Morten Grud Rasmussen

Asymptotic Completeness in Quantum Field Theory: Translation Invariant Nelson Type Models Restricted to the Vacuum and One-Particle Sectors

Time-dependent scattering theory for a large class of translation invariant models, including the Nelson and Polaron models, restricted to the vacuum and one-particle sectors is studied. We formulate and prove asymptotic completeness for these models. The translation invariance imply that the Hamiltonians considered are fibered with respect to the total momentum. On the way to asymptotic completeness we determine the spectral structure of the fiber Hamiltonians, establish a Mourre estimate and derive a geometric asymptotic completeness statement as an intermediate step.

The translation invariant massive Nelson model: II. The continuous spectrum below the two-boson threshold

In this paper we continue the study of the energy-momentum spectrum of a class of translation invariant, linearly coupled, and massive Hamiltonians from non-relativistic quantum field theory. The class contains the Hamiltonians of E. Nelson (J Math Phys 5:1190–1197, 1964) and H. Fröhlich (Adv Phys 3:325–362, 1954). In Møller (Ann Henri Poincaré 6:1091–1135, 2005; Rev Math Phys 18:485–517, 2006) one of us previously investigated the structure of the ground state mass shell and the bottom of the continuous energy-momentum spectrum. Here we study the continuous energy-momentum spectrum itself up to the two-boson threshold, the threshold for energetic support of two-boson scattering states. We prove that non-threshold embedded mass shells have finite multiplicity and can accumulate only at thresholds. We furthermore establish the non-existence of singular continuous energy-momentum spectrum. Our results hold true for all values of the particle-field coupling strength but only below the two-boson threshold. The proof revolves around the construction of a certain relative velocity vector field used to construct a conjugate operator in the sense of Mourre.

REST based service composition: Exemplified in a care network scenario

This paper presents an ongoing work developing and testing a Service Composition framework based upon the REST architecture named SECREST. A minimalistic approach have been favored instead of a creating a complete infrastructure. One focus has been on the systems interaction model. Indeed, an aim is to allow users in different healthcare scenarios to experiment with service composition to support highly individual and changing needs.

Spectral Deformation for Two-Body Dispersive Systems with e.g. the Yukawa Potential

We find an explicit closed formula for the k’th iterated commutator adAk(HV(ξ))

On the optical properties of carbon nanotubes. Part I. A general formula for the dynamical optical conductivity

{\text{ad}_{A}^{k}}(H_{V}(\xi ))

Storage and balancing synergies in a fully or highly renewable pan-European power system

of arbitrary order k ⩾ 1 between a Hamiltonian HV(ξ)=Mωξ+SV̌

Fundamental Properties of and Transition to a Fully Renewable Pan-European Power System

H_{V}(\xi )=M_{\omega _{\xi }}+S_{\check V}

A Taylor-like expansion of a commutator with a function of self-adjoint, pairwise commuting operators

and a conjugate operator A=𝔦2(vξ⋅∇+∇⋅vξ)

Projection operators on matrix weighted Lp and a simple sufficient Muckenhoupt condition

A=\frac{\mathfrak{i}}{2}(v_{\xi}\cdot\nabla+\nabla\cdot v_{\xi})

Optimal Combination of Storage and Balancing in a 100% Renewable European Power System

, where Mωξ