Infraparticle Scattering States in Non-Relativistic QED: II. Mass Shell Properties

We study the infrared problem in the usual model of QED with non-relativistic matter. We prove spectral and regularity properties characterizing the mass shell of an electron and one-electron infraparticle states of this model. Our results are crucial for the construction of infraparticle scattering states, which are treated in a separate paper.Comment: AMS Latex, 45 pages, 2 figure

Adaiabtic theorems and reversible isothermal processes

Isothermal processes of a finitely extended, driven quantum system in contact with an infinite heat bath are studied from the point of view of quantum statistical mechanics. Notions like heat flux, work and entropy are defined for trajectories of states close to, but distinct from states of joint thermal equilibrium. A theorem characterizing reversible isothermal processes as quasi-static processes (''isothermal theorem'') is described. Corollaries concerning the changes of entropy and free energy in reversible isothermal processes and on the 0th law of thermodynamics are outlined

Polaron action for multimode dispersive phonon systems

Path-integral approach to the tight-binding polaron is extended to multiple optical phonon modes of arbitrary dispersion and polarization. The non-linear lattice effects are neglected. Only one electron band is considered. The electron-phonon interaction is of the density-displacement type, but can be of arbitrary spatial range and shape. Feynman's analytical integration of ion trajectories is performed by transforming the electron-ion forces to the basis in which the phonon dynamical matrix is diagonal. The resulting polaron action is derived for the periodic and shifted boundary conditions in imaginary time. The former can be used for calculating polaron thermodynamics while the latter for the polaron mass and spectrum. The developed formalism is the analytical basis for numerical analysis of such models by path-integral Monte Carlo methods.Comment: 9 page

Non-demolition measurements of observables with general spectra

It has recently been established that, in a non-demolition measurement of an observable $\mathcal{N}$ with a finite point spectrum, the density matrix of the system approaches an eigenstate of $\mathcal{N}$, i.e., it "purifies" over the spectrum of $\mathcal{N}$. We extend this result to observables with general spectra. It is shown that the spectral density of the state of the system converges to a delta function exponentially fast, in an appropriate sense. Furthermore, for observables with absolutely continuous spectra, we show that the spectral density approaches a Gaussian distribution over the spectrum of $\mathcal{N}$. Our methods highlight the connection between the theory of non-demolition measurements and classical estimation theory.Comment: 22 page

Stellar evolution of massive stars at very low metallicities

Recently, measurements of abundances in extremely metal poor (EMP) stars have brought new constraints on stellar evolution models. In an attempt to explain the origin of the abundances observed, we computed pre--supernova evolution models, explosion models and the related nucleosynthesis. In this paper, we start by presenting the pre-SN models of rotating single stars with metallicities ranging from solar metallicity down to almost metal free. We then review key processes in core-collapse and bounce, before we integrate them in a simplistic parameterization for 3D MHD models, which are well underway and allow one to follow the evolution of the magnetic fields during collapse and bounce. Finally, we present explosive nucleosynthesis results including neutrino interactions with matter, which are calculated using the outputs of the explosion models. The main results of the pre-SN models are the following. First, primary nitrogen is produced in large amount in models with an initial metallicity $Z=10^{-8}$. Second, at the same metallicity of $Z=10^{-8}$ and for models with an initial mass larger than about 60 Mo, rotating models may experience heavy mass loss (up to more than half of the initial mass of the star). The chemical composition of these winds can qualitatively reproduce the abundance patterns observed at the surface of carbon-rich EMP stars. Explosive nucleosynthesis including neutrino-matter interactions produce improved abundances for iron group elements, in particular for scandium and zinc. It also opens the way to a new neutrino and proton rich process ($\nu$p-process) able to contribute to the nucleosynthesis of elements with A > 64. (Abridged)Comment: 29 pages, 10 figures, Reviews of Modern Astronomy 19, proceedings for 79th Annual Scientific Meeting of the Deutsche Astronomische Gesellschaft 200

Spin - or, actually: Spin and Quantum Statistics

The history of the discovery of electron spin and the Pauli principle and the mathematics of spin and quantum statistics are reviewed. Pauli's theory of the spinning electron and some of its many applications in mathematics and physics are considered in more detail. The role of the fact that the tree-level gyromagnetic factor of the electron has the value g = 2 in an analysis of stability (and instability) of matter in arbitrary external magnetic fields is highlighted. Radiative corrections and precision measurements of g are reviewed. The general connection between spin and statistics, the CPT theorem and the theory of braid statistics are described.Comment: 50 pages, no figures, seminar on "spin

On the Atomic Photoeffect in Non-relativistic QED

In this paper we present a mathematical analysis of the photoelectric effect for one-electron atoms in the framework of non-relativistic QED. We treat photo-ionization as a scattering process where in the remote past an atom in its ground state is targeted by one or several photons, while in the distant future the atom is ionized and the electron escapes to spacial infinity. Our main result shows that the ionization probability, to leading order in the fine-structure constant, $\alpha$, is correctly given by formal time-dependent perturbation theory, and, moreover, that the dipole approximation produces an error of only sub-leading order in $\alpha$. In this sense, the dipole approximation is rigorously justified.Comment: 25 page

Ellipsoidal Coulomb Crystals in a Linear Radiofrequency Trap

A static quadrupole potential breaks the cylindrical symmetry of the effective potential of a linear rf trap. For a one-component fluid plasma at low temperature, the resulting equilibrium charge distribution is predicted to be an ellipsoid. We have produced laser-cooled Be$^+$ ellipsoidal ion crystals and found good agreement between their shapes and the cold fluid prediction. In two-species mixtures, containing Be$^+$ and sympathetically cooled ions of lower mass, a sufficiently strong static quadrupole potential produces a spatial separation of the species.Comment: 4 pages, 3 figure

Multi-Particle Anderson Localisation: Induction on the Number of Particles

This paper is a follow-up of our recent papers \cite{CS08} and \cite{CS09} covering the two-particle Anderson model. Here we establish the phenomenon of Anderson localisation for a quantum $N$-particle system on a lattice $\Z^d$ with short-range interaction and in presence of an IID external potential with sufficiently regular marginal cumulative distribution function (CDF). Our main method is an adaptation of the multi-scale analysis (MSA; cf. \cite{FS}, \cite{FMSS}, \cite{DK}) to multi-particle systems, in combination with an induction on the number of particles, as was proposed in our earlier manuscript \cite{CS07}. Similar results have been recently obtained in an independent work by Aizenman and Warzel \cite{AW08}: they proposed an extension of the Fractional-Moment Method (FMM) developed earlier for single-particle models in \cite{AM93} and \cite{ASFH01} (see also references therein) which is also combined with an induction on the number of particles. An important role in our proof is played by a variant of Stollmann's eigenvalue concentration bound (cf. \cite{St00}). This result, as was proved earlier in \cite{C08}, admits a straightforward extension covering the case of multi-particle systems with correlated external random potentials: a subject of our future work. We also stress that the scheme of our proof is \textit{not} specific to lattice systems, since our main method, the MSA, admits a continuous version. A proof of multi-particle Anderson localization in continuous interacting systems with various types of external random potentials will be published in a separate papers

Orbital ordering in transition-metal compounds: I. The 120-degree model

We study the classical version of the 120-degree model. This is an attractive nearest-neighbor system in three dimensions with XY (rotor) spins and interaction such that only a particular projection of the spins gets coupled in each coordinate direction. Although the Hamiltonian has only discrete symmetries, it turns out that every constant field is a ground state. Employing a combination of spin-wave and contour arguments we establish the existence of long-range order at low temperatures. This suggests a mechanism for a type of ordering in certain models of transition-metal compounds where the very existence of long-range order has heretofore been a matter of some controversy.Comment: 40 pages, 1 eps fig; a revised version correcting a bunch of small error