The subgroup growth spectrum of virtually free groups

For a finitely generated group $\Gamma$ denote by $\mu(\Gamma)$ the growth coefficient of $\Gamma$, that is, the infimum over all real numbers $d$ such that $s_n(\Gamma)<n!^d$. We show that the growth coefficient of a virtually free group is always rational, and that every rational number occurs as growth coefficient of some virtually free group. Moreover, we describe an algorithm to compute $\mu$

Momentum isotropisation in random potentials

When particles are multiply scattered by a random potential, their momentum distribution becomes isotropic on average. We study this quantum dynamics numerically and with a master equation. We show how to measure the elastic scattering time as well as characteristic isotropisation times, which permit to reconstruct the scattering phase function, even in rather strong disorder.Comment: 5 pages, paper contributed to Lyon BEC 2012; v2 minor changes, version published in prin

Strong Anderson localization in cold atom quantum quenches

Signatures of strong Anderson localization in the momentum distribution of a cold atom cloud after a quantum quench are studied. We consider a quasi one-dimensional cloud initially prepared in a well defined momentum state, and expanding for some time in a disorder speckle potential. Anderson localization leads to a formation of a coherence peak in the \emph{forward} scattering direction (as opposed to the common weak localization backscattering peak). We present a microscopic, and fully time resolved description of the phenomenon, covering the entire diffusion--to--localization crossover. Our results should be observable by present day technology.Comment: 4 pages, 2 figures, published versio

Echo spectroscopy of Anderson localization

We propose a conceptually new framework to study the onset of Anderson localization in disordered systems. The idea is to expose waves propagating in a random scattering environment to a sequence of short dephasing pulses. The system responds through coherence peaks forming at specific echo times, each echo representing a particular process of quantum interference. We suggest a concrete realization for cold gases, where quantum interferences are observed in the momentum distribution of matter waves in a laser speckle potential. This defines a challenging, but arguably realistic framework promising to yield unprecedented insight into the mechanisms of Anderson localization.Comment: 14 pages, 7 figures; published versio

Spin effects in strong-field laser-electron interactions

The electron spin degree of freedom can play a significant role in relativistic scattering processes involving intense laser fields. In this contribution we discuss the influence of the electron spin on (i) Kapitza-Dirac scattering in an x-ray laser field of high intensity, (ii) photo-induced electron-positron pair production in a strong laser wave and (iii) multiphoton electron-positron pair production on an atomic nucleus. We show that in all cases under consideration the electron spin can have a characteristic impact on the process properties and their total probabilities. To this end, spin-resolved calculations based on the Dirac equation in the presence of an intense laser field are performed. The predictions from Dirac theory are also compared with the corresponding results from the Klein-Gordon equation.Comment: 9 pages, 6 figure

SAFT-γ force field for the simulation of molecular fluids: 4. A single-site coarse-grained model of water applicable over a wide temperature range

In this work, we develop coarse-grained (CG) force fields for water, where the effective CG intermolecular interactions between particles are estimated from an accurate description of the macroscopic experimental vapour-liquid equilibria data by means of a molecular-based equation of state. The statistical associating fluid theory for Mie (generalised Lennard-Jones) potentials of variable range (SAFT-VR Mie) is used to parameterise spherically symmetrical (isotropic) force fields for water. The resulting SAFT-γ CG models are based on the Mie (8-6) form with size and energy parameters that are temperature dependent; the latter dependence is a consequence of the angle averaging of the directional polar interactions present in water. At the simplest level of CG where a water molecule is represented as a single bead, it is well known that an isotropic potential cannot be used to accurately reproduce all of the thermodynamic properties of water simultaneously. In order to address this deficiency, we propose two CG potential models of water based on a faithful description of different target properties over a wide range of temperatures: our CGW1-vle model is parameterised to match the saturated-liquid density and vapour pressure; our other CGW1-ift model is parameterised to match the saturated-liquid density and vapour-liquid interfacial tension. A higher level of CG corresponding to two water molecules per CG bead is also considered: the corresponding CGW2-bio model is developed to reproduce the saturated-liquid density and vapour-liquid interfacial tension in the physiological temperature range, and is particularly suitable for the large-scale simulation of bio-molecular systems. A critical comparison of the phase equilibrium and transport properties of the proposed force fields is made with the more traditional atomistic models

Electron-magnon scattering in elementary ferromagnets from first principles: lifetime broadening and band anomalies

We study the electron-magnon scattering in bulk Fe, Co, and Ni within the framework of many-body perturbation theory implemented in the full-potential linearized augmented-plane-wave method. To this end, a $\mathbf{k}$-dependent self-energy ($GT$ self-energy) describing the scattering of electrons and magnons is constructed from the solution of a Bethe-Salpeter equation for the two-particle (electron-hole) Green function, in which single-particle Stoner and collective spin-wave excitations (magnons) are treated on the same footing. Partial self-consistency is achieved by the alignment of the chemical potentials. The resulting renormalized electronic band structures exhibit strong spin-dependent lifetime effects close to the Fermi energy, which are strongest in Fe. The renormalization can give rise to a loss of quasiparticle character close to the Fermi energy, which we attribute to electron scattering with spatially extended spin waves. This scattering is also responsible for dispersion anomalies in conduction bands of iron and for the formation of satellite bands in nickel. Furthermore, we find a band anomaly at a binding energy of 1.5~eV in iron, which results from a coupling of the quasihole with single-particle excitations that form a peak in the Stoner continuum. This band anomaly was recently observed in photoemission experiments. On the theory side, we show that the contribution of the Goldstone mode to the $GT$ self-energy is expected to (nearly) vanish in the long-wavelength limit. We also present an in-depth discussion about the possible violation of causality when an incomplete subset of self-energy diagrams is chosen

Factorization in hard diffraction

In this talk, I reviewed the role of factorization in diffraction hard scattering.Comment: Talk presented at the Ringberg Workshop on ``New Trends in HERA Physics 2001''. 10 pages, 6 postscript figures. Misprints correcte