On the Smooth Feshbach-Schur Map

A new variant of the Feshbach map, called smooth Feshbach map, has been introduced recently by Bach et al., in connection with the renormalization analysis of non-relativistic quantum electrodynamics. We analyze and clarify its algebraic and analytic properties, and we generalize it to non-selfadjoint partition operators $\chi$ and \chib.Comment: 8 page

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

Newell’s shearwater population modeling for Habitat Conservation Plan and Recovery Planning

Reports were scanned in black and white at a resolution of 600 dots per inch and were converted to text using Adobe Paper Capture Plug-in.The Newell’s shearwater (Puffinus auricularis newelli), an IUCN and ESA listed species, faces terrestrial threats from predation, fallout (attraction to artificial lights) and collision with powerlines. Various indices suggest the population has declined by ~75% in the past two decades. Population modeling is required for Habitat Conservation Plan (HCP) and Recovery Planning to consider the benefits of existing and proposed management actions to the Kauai population. Population scenarios modeled here included a) stable, realistic and optimal growth; b) threats of predation, fallout and powerline collision; and c) management actions of minimizing fallout and powerline mortality, the Save Our Shearwater rescue program, predator control, predator eradication and chick translocation. The growth rate (lambda) produced in our worst case threat scenario for all threats (0.906) fell within the range of annual change suggested by ornithological radar data from 1993- 2010 using only Newell’s shearwater traffic (0.899), and Save Our Shearwater data of Newell’s shearwater fledglings from 1988-2009 (0.905).In our efforts we drew heavily from existing field studies and modeling undertaken by PRBO Conservation Science researchers who produced the EPRI Kauai Endangered Seabird Study (Ainley et al. 1995). Much of these current efforts are owed to PRBO Conservation Science. We thank A. Erichsen and D. Leonard for helpful discussion and D. Ainley, D. Duffy and W. Satterthwaite for valuable reviews of this work

A vanishing theorem for operators in Fock space

We consider the bosonic Fock space over the Hilbert space of transversal vector fields in three dimensions. This space carries a canonical representation of the group of rotations. For a certain class of operators in Fock space we show that rotation invariance implies the absence of terms which either create or annihilate only a single particle. We outline an application of this result in an operator theoretic renormalization analysis of Hamilton operators, which occur in non-relativistic qed.Comment: 14 page

On the Atomic Photoeffect in Non-relativistic QED

In this paper we present a mathematical analysis of the photoelectric effect for one-electron atoms in the framework of non-relativistic QED. We treat photo-ionization as a scattering process where in the remote past an atom in its ground state is targeted by one or several photons, while in the distant future the atom is ionized and the electron escapes to spacial infinity. Our main result shows that the ionization probability, to leading order in the fine-structure constant, $\alpha$, is correctly given by formal time-dependent perturbation theory, and, moreover, that the dipole approximation produces an error of only sub-leading order in $\alpha$. In this sense, the dipole approximation is rigorously justified.Comment: 25 page

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

On the Magnetic Pekar Functional and the Existence of Bipolarons

First, this paper proves the existence of a minimizer for the Pekar functional including a constant magnetic field and possibly some additional local fields that are energy reducing. Second, the existence of the aforementioned minimizer is used to establish the binding of polarons in the model of Pekar-Tomasevich including external fields.Comment: 13 page

Binding threshold for the Pauli-Fierz operator

For the Pauli-Fierz operator with a short range potential we study the binding threshold as a function of the fine structure constant $\alpha$ and show that it converges to the binding threshold for the Schr\"odinger operator in the small $\alpha$ limit