The theory of Hawking radiation can be tested in laboratory analogues of black holes. We use light pulses in nonlinear fiber optics to establish artificial event horizons. Each pulse generates a moving perturbation of the refractive index via the Kerr effect. Probe light perceives this as an event horizon when its group velocity, slowed down by the perturbation, matches the speed of the pulse. We have observed in our experiment that the probe stimulates Hawking radiation, which occurs in a regime of extreme nonlinear fiber optics where positive and negative frequencies mix.

Abstract. As it has been proven, the determination of general one-dimensional Schrödinger Hamiltonians having third-order differential ladder operators requires to solve the Painlevé IV equation. In this work, it will be shown that some specific subsets of the higher-order supersymmetric partners of the harmonic oscillator possess third-order differential ladder operators. This allows us to introduce a simple technique for generating solutions of the Painlevé IV equation. Finally, we classify these solutions into three relevant hierarchies.

The RGSZ1 and RGSZ2 proteins, members of the RGS-Rz subfamily of GTPase-activating proteins (GAP), are involved in Mu-opioid receptor desensitization. The expression of these proteins, as well as of their main target the Gz protein, is virtually restricted to the nervous tissue. In synaptosomal membranes, these Rz proteins undergo post-translational modifications such as glycosylation and phosphorylation, and they may covalently attach to small ubiquitin-like modifier (SUMO) proteins. While RGSZ1 exists in conjugated and non-conjugated forms, RGSZ2 is mostly conjugated to SUMO-1, SUMO-2 and SUMO-3 proteins. These sumoylated forms of the GAPs readily associated with Mu-opioid receptors but they associated only poorly with Delta receptors. Furthermore, Gai2 and Gaz subunits co-precipitated with the sumoylated forms of RGSZ1/Z2 proteins, but to a lesser extent with the Ser phosphorylated SUMO-free form of RGSZ1. Upon Mu-opioid receptor activation, there is a strong increase in the association of Ga proteins with RGSZ2 proteins that persists for intervals longer than 24 h. This effect probably accounts for their role in Mu-opioid receptor desensitization. Only a moderate increase was observed with RGSZ1, the non-sumoylated form of which probably acts as an efficient GAP for these Ga subunits. Therefore, sumoylation regulates the biological activity of RGS-Rz proteins and it is likely that it serves to switch their behavior, from that of a GAP for activated Ga subunits to that of a scaffold protein for specific signaling proteins.

The confluent SUSY QM usually involves a second-order SUSY transformation where the two factorization energies converge to a single value. In order to achieve it, one generally needs to solve an indefinite integral, which limits the actual systems to which it can be applied. Nevertheless, not so long ago, an alternative method to achieve this transformation was developed through a Wronskian differential formula [Phys Lett. A 3756 (2012) 692]. In the present work, we consider the k-confluent SUSY transformation, where k factorization energies merge into a single value, and we develop a generalized Wronskian differential formula for this case. Furthermore, we explicitly work out general formulas for the third-and fourth-order cases and we present as examples the free particle and the single-gap Lamé potentials.

Hawking radiation has been regarded as a more general phenomenon than in gravitational physics, in particular in laboratory analogs of the event horizon. Here we consider the fiber-optical analog of the event horizon, where intense light pulses in fibers establish horizons for probe light. Then, we calculate the Hawking spectrum in an experimentally realizable system. We found that the Hawking radiation is peaked around group-velocity horizons in which the speed of the pulse matches the group velocity of the probe light. The radiation nearly vanishes at the phase horizon where the speed of the pulse matches the phase velocity of light.