Supernovae Shedding Light on Gamma-Ray Bursts

We review the observational status of the Supernova (SN)/Gamma-Ray Burst (GRB) connection. In section 2 we provide a short summary of the observational properties of core-collapse SNe. In sections 3-6 we review the circumstantial evidences and the direct observations that support the existence of a deep connection between the death of massive stars and GRBs. Present data suggest that SNe associated with GRBs form a heterogeneous class of objects including both bright and faint Hypernovae and perhaps also `standard' Ib/c events. In section 7, we provide an empirical estimate of the rate of Hypernovae, for a ``MilkyWay-like'' galaxy, of about $\sim 2.6\times 10^{-4}$ yr$^{-1}$ that may imply the ratio GRB/Hypernovae to be in the range $\sim 0.03-0.7$. In the same framework we find the ratio GRB/SNe-Ibc to be $\sim 0.008\div 0.05$. In section 8 we discuss the possible existence of a lag between the SN explosion and the associated gamma-ray event. In the few SN/GRB associations so far discovered the SN explosions and GRB events appear to go off simultaneously. In section 9 we present the conclusions and highlight the open problems that Swift hopefully will allow us to solve.Comment: 20 pages, 13 figures, invited review at the 4th Workshop Gamma-Ray Bursts in the Afterglow Era, Rome,18-22 October 2004. Editors: L. Piro, L. Amati, S. Covino, and B. Gendre. Il Nuovo Cimento, in pres

Invisible defects in complex crystals

We show that invisible localized defects, i.e. defects that can not be detected by an outside observer, can be realized in a crystal with an engineered imaginary potential at the defect site. The invisible defects are synthesized by means of supersymmetric (Darboux) transformations of an ordinary crystal using band-edge wave functions to construct the superpotential. The complex crystal has an entire real-valued energy spectrum and Bragg scattering is not influenced by the defects. An example of complex crystal synthesis is presented for the Mathieu potential

Non-Hermitian time-dependent perturbation theory: asymmetric transitions and transitionless interactions

The ordinary time-dependent perturbation theory of quantum mechanics, that describes the interaction of a stationary system with a time-dependent perturbation, predicts that the transition probabilities induced by the perturbation are symmetric with respect to the initial an final states. Here we extend time-dependent perturbation theory into the non-Hermitian realm and consider the transitions in a stationary Hermitian system, described by a self-adjoint Hamiltonian $\hat{H}_0$, induced by a time-dependent non-Hermitian interaction $f(t) \hat{P}$. In the weak interaction (perturbative) limit, the transition probabilities generally turn out to be {\it asymmetric} for exchange of initial and final states. In particular, for a temporal shape $f(t)$ of the perturbation with one-sided Fourier spectrum, i.e. with only positive (or negative) frequency components, transitions are fully unidirectional, a result that holds even in the strong interaction regime. Interestingly, we show that non-Hermitian perturbations can be tailored to be transitionless, i.e. the perturbation leaves the system unchanged as if the interaction had not occurred at all, regardless the form of $\hat{H}_0$ and $\hat{P}$. As an application of the results, we discuss asymmetric (chiral) behavior of dynamical encircling of an exceptional point in a two- and three-level system.Comment: final version, to appear in Annals of Physic

Low-energy doublons in the ac-driven two-species Hubbard model

The hopping dynamics of two fermionic species with different effective masses in the one-dimensional Hubbard model driven by an external field is theoretically investigated. A multiple-time-scale asymptotic analysis of the driven asymmetric Hubbard model shows that a high-frequency bichromatic external field can sustain a new kind of low-energy particle bound state (doublon), in which two fermions of different species occupy nearest neighbor sites and co-tunnel along the lattice. The predictions of the asymptotic analysis are confirmed by direct numerical simulations of the two-particle Hubbard Hamiltonian.Comment: 4 figure

Coherent perfect absorbers for transient, periodic or chaotic optical fields: time-reversed lasers beyond threshold

Recent works [Y.D. Chong {\it et al.}, Phys. Rev. Lett. {\bf 105}, 053901 (2010); W. Wan {\it et al.}, Science {\bf 331}, 889 (2011)] have shown that the time-reversed process of lasing at threshold realizes a coherent perfect absorber (CPA). In a CPA, a lossy medium in an optical cavity with a specific degree of dissipation, equal in modulus to the gain of the lasing medium, can perfectly absorb coherent optical waves at discrete frequencies that are the time-reversed counterpart of the lasing modes. Here the concepts of time-reversal of lasing and CPA are extended for optical radiation emitted by a laser operated in an arbitrary (and generally highly-nonlinear) regime, i.e. for transient, chaotic or periodic coherent optical fields. We prove that any electromagnetic signal $E(t)$ generated by a laser system \textbf{S} operated in an arbitrary regime can be perfectly absorbed by a CPA device $\bf{S'}$ which is simply realized by placing inside \textbf{S} a broadband linear absorber (attenuator) of appropriate transmittance. As examples, we discuss CPA devices that perfectly absorb a chaotic laser signal and a frequency-modulated optical wave.Comment: 9 pages, 3 figure; to appear in Phys. Rev.

Absence of Floquet scattering in oscillating non-Hermitian potential wells

Scattering of a quantum particle from an oscillating barrier or well does not generally conserve the particle energy owing to energy exchange with the photon field, and an incoming particle-free state is scattered into a set of outgoing (transmitted and reflected) free states according to Floquet scattering theory. Here we introduce two families of oscillating non-Hermitian potential wells in which Floquet scattering is fully suppressed for any energy of the incident particle. The scattering-free oscillating potentials are synthesized by application of the Darboux transformation to the time-dependent Schr\"{o}dinger equation. For one of the two families of scattering-free potentials, the oscillating potential turns out to be fully invisible.Comment: 5 figure

Transparency at the interface between two isospectral crystals

Reflection at an interface separating two different media is a rather universal phenomenon which arises because of wave mismatching at the interface. By means of supersymmetric quantum mechanics methods, it is shown that a fully transparent interface can be realized, connecting two isospectral but different one-dimensional crystals. An example of reflectionless interface is presented for the sinusoidal (Mathieu) crystal connected to a non-sinusoidal potential by a transparent domain wall.Comment: 4 figures, to appear in EP

Rebirth of Novae as Distance Indicators Due to Efficient Large Telescopes

Nova outbursts are the result of strong thermonuclear runaways on the surface of a white dwarf accreting Hydrogen-rich material from a small mass companion. These giant explosions cause the star to increase its brightness by hundreds of thousands of times then making these objects powerful standard candles useful to measure the extragalactic distances.We have used the Very Large Telescope, located in the Chilean Atacama desert, to search for novae in NGC 1316--an early type galaxy in the Fornax cluster. We discovered 4 novae with 3h of observing time. The use of 8-10m class telescopes coupled with new detectors, can dramatically improve the efficiency of nova searches in extragalactic systems.Comment: 4 pages + 2 plot