The twilight zone in the parametric evolution of eigenstates: beyond perturbation theory and semiclassics

Considering a quantized chaotic system, we analyze the evolution of its eigenstates as a result of varying a control parameter. As the induced perturbation becomes larger, there is a crossover from a perturbative to a non-perturbative regime, which is reflected in the structural changes of the local density of states. For the first time the {\em full} scenario is explored for a physical system: an Aharonov-Bohm cylindrical billiard. As we vary the magnetic flux, we discover an intermediate twilight regime where perturbative and semiclassical features co-exist. This is in contrast with the {\em simple} crossover from a Lorentzian to a semicircle line-shape which is found in random-matrix models.Comment: 4 pages, 4 figures, improved versio

Conductivity and entanglement entropy of high dimensional holographic superconductors

We investigate the dependence of the conductivity and the entanglement entropy on the space-time dimensionality $d$ in two holographic superconductors: one dual to a quantum critical point with spontaneous symmetry breaking, and the other modeled by a charged scalar that condenses at a sufficiently low temperature in the presence of a Maxwell field. In both cases the gravity background is asymptotically Anti de Sitter (AdS). In the large $d$ limit we obtain explicit analytical results for the conductivity at zero temperature and the entanglement entropy by a $1/d$ expansion. We show that the entanglement entropy is always smaller in the broken phase. As dimensionality increases, the entanglement entropy decreases, the coherence peak in the conductivity becomes narrower and the ratio between the energy gap and the critical temperature decreases. These results suggest that the condensate interactions become weaker in high spatial dimensions.Comment: 38 pages, 7 figure

Contractions of low-dimensional nilpotent Jordan algebras

In this paper we classify the laws of three-dimensional and four-dimensional nilpotent Jordan algebras over the field of complex numbers. We describe the irreducible components of their algebraic varieties and extend contractions and deformations among them. In particular, we prove that J2 and J3 are irreducible and that J4 is the union of the Zariski closures of two rigid Jordan algebras.Comment: 12 pages, 3 figure

Dynamic reorganization of vortex matter into partially disordered lattices

We report structural evidence of dynamic reorganization in vortex matter in clean NbSe$_2$ by joint small angle neutron scattering and ac-susceptibility measurements. The application of oscillatory forces in a transitional region near the order-disorder transition results in robust bulk vortex lattice configurations with an intermediate degree of disorder. These dynamically-originated configurations correlate with intermediate pinning responses previously observed, resolving a long standing debate regarding the origin of such responses.Comment: 9 pages, 7 figures. To be published in Physical Review Letter