Multiple bound states in scissor-shaped waveguides

We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle $\theta$. Such a four-terminal junction with a tunable $\theta$ can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for $\theta=90^o$ there is one proper bound state and one eigenvalue embedded in the continuum. We show that the number of eigenvalues becomes larger with increasing asymmetry and the bound-state energies are increasing as functions of $\theta$ in the interval $(0,90^o)$. Moreover, states which are sufficiently strongly bent exist in pairs with a small energy difference and opposite parities. Finally, we discuss how with increasing $\theta$ the bound states transform into the quasi-bound states with a complex wave vector.Comment: 6 pages, 6 figure

An Experimentally Realizable Weiss Model for Disorder-Free Glassiness

We summarize recent work on a frustrated periodic long-range Josephson array in a parameter regime where its dynamical behavior is identical to that of the $p=4$ disordered spherical model. We also discuss the physical requirements imposed by the theory on the experimental realization of this superconducting network.Comment: 6 pages, LaTeX, 2 Postscript figure

Conductance and persistent current of a quantum ring coupled to a quantum wire under external fields

The electronic transport of a noninteracting quantum ring side-coupled to a quantum wire is studied via a single-band tunneling tight-binding Hamiltonian. We found that the system develops an oscillating band with antiresonances and resonances arising from the hybridization of the quasibound levels of the ring and the coupling to the quantum wire. The positions of the antiresonances correspond exactly to the electronic spectrum of the isolated ring. Moreover, for a uniform quantum ring the conductance and the persistent current density were found to exhibit a particular odd-even parity related with the ring-order. The effects of an in-plane electric field was also studied. This field shifts the electronic spectrum and damps the amplitude of the persistent current density. These features may be used to control externally the energy spectra and the amplitude of the persistent current.Comment: Revised version, 7 pages and 9 figures. To appear in Phys. Rev.

Exponential decay of Laplacian eigenfunctions in domains with branches

The behavior of Laplacian eigenfunctions in domains with branches is investigated. If an eigenvalue is below a threshold which is determined by the shape of the branch, the associated eigenfunction is proved to exponentially decay inside the branch. The decay rate is twice the square root of the difference between the threshold and the eigenvalue. The derived exponential estimate is applicable for arbitrary domains in any spatial dimension. Numerical simulations illustrate and further extend the theoretical estimate

GRB 171010A/SN 2017htp: a GRB-SN at z = 0.33

The number of supernovae known to be connected with long-duration gamma-ray bursts (GRBs) is increasing and the link between these events is no longer exclusively found at low redshift (z ≲ 0.3) but is well established also at larger distances. We present a new case of such a liaison at z = 0.33 between GRB 171010A and SN 2017htp. It is the second closest GRB with an associated supernova of only three events detected by Fermi-LAT. The supernova is one of the few higher redshift cases where spectroscopic observations were possible and shows spectral similarities with the well-studied SN 1998bw, having produced a similar Ni mass (⁠ M Ni =0.33±0.02 M ⊙ MNi=0.33±0.02 M⊙ ⁠) with slightly lower ejected mass (⁠ M ej =4.1±0.7 M ⊙ Mej=4.1±0.7 M⊙ ⁠) and kinetic energy (⁠ E K =8.1±2.5× 10 51 erg EK=8.1±2.5×1051 erg ⁠). The host-galaxy is bigger in size than typical GRB host galaxies, but the analysis of the region hosting the GRB revealed spectral properties typically observed in GRB hosts and showed that the progenitor of this event was located in a very bright H ii region of its face-on host galaxy, at a projected distance of ∼ 10 kpc from its galactic centre. The star-formation rate (SFRGRB ∼ 0.2 M⊙ yr−1) and metallicity (12 + log(O/H) ∼8.15 ± 0.10) of the GRB star-forming region are consistent with those of the host galaxies of previously studied GRB–SN systems