Ground States in the Spin Boson Model

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory

Uniqueness of the ground state in the Feshbach renormalization analysis

In the operator theoretic renormalization analysis introduced by Bach, Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page

Use of remote sensing for hydrological parameterisation of Alpine catchments

International audiencePhysically-based water balance models require a realistic parameterisation of land surface characteristics of a catchment. Alpine areas are very complex with strong topographically-induced gradients of environmental conditions, which makes the hydrological parameterisation of Alpine catchments difficult. Within a few kilometres the water balance of a region (mountain peak or valley) can differ completely. Hence, remote sensing is invaluable for retrieving hydrologically relevant land surface parameters. The assimilation of the retrieved information into the water balance model PROMET is demonstrated for the Toce basin in Piemonte/Northern Italy. In addition to land use, albedos and leaf area indices were derived from LANDSAT-TM imagery. Runoff, modelled by a water balance approach, agreed well with observations without calibration of the hydrological model. Keywords: PROMET, fuzzy logic based land use classification, albedo, leaf area inde

A Note on Polarization Vectors in Quantum Electrodynamics

A photon of momentum k can have only two polarization states, not three. Equivalently, one can say that the magnetic vector potential A must be divergence free in the Coulomb gauge. These facts are normally taken into account in QED by introducing two polarization vectors epsilon_\lambda(k) with lambda in {1,2}, which are orthogonal to the wave-vector k. These vectors must be very discontinuous functions of k and, consequently, their Fourier transforms have bad decay properties. Since these vectors have no physical significance there must be a way to eliminate them and their bad decay properties from the theory. We propose such a way here.Comment: 6 pages late

A finite difference solution for the cylindrical expansion of a gas cloud into vacuum

Finite difference method for solution of cylindrical expansion of gas cloud into vacuu

Ferromagnetism of the Hubbard Model at Strong Coupling in the Hartree-Fock Approximation

As a contribution to the study of Hartree-Fock theory we prove rigorously that the Hartree-Fock approximation to the ground state of the d-dimensional Hubbard model leads to saturated ferromagnetism when the particle density (more precisely, the chemical potential mu) is small and the coupling constant U is large, but finite. This ferromagnetism contradicts the known fact that there is no magnetization at low density, for any U, and thus shows that HF theory is wrong in this case. As in the usual Hartree-Fock theory we restrict attention to Slater determinants that are eigenvectors of the z-component of the total spin, {S}_z = sum_x n_{x,\uparrow} - n_{x,\downarrow}, and we find that the choice 2{S}_z = N = particle number gives the lowest energy at fixed 0 < mu < 4d.Comment: v2: Published version. 30 pages latex. Changes in title, abstract, introductio