We obtain a bifurcation result for solutions of the Lorentz equation in a semiRiemannian manifold; such solutions are critical points of a certain strongly indefinite functionals defined in terms of the semi-Riemannian metric and the magnetic field. The flow of the Jacobi equation along each solution preserves the so-called magnetic symplectic form, and the corresponding curve in the symplectic...

This paper is the continuation of [6], where Victor Guillemin and I proved the following result: the Taylor expansion of a potential V (x) (x ∈ R) at a non degenerate critical point x0 of V , satisfying V (x0) 6= 0, is determined by the semi-classical spectrum of the associated Schrödinger operator near the corresponding critical value V (x0). Here, I prove results which are stronger in some as...

This paper is the continuation of [4], where Victor Guillemin and I proved the following result: the Taylor expansion of the potential V (x) (x ∈ R) at a non degenerate critical point x0 of V , satisfying V (x0) 6= 0, is determined by the semi-classical spectrum of the associated Schrödinger operator near the corresponding critical value V (x0). Here, I prove results which are stronger in some ...

The pseudogap Anderson impurity model provides a paradigm for understanding local quantum phase transitions, in this case between generalised fermi liquid and degenerate local moment phases. Here we develop a non-perturbative local moment approach to the generic asymmetric model, encompassing all energy scales and interaction strengths and leading thereby to a rich description of the problem. W...

This paper is the continuation of [4], where Victor Guillemin and I proved the following result: the Taylor expansion of the potential V (x) (x ∈ R) at a non degenerate critical point x0 of V , satisfying V (x0) 6= 0, is determined by the semi-classical spectrum of the associated Schrödinger operator near the corresponding critical value V (x0). Here, I prove results which are stronger in some ...

Doubly-degenerate binary systems consisting of two white dwarfs both composed of carbon and oxygen and close enough that mass is transferred from the less massive to the more massive are possible progenitors of type Ia supernovae. If the mass transfer rate is slow enough that the accreting white dwarf can reach a mass of 1.38M⊙ then it can ignite carbon degenerately at its centre. This can lead...

Abstract. We consider semi-classical Schrödinger operator P (h) = −h∆ + V (x) in R such that the analytic potential V has a non-degenerate critical point x0 = 0 with critical value E0 and we can define resonances in some fixed neighborhood of E0 when h > 0 is small enough. If the eigenvalues of the Hessian are Z-independent the resonances in h-neighborhood of E0 (δ > 0) can be calculated explic...

In earlier work, carrying out numerical simulations of the Ricci flows of families of rotationally symmetric geometries on S3, we have found strong support for the contention that (at least in the rotationally symmetric case) the Ricci flow for a “critical” initial geometry– one which is at the transition point between initial geometries (on S3) whose volume-normalized Ricci flows develop a sin...

The classical pitchfork of singularity theory is a twice-degenerate bifurcation that typically occurs in dynamical system models exhibiting Z2 symmetry. Nonclassical pitchfork singularities also occur in many non-symmetric systems, where the total bifurcation environment is usually more complex. In this paper threedimensional manifolds of critical points, or limit-point shells, are introduced b...