Recently, dynamical phase transitions have been identified based on the nonanalytic behavior of the Loschmidt echo in the thermodynamic limit [Heyl et al., Phys. Rev. Lett. 110, 135704 (2013)]. By introducing conditional probability amplitudes, we show how dynamical phase transitions can be further classified, both mathematically, and potentially in experiment. This leads to the definition of f...

We consider the quasiminima of the energy functional Z Ω A(x,∇u) + F (x, u) dx , where A(x,∇u) ∼ |∇u| and F is a double-well potential. We show that the Lipschitz quasiminima, which satisfy an equipartition of energy condition, possess density estimates of Caffarelli-Cordoba-type, that is, roughly speaking, the complement of their interfaces occupies a positive density portion of balls of large...

Abstract: This paper will examine recent work on the phase tranThis paper will examine recent work on the phase transitions that appear in collective behavior of insect populations. Basic models will be defined and then compared with experimental results. These results indicate that the collective behvior can be predicted without having to model the complexity of the individual biological entity.

The results concerning long range order for random colourings on planar quasi-transitive graphs will be explained and the proof will be outlined. Based on joint works with A. Sokal and J. Swart.

Phase transitions typically occur in combinatorial computational problems and have important consequences, especially with the current spread of statistical relational learning and of sequence learning methodologies. In Phase Transitions in Machine Learning the authors begin by describing in detail this phenomenon and the extensive experimental investigation that supports its presence. They the...

The scaling theory of critical phenomena has been successfully extended for classical first order transitions even though the correlation length does not diverge in these transitions. In this paper we apply the scaling ideas to quantum first order transitions. The usefulness of this approach is illustrated treating the problems of a superconductor coupled to a gauge field and of a biquadratic H...