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

Kramers degeneracy theorem in nonrelativistic QED

Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed total momentum is also investigated.Comment: LaTex, 11 page

Absence of Ground States for a Class of Translation Invariant Models of Non-relativistic QED

We consider a class of translation invariant models of non-relativistic QED with net charge. Under certain natural assumptions we prove that ground states do not exist in the Fock space

Ground State and Resonances in the Standard Model of Non-relativistic QED

We prove existence of a ground state and resonances in the standard model of the non-relativistic quantum electro-dynamics (QED). To this end we introduce a new canonical transformation of QED Hamiltonians and use the spectral renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change

Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in Physics Please Lakshmanan for figures (e-mail: [email protected]

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

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\'

DIFFUSE IDIOPATHIC SKELETAL HYPEROSTOSIS (DISH) OF THE ELBOW: A CAUSE OF ELBOW PAIN? A CONTROLLED STUDY

Elbow pain is a common complaint and elbow hyperostosis a frequent radiological condition. However, little is known about the association between the clinical and radiological findings. To evaluate the relationship between spinal and extraspinal hyperostotic features and the clinical relevance of elbow hyperostosis we have performed the first controlled, double-blinded study of 85 hospitalized probands, 33 with and 52 without thoracospinal hyperostosis on lateral chest X-ray. Elbow and shoulder hyperostosis were graded on bilateral standard radiographs. Elbow pain was assessed by an interviewer using a standardized questionnaire and extraskeletal causes of elbow pain were recorded. The prevalence of elbow hyperostosis was increased in cases with thoracospinal hyperostosis compared to controls (82% versus 58%, X2 = 5.32, P<0.025, n = 85, odds ratio (OR) 3.30 (95% Cl 1.16-9.35)). Similarly, the prevalence of elbow hyperostosis was increased in cases with shoulder hyperostosis compared to controls (83% versus 60%, x2 = 4.51, P<0.05, n = 84, OR = 3.20 (95% CI 1.06-9.66)), emphasizing the multifocal nature of hyperostotic features. Elbow pain was only slightly more prevalent in cases with elbow hyperostosis compared to controls (21% versus l3%, x2 = 0.75, NS, OR = 1.84 (95% CI 0.46-7.44)). We conclude that elbow hyperostosis is a radiological finding of doubtful clinical relevanc