In dimension 1, we show that the Taylor expansion of a “generic” potential near a non degenerate critical point can be recovered from the knowledge of the semi-classical spectrum of the associated Schrödinger operator near the corresponding critical value. Contrary to the work of previous authors, we do not assume that the potential is even. The classical Birkhoff normal form does not contain e...

The Berezinskii-Kosterlitz-Thouless 1) 4) (BKT, or simply KT) quantum phase transition in one-dimensional systems is the transition between the gapless state and the gapful state. As is well known, the critical behavior of the BKT transition is highly singular and sometimes called “pathological”. In finite systems, this high singularity appears as severe slowly-converging logarithmic size corre...

Recall that a (hyper)graph is d-degenerate if every of its nonempty subgraphs has a vertex of degree at most d. Every d-degenerate (hyper)graph is (easily) (d + 1)colorable. A (hyper)graph is almost d-degenerate if it is not d-degenerate, but every its proper subgraph is d-degenerate. In particular, if G is almost (k − 1)-degenerate, then after deleting any edge it is k-colorable. For k ≥ 2, we...

As shown by Ashtekar in the mid 80’s, general relativity can be extended to incorporate degenerate metrics. This extension is not unique, however, as one can change the form of the hamiltonian constraints and obtain an alternative degenerate extension of general relativity that disagrees with Ashtekar’s original theory when the triads vectors are degenerate. In this paper, the constraint algebr...

Over the years, studies of collective properties of medium and heavy mass nuclei in the framework of the Interacting Boson Approximation (IBA) model have focused on finite boson numbers, corresponding to valence nucleon pairs in specific nuclei. Attention to large boson numbers has been motivated by the study of shape/phase transitions from one limiting symmetry of IBA to another, which become ...

In this paper, the problem of bifurcation of limit cycles from degenerate singular point and infinity in a class of septic polynomial differential systems is investigated. Using the computer algebra system Mathematica, the limit cycle configurations of {(8), 3} and {(3), 6} are obtained under synchronous perturbation at degenerate singular point and infinity. To our knowledge, up to now, this i...

We construct blowing-up sign-changing solutions to some nonlinear critical equations by glueing a standard bubble to a degenerate function. We develop a new method based on analyticity to perform the glueing when the critical manifold of solutions is degenerate and no Bianchi–Egnell type condition holds.

I discuss several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature Tχ implies that the ρ and a1 vector mesons are degenerate in mass. In a gauged linear sigma model the ρ mass increases with temperature, mρ(Tχ) > mρ(0). I conjecture that at Tχ the thermal ρ− a1 peak is relative...

I discuss several topics in the applications of chiral symmetry at nonzero temperature. First, where does the rho go? The answer: up. The restoration of chiral symmetry at a temperature T implies that the and a 1 vector mesons are degenerate in mass. In a gauged linear sigma model the mass increases with temperature, m (T) > m (0). I conjecture that at T the thermal ? a 1 peak is relatively hig...