12,259 research outputs found
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
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