Thermal Ionization

In the context of an idealized model describing an atom coupled to black-body radiation at a sufficiently high positive temperature, we show that the atom will end up being ionized in the limit of large times. Mathematically, this is translated into the statement that the coupled system does not have any time-translation invariant state of positive (asymptotic) temperature, and that the expectation value of an arbitrary finite-dimensional projection in an arbitrary initial state of positive (asymptotic) temperature tends to zero, as time tends to infinity. These results are formulated within the general framework of $W^*$-dynamical systems, and the proofs are based on Mourre's theory of positive commutators and a new virial theorem. Results on the so-called standard form of a von Neumann algebra play an important role in our analysis

Asymptotic completeness in dissipative scattering theory

We consider an abstract pseudo-Hamiltonian for the nuclear optical model, given by a dissipative operator of the form $H = H_V - i C^* C$, where $H_V = H_0 + V$ is self-adjoint and $C$ is a bounded operator. We study the wave operators associated to $H$ and $H_0$. We prove that they are asymptotically complete if and only if $H$ does not have spectral singularities on the real axis. For Schr\"odinger operators, the spectral singularities correspond to real resonances.Comment: 48 page

Gauge Invariance and Anomalies in Condensed Matter Physics

This paper begins with a summary of a powerful formalism for the study of electronic states in condensed matter physics called "Gauge Theory of States/Phases of Matter." The chiral anomaly, which plays quite a prominent role in that formalism, is recalled. I then sketch an application of the chiral anomaly in 1+1 dimensions to quantum wires. Subsequently, some elements of the quantum Hall effect in two-dimensional (2D) gapped ("incompressible") electron liquids are reviewed. In particular, I discuss the role of anomalous chiral edge currents and of anomaly inflow in 2D gapped electron liquids with explicitly or spontaneously broken time reversal, i.e., in Hall- and Chern insulators. The topological Chern-Simons action yielding the transport equations valid in the bulk of such systems and the associated anomalous edge action are derived. The results of a general classification of "abelian" Hall insulators are outlined. After some remarks on induced Chern-Simons actions, I sketch results on certain 2D chiral photonic wave guides. I then continue with an analysis of chiral edge spin-currents and the bulk response equations in time-reversal invariant 2D topological insulators of electron gases with spin-orbit interactions. The "chiral magnetic effect" in 3D systems and axion-electrodynamics are reviewed next. This prepares the ground for an outline of a general theory of 3D topological insulators, including "axionic insulators". Some remarks on Weyl semi-metals, which exhibit the chiral magnetic effect, and on Mott transitions in 3D systems with dynamical axion-like degrees of freedom conclude this review.}Comment: 4 figures, 42 pages; will appear in 'Journal of Mathematical Physics' (AIP publishing

After the Dark Ages

After recalling some puzzles in cosmology and briefly reviewing the Friedmann-Lema\^itre cosmos a simple unified model of the ``Dark Sector'' is described. This model involves a scalar field and a pseudo-scalar axion field that give rise to Dark Energy in the form of ``quintessence'' and to ``fuzzy'' Dark Matter, respectively. Predictions of the model concerning the late-time evolution of the Universe and possible implications for the problem of the observed Matter-Antimatter Asymmetry in the Universe are sketched.Comment: 17 pages (including bibliography), no figure