Thermodynamics phase transition and Hawking radiation of the Schwarzschild black hole with quintessence-like matter and a deficit solid angle

In this paper, we investigate the thermodynamics and Hawking radiation of Schwarzschild black hole with quintessence-like matter and deficit solid angle. From the metric of the black hole, we derive the expressions of temperature and specific heat using the laws of black hole thermodynamics. Using the null geodesics method and Parikh–Wilczeck tunneling method, we derive the expressions of Boltzmann factor and the change of Bekenstein–Hawking entropy for the black hole. The behaviors of the temperature, specific heat, Boltzmann factor and the change of Bekenstein entropy versus the deficit solid angle (\(\epsilon ^{2}\)) and the density of static spherically symmetric quintessence-like matter (\(\rho _{0}\)) were explicitly plotted. The results show that, when the deficit solid angle (\(\epsilon ^{2}\)) and the density of static spherically symmetric quintessence-like matter at \(r=1\) (\(\rho _{0}\)) vanish \((\rho _{0}=\epsilon =0)\), these four thermodynamics quantities are reduced to those obtained for the simple case of Schwarzschild black hole. For low entropies, the presence of quintessence-like matter induces a first order phase transition of the black hole and for the higher values of the entropies, we observe the second order phase transition. When increasing \(\rho _{0}\), the transition points are shifted to lower entropies. The same thing is observed when increasing \(\epsilon ^{2}\). In the absence of quintessence-like matter (\(\rho _{0}=0\)), these transition phenomena disappear. Moreover the rate of radiation decreases when increasing \(\rho _{0}\) or \((\epsilon ^2)\).     

Three paths toward the quantum angle operator

We examine mathematical questions around angle (or phase) operator associated with a number operator through a short list of basic requirements. We implement three methods of construction of quantum angle. The first one is based on operator theory and parallels the definition of angle for the upper half-circle through its cosine and completed by a sign inversion. The two other methods are integral quantization generalizing in a certain sense the Berezin–Klauder approaches. One method pertains to Weyl–Heisenberg integral quantization of the plane viewed as the phase space of the motion on the line. It depends on a family of “weight” functions on the plane. The third method rests upon coherent state quantization of the cylinder viewed as the phase space of the motion on the circle. The construction of these coherent states depends on a family of probability distributions on the line.     

Lithium solvation in a PMMA membrane plasticized by a lithium‐conducting ionic liquid based on 1‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide

The Raman and Infrared (IR) spectra of poly(methyl methacrylate) (PMMA) membranes plasticized by ionic liquids of the (1 − x)[1‐butyl‐3‐methylimidazolium bis(trifluoromethanesulfonyl)imide (BMITFSI)],xLiTFSI type, where BMI⁺ is the 1‐butyl‐3‐methylimidazolium cation and TFSI⁻ the bis(trifluoromethanesulfonyl)imide anion, are analyzed for a lithium bis(trifluoromethane sulfone)imide (LiTFSI) mole fraction x = 0.23 and PMMA contents from 0 to 50 wt%. The lithium is found to have an average coordination of about three CO groups and less than one TFSI⁻ anion. It plays the role of a cross‐linker between the ester groups of PMMA and the nonvolatile ionic liquid. Addition of PMMA to the (1 − x)(BMITFSI),xLiTFSI ionic liquid lowers the conductivity but might improve the lithium transference number by transforming the [Li(TFSI)₂]⁻ anionic clusters present in the pure ionic liquid into a mixed coordination by ester groups and TFSI⁻ anions. Copyright © 2008 John Wiley & Sons, Ltd.     

Epitaxial relationships between Al,Ag and GaAs{001} surfaces

Detailed results concerning the orientation of Al and Ag layers grown by MBE onto GaAs{001} surfaces are reported. The observed crystallographic relationships have been found to depend only on the growth temperature in the case of Ag, while for Al the situation is more complex. Possible effects of other parameters such as structure and stoichiometry of the starting GaAs surface and growth rate, are discussed and compared with other results recently reported.     

Perturbation about the mean field critical point

We consider two models that are small perturbations of Gaussian or mean field models: the first one is a double well /4⁴ — /2² perturbation of a massless Gaussian lattice field in the weak coupling limit (0, proportional to ). The other consists of a spin 1/2 Ising model with long-range Kac type interactions; the inverse range of the interaction, , is the small parameter. The second model is related to the first one via a sine-Gordon transformation. The lattice ^d has dimensiond3.In both cases we derive an asymptotic estimate to first order (in or ²) on the location of the critical point. Moreover, we prove bounds on the remainder of an expansion in or around the Gaussian or mean field critical points.The appendix, due to E. Speer, contains an extension of Weinberg's theorem on the divergence of Feynman graphs which is used in the proofs.Supported by NSF Grant # MCS 78-01885Supported by NSF Grant # PHY 78-15920     

All-optical switching in silicon photonic crystal waveguides by use of the plasma dispersion effect

Silicon photonic crystals offer new ways of controlling the propagation of light as well as new tools for the realization of high-density optical integration on monolithic substrates. However, silicon does not possess the strong nonlinearities that are commonly used in the dynamic control of optical devices. Such dynamic control is nevertheless essential if silicon is to provide the higher levels of functionality that are required for optical integration. We demonstrate that the combination of the refractive index change caused by the presence of photoexcited carriers, or so-called plasma dispersion, and photonic crystal properties such as photonic bandgaps, constitutes a powerful tool for active control of light in silicon integrated devices. We show close to 100% modulation depth near the photonic crystal band edge.     

Helium and point defect accumulation: (i) microstructure and mechanical behaviour

Ferritic/martensitic (F/M) steels are good candidate structural materials for the future fusion reactors and spallation sources. However, irradiation of steels is known to produce hardening, loss of ductility, shift in ductile to brittle transition temperature (DBTT) and reduction of fracture toughness and creep resistance starting at low doses. Helium (He), produced by transmutation during the irradiation, also impacts mechanical properties. Numerous experimental and theoretical studies on the evolution of the microstructure of steels under irradiation have been conducted until now. We review the effect of irradiation-induced point defects and in particular of He on the mechanical properties of F/M steels. To cite this article: R. Schäublin et al., C. R. Physique 9 (2008).     

Reversible photomechanical switching of individual engineered molecules at a metallic surface

We have observed reversible light-induced mechanical switching for individual organic molecules bound to a metal surface. Scanning tunneling microscopy (STM) was used to image the features of individual azobenzene molecules on Au(111) before and after reversibly cycling their mechanical structure between trans and cis states using light. Azobenzene molecules were engineered to increase their surface photomechanical activity by attaching varying numbers of tert-butyl (TB) ligands ("legs") to the azobenzene phenyl rings. STM images show that increasing the number of TB legs "lifts" the azobenzene molecules from the substrate, thereby increasing molecular photomechanical activity by decreasing molecule-surface coupling.     

GISAXS study of carbon nanotubes grown by CVD

We report a quantitative Grazing Incidence Small Angle X‐ray Scattering (GISAXS) study of a dense film of mutually oriented carbon nanotubes (CNTs) grown by a catalytically‐activated DC HF CCVD process after dispersion of metallic catalytic (Co) islands on SiO₂/Si(100) substrates. The GISAXS pattern analysis is expanded to non‐correlated surface science systems and is based on CNTs density, characteristic lengths, atomic Co dispersion throughout the CNTs and roughnesses of uncorrelated particles. The results are closely compared to SEM and TEM observations. The GISAXS patterns, even dominated by envelope features of disordered objects, provide significant complementary quantitative data about CNTs films. The results underline that cobalt continuously fills the nanotube in the course of the growth and that the CNTs experience a large tendency toward mutual alignment. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Vowel Intelligibility in Classical Singing

Vowel intelligibility during singing is an important aspect of communication during performance. The intelligibility of isolated vowels sung by Western classically trained singers has been found to be relatively low, in fact, decreasing as pitch rises, and it is lower for women than for men. The lack of contextual cues significantly deteriorates vowel intelligibility. It was postulated in this study that the reduced intelligibility of isolated sung vowels may be partly from the vowels used by the singers in their daily vocalises. More specifically, if classically trained singers sang only a few American English vowels during their vocalises, their intelligibility for American English vowels would be less than for those classically trained singers who usually vocalize on most American English vowels. In this study, there were 21 subjects (15 women, 6 men), all Western classically trained performers as well as teachers of classical singing. They sang 11 words containing 11 different American English vowels, singing on two pitches a musical fifth apart. Subjects were divided into two groups, those who normally vocalize on 4, 5, or 6 vowels, and those who sing all 11 vowels during their daily vocalises. The sung words were cropped to isolate the vowels, and listening tapes were created. Two listening groups, four singing teachers and five speech-language pathologists, were asked to identify the vowels intended by the singers. Results suggest that singing fewer vowels during daily vocalises does not decrease intelligibility compared with singing the 11 American English vowels. Also, in general, vowel intelligibility was lower with the higher pitch, and vowels sung by the women were less intelligible than those sung by the men. Identification accuracy was about the same for the singing teacher listeners and the speech-language pathologist listeners except for the lower pitch, where the singing teachers were more accurate.