Structure of trajectories of complex-matrix eigenvalues in the Hermitian-non-Hermitian transition

The statistical properties of trajectories of eigenvalues of Gaussian complex matrices whose Hermitian condition is progressively broken are investigated. It is shown how the ordering on the real axis of the real eigenvalues is reflected in the structure of the trajectories and also in the final distribution of the eigenvalues in the complex plane.

EVOLUTIONARY TRAJECTORIES OF ULTRACOMPACT "BLACK WIDOW" PULSARS WITH VERY LOW MASS COMPANIONS

The existence of millisecond pulsars with planet-mass companions in close orbits is challenging from the stellar evolution point of view. We calculate in detail the evolution of binary systems self-consistently, including mass transfer, evaporation, and irradiation of the donor by X-ray feedback, demonstrating the existence of a new evolutionary path leading to short periods and compact donors as required by the observations of PSR J1719-1438. We also point out the alternative of an exotic nature of the companion planet-mass star.

Scaling invariance for the escape of particles from a periodically corrugated waveguide

The escape dynamics of a classical light ray inside a corrugated waveguide is characterised by the use of scaling arguments. The model is described via a two-dimensional nonlinear and area preserving mapping. The phase space of the mapping contains a set of periodic islands surrounded by a large chaotic sea that is confined by a set of invariant tori. When a hole is introduced in the chaotic sea, letting the ray escape, the histogram of frequency of the number of escaping particles exhibits rapid growth, reaching a maximum value at n(p) and later decaying asymptotically to zero. The behaviour of the histogram of escape frequency is characterised using scaling arguments. The scaling formalism is widely applicable to critical phenomena and useful in characterisation of phase transitions, including transitions from limited to unlimited energy growth in two-dimensional time varying billiard problems. (C) 2011 Elsevier B.V. All rights reserved.