Asymptotic boundary layer method for unstable trajectories : Semiclassical expansions for individual scar wavefunctions.

We extend the asymptotic boundary layer (ABL) method, originally developed for stable resonator modes, to the description of individual wave functions localized around unstable periodic orbits. The formalism applies to the description of scar states in fully or partially chaotic quantum systems, and also allows for the presence of smooth and sharp potentials, as well as magnetic fields. We argue that the separatrix wave function provides the largest contribution to the scars on a single wave function. This agrees with earlier results on the wave-function asymptotics and on the quantization condition of the scar states. Predictions of the ABL formalism are compared with the exact numerical solution for a strip resonator with a parabolic confinement potential and a magnetic field

Screening of pair fluctuations in superconductors with coupled shallow and deep bands: a route to higher temperature superconductivity

A combination of strong Cooper pairing and weak superconducting fluctuations is crucial to achieve and stabilize high-Tc superconductivity. We demonstrate that a coexistence of a shallow carrier band with strong pairing and a deep band with weak pairing, together with the Josephson-like pair transfer between the bands to couple the two condensates, realizes an optimal multicomponent superconductivity regime: it preserves strong pairing to generate large gaps and a very high critical temperature but screens the detrimental superconducting fluctuations, thereby suppressing the pseudogap state. Surprisingly, we find that the screening is very efficient even when the inter-band coupling is very small. Thus, a multi-band superconductor with a coherent mixture of condensates in the BCS regime (deep band) and in the BCS-BEC crossover regime (shallow band) offers a promising route to higher critical temperatures.Comment: 8 pages, 1 figure, including supplemental material