A family of Schr\"odinger operators whose spectrum is an interval

By approximation, I show that the spectrum of the Schr\"odinger operator with potential $V(n) = f(n\rho \pmod 1)$ for f continuous and $\rho > 0$, $\rho \notin \N$ is an interval.Comment: Comm. Math. Phys. (to appear

Permanent Superhumps in V1974 Cyg

We present results of 32 nights of CCD photometry of V1974 Cygni, from the years 1994 and 1995. We verify the presence of two distinct periodicities in the light curve: 0.0812585 day~1.95 hours and 0.0849767 d~2.04 hr. We establish that the shorter periodicity is the orbital period of the underlying binary system. The longer period oscillates with an average value of |dot(P)| ~ 3x10^(7)--typical to permanent superhumps. The two periods obey the linear relation between the orbital and superhump periods that holds among members of the SU Ursae Majoris class of dwarf novae. A third periodicity of 0.083204 d~2.00 hr appeared in 1994 but not in 1995. It may be related to the recently discovered anti-superhump phenomenon. These results suggest a linkage between the classical nova V1974 Cyg and the SU UMa stars, and indicate the existence of an accretion disk and permanent superhumps in the system no later than 30 months after the nova outburst. From the precessing disk model of the superhump phenomenon we estimate that the mass ratio in the binary system is between 2.2 and 3.6. Combined with previous results this implies a white dwarf mass of 0.75-1.07 M sun.Comment: 11 pages, 10 eps. figures, Latex, accepted for publication in MNRA

A quantitative central limit theorem for linear statistics of random matrix eigenvalues

It is known that the fluctuations of suitable linear statistics of Haar distributed elements of the compact classical groups satisfy a central limit theorem. We show that if the corresponding test functions are sufficiently smooth, a rate of convergence of order almost $1/n$ can be obtained using a quantitative multivariate CLT for traces of powers that was recently proven using Stein's method of exchangeable pairs.Comment: Title modified; main result stated under slightly weaker conditions; accepted for publication in the Journal of Theoretical Probabilit

Morphologies of laser-induced damage in hafnia-silica multilayer mirror and polarizer coatings

Hafnium-silica multilayer mirrors and polarizers were deposited by e-beam evaporation onto BK7 glass substrates. The mirrors and polarizers were coated for operation at 1053 nm at 45{degree} and at Brewster`s angle (56{degree}), respectively. They were tested with a single 3-ns laser pulse. Morphology of the laser-induced damage was characterized by optical and scanning electron microscopy. Four distinct damage morphologies were found: pits, flatbottom pits, scalds, and delaminates. The pits and flat bottom pits (<30{mu}m dia) were detected at lower fluences (as low as 5 J/cm{sup 2}). The pits seemed to result from ejection of nodular defects by causing local enhancement of the electric field. Scalds and delaminates could be observed at higher fluences (above 13 J/cm{sup 2}) and seemed to result from the formation of plasmas on the surface. These damage types often originated at pits and were less than 300 {mu}m diameter; their size increased almost linearly with fluence. Finally, effects of the damage on the beam (reflectivity degradation and phase modulations) were measured

Quantum-Logic Gate between Two Optical Photons with an Average Efficiency above 40%

Optical qubits uniquely combine information transfer in optical fibers with a good processing capability and are therefore attractive tools for quantum technologies. A large challenge, however, is to overcome the low efficiency of two-qubit logic gates. The experimentally achieved efficiency in an optical controlled NOT (CNOT) gate reached approximately 11% in 2003 and has seen no increase since. Here we report on a new platform that was designed to surpass this long-standing record. The new scheme avoids inherently probabilistic protocols and, instead, combines aspects of two established quantum nonlinear systems: atom-cavity systems and Rydberg electromagnetically induced transparency. We demonstrate a CNOT gate between two optical photons with an average efficiency of 41.7(5)% at a postselected process fidelity of 81(2)%. Moreover, we extend the scheme to a CNOT gate with multiple target qubits and produce entangled states of presently up to five photons. All these achievements are promising and have the potential to advance optical quantum information processing in which almost all advanced protocols would profit from high-efficiency logic gates.Comment: In this revision, we extend the discussion of the efficiency in Sec. IV.C and we add models in appendices B, E, and L-

A laser-induced mouse model with long-term intraocular pressure elevation

Purpose: To develop and characterize a mouse model with intraocular pressure (IOP) elevation after laser photocoagulation on the trabecular meshwork (TM), which may serve as a model to investigate the potential of stem cell-based therapies for glaucoma. Methods: IOP was measured in 281 adult C57BL/6 mice to determine normal IOP range. IOP elevation was induced unilaterally in 50 adult mice, by targeting the TM through the limbus with a 532-nm diode laser. IOP was measured up to 24 weeks post-treatment. The optic nerve damage was detected by electroretinography and assessed by semiautomatic counting of optic nerve axons. Effects of laser treatment on the TM were evaluated by histology, immunofluorescence staining, optical coherence tomography (OCT) and transmission electron microscopy (TEM). Results: The average IOP of C57BL/6 mice was 14.5±2.6 mmHg (Mean ±SD). After laser treatment, IOP averaged above 20 mmHg throughout the follow-up period of 24 weeks. At 24 weeks, 57% of treated eyes had elevated IOP with the mean IOP of 22.5±2.5 mmHg (Mean ±SED). The difference of average axon count (59.0%) between laser treated and untreated eyes was statistically significant. Photopic negative response (PhNR) by electroretinography was significantly decreased. CD45+ inflammatory cells invaded the TM within 1 week. The expression of SPARC was increased in the TM from 1 to 12 weeks. Histology showed the anterior chamber angle open after laser treatment. OCT indicated that most of the eyes with laser treatment had no synechia in the anterior chamber angles. TEM demonstrated disorganized and compacted extracellular matrix in the TM. Conclusions: An experimental murine ocular hypertension model with an open angle and optic nerve axon loss was produced with laser photocoagulation, which could be used to investigate stem cell-based therapies for restoration of the outflow pathway integrity for ocular hypertension or glaucoma. Copyright

Growth of laser-induced damage during repetitive illumination of HfO2-SiO2 multilayer mirror and polarizer coatings

As peak fluence of high power lasers is increased, it becomes necessary to tolerate damage on mirrors, polarizers. To study how different types of damage morphologies initiate and grow during repetitive illumination, hafnia-silica multilayer mirror and polarizer coatings were laser damage tested. The coatings were prepared by e-beam evaporation and irradiated with a 3-ns pulse at 1064 nm. The damage morphology was recorded after each shot to determine the types of damage that cause massive unstable failure and lower the optic`s functional damage threshold. Results were summarized on damage stability maps plotting the average damage size vs number of shots for fluences ranging from 10 to 40 J/cm{sup 2}. The maps indicate that the commonly observed damage morphologies (pits, flat bottom pits, scalds, outer layer delamination) have distinct growth behaviors and influence the value of the functional damage threshold differently. While pits are stable up to fluences as high as 40 J/cm{sup 2}, flat bottom pits can grow during repetitive illumination above a critical fluence of about 35 J/cm{sup 2}. Scalds are formed in the first shot and never grow at fluences below 40 J/cm{sup 2}. Finally, delaminates are highly unstable and have the potential for damaging the coating catastrophically above 15 J/cm{sup 2}. Results show that delaminate damage should be prevented; this knowledge has allowed coatings development efforts to focus on eliminating the origin of such damage morphology

Assays to monitor aggrephagy in Drosophila brain

Accumulation of ubiquitinated protein aggregates is a hallmark of most ageingrelated neurodegenerative disorders. Autophagy has been found to be involved in the selective clearance of these protein aggregates, and this process is called aggrephagy. Here we provide two protocols for the investigation of protein aggregation and their removal by autophagy using western blotting and immunofluorescence techniques in Drosophila brain. Investigating the role of aggrephagy at the cellular and organismal level is important for the development of therapeutic interventions against ageing-related diseases