformal field theory
We define and study two-dimensional, chiral conformal field theory by the methods of algebraic field theory. We start by characterizing the vacuum sectors of such theories and show that, under veryExpand
Solitary Wave Dynamics in an External Potential
We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger equations with an external potential. The equations have the feature that in the absence of the externalExpand
The random walk representation of classical spin systems and correlation inequalities
Ferromagnetic lattice spin systems can be expressed as gases of random walks interacting via a soft core repulsion. By using a mixed spinrandom walk representation we present a unified approach toExpand
The Kosterlitz-Thouless transition in two-dimensional Abelian spin systems and the Coulomb gas
We rigorously establish the existence of a Kosterlitz-Thouless transition in the rotator, the Villain, the solid-on-solid, and the ℤn models, forn large enough, and in the Coulomb lattice gas, in twoExpand
Self-consistent evolution of magnetic fields and chiral asymmetry in the early universe.
It is shown that the evolution of magnetic fields in a primordial plasma, filled with standard model particles at temperatures T≳10 MeV, is strongly affected by the chiral anomaly, which may strongly affect many processes in the early Universe. Expand
The phase transition in the one-dimensional Ising Model with 1/r2 interaction energy
We prove the existence of a spontaneous magnetization at low temperature for the one-dimensional Ising Model with 1/r2 interaction energy.
Existence of Dressed One Electron States in a Class of Persistent Models
In this paper the dynamics of a class of simple models (so called persistent models) including Nelson's model is studied. These models describe conserved, non relativistic, scalar electronsExpand