On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction

In the mean-field limit the dynamics of a quantum Bose gas is described by a Hartree equation. We present a simple method for proving the convergence of the microscopic quantum dynamics to the Hartree dynamics when the number of particles becomes large and the strength of the two-body potential tends to 0 like the inverse of the particle number. Our method is applicable for a class of singular interaction potentials including the Coulomb potential. We prove and state our main result for the Heisenberg-picture dynamics of "observables", thus avoiding the use of coherent states. Our formulation shows that the mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato smoothing estimate (Lemma 6.1

On Blowup for time-dependent generalized Hartree-Fock equations

We prove finite-time blowup for spherically symmetric and negative energy solutions of Hartree-Fock and Hartree-Fock-Bogoliubov type equations, which describe the evolution of attractive fermionic systems (e. g. white dwarfs). Our main results are twofold: First, we extend the recent blowup result of [Hainzl and Schlein, Comm. Math. Phys. \textbf{287} (2009), 705--714] to Hartree-Fock equations with infinite rank solutions and a general class of Newtonian type interactions. Second, we show the existence of finite-time blowup for spherically symmetric solutions of a Hartree-Fock-Bogoliubov model, where an angular momentum cutoff is introduced. We also explain the key difficulties encountered in the full Hartree-Fock-Bogoliubov theory.Comment: 24 page

Kosterlitz-Thouless Transition Line for the Two Dimensional Coulomb Gas

With a rigorous renormalization group approach, we study the pressure of the two dimensional Coulomb Gas along a small piece of the Kosterlitz-Thouless transition line, i.e. the boundary of the dipole region in the activity-temperature phase-space.Comment: 61 pages, 2 figure

Three-dimensional dynamic MR-hysterosalpingography; a new, low invasive, radiation-free and less painful radiological approach to female infertility

BACKGROUND: The purpose of this study was to propose a new method for imaging the uterine cavity and Fallopian tube patency by three-dimensional dynamic magnetic resonance hysterosalpingography (3D dMR-HSG) and to analyse if, by using a higher viscosity contrast solution, direct visualization of the Fallopian tubes may be achieved by this new technique. METHODS: 10 consecutive infertile women underwent 3D dMR-HSG and conventional HSG as gold standard. 3D dMR-HSG consisted of injection of 20 ml of a gadolinium-polyvidone solution into the uterine cavity while acquiring five consecutive three-dimensional (3D) T1-weighted MR-sequences. RESULTS: In three patients the catheter became dislodged during 3D dMR-HSG. However, in one of these patients the examination was still partially diagnostic. Imaging findings of 3D dMR-HSG showed good correlation with conventional hysterosalpingography and allowed 3D imaging of the uterine cavity and of Fallopian tube patency in 8/10 patients and direct visualization of the Fallopian tubes in 5/7 patients. CONCLUSION: 3D dMR-HSG represents a new and promising imaging approach to female infertility causing less pain and avoiding exposure of the ovaries to ionizing radiation. By using a higher viscosity MR-contrast agent it allows not only visualization of uterine cavity and Fallopian tube patency but also direct visualization of Fallopian tube

Localization criteria for Anderson models on locally finite graphs

We prove spectral and dynamical localization for Anderson models on locally finite graphs using the fractional moment method. Our theorems extend earlier results on localization for the Anderson model on \ZZ^d. We establish geometric assumptions for the underlying graph such that localization can be proven in the case of sufficiently large disorder

Universality Class of O(N)O(N) Models

We point out that existing numerical data on the correlation length and magnetic susceptibility suggest that the two dimensional $O(3)$ model with standard action has critical exponent $\eta=1/4$, which is inconsistent with asymptotic freedom. This value of $\eta$ is also different from the one of the Wess-Zumino-Novikov-Witten model that is supposed to correspond to the $O(3)$ model at $\theta=\pi$.Comment: 8 pages, with 3 figures included, postscript. An error concerning the errors has been correcte

Towards a construction of inclusive collision cross-sections in the massless Nelson model

The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field theory. Relying on these insights, we take first steps towards a non-perturbative construction of inclusive collision cross-sections in the massless Nelson model. We show that our proposal is consistent with the standard scattering theory in the absence of the infrared problem and discuss its status in the infrared-singular case.Comment: 23 pages, LaTeX. As appeared in Ann. Henri Poincar\'

Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method

A technically convenient signature of Anderson localization is exponential decay of the fractional moments of the Green function within appropriate energy ranges. We consider a random Hamiltonian on a lattice whose randomness is generated by the sign-indefinite single-site potential, which is however sign-definite at the boundary of its support. For this class of Anderson operators we establish a finite-volume criterion which implies that above mentioned the fractional moment decay property holds. This constructive criterion is satisfied at typical perturbative regimes, e. g. at spectral boundaries which satisfy 'Lifshitz tail estimates' on the density of states and for sufficiently strong disorder. We also show how the fractional moment method facilitates the proof of exponential (spectral) localization for such random potentials.Comment: 29 pages, 1 figure, to appear in AH

Fock Representations of Quantum Fields with Generalized Statistic

We develop a rigorous framework for constructing Fock representations of quantum fields obeying generalized statistics associated with certain solutions of the spectral quantum Yang-Baxter equation. The main features of these representations are investigated. Various aspects of the underlying mathematical structure are illustrated by means of explicit examples.Comment: 26 pages, Te

Scattering States of Plektons (PARTICLES with Braid Group Statistics) in 2+1 Dimensional Quantum Field Theory

A Haag-Ruelle scattering theory for particles with braid group statistics is developed, and the arising structure of the Hilbert space of multiparticle states is analyzed.Comment: 18 pages, LATEX, DAMTP-94-9