Glassy Phase Transition and Stability in Black Holes

Black hole thermodynamics, confined to the semi-classical regime, cannot address the thermodynamic stability of a black hole in flat space. Here we show that inclusion of correction beyond the semi-classical approximation makes a black hole thermodynamically stable. This stability is reached through a phase transition. By using Ehrenfest's scheme we further prove that this is a glassy phase transition with a Prigogine-Defay ratio close to 3. This value is well placed within the desired bound (2 to 5) for a glassy phase transition. Thus our analysis indicates a very close connection between the phase transition phenomena of a black hole and glass forming systems. Finally, we discuss the robustness of our results by considering different normalisations for the correction term.Comment: v3, minor changes over v2, references added, LaTeX-2e, 18 pages, 3 ps figures, to appear in Eour. Phys. Jour.

3D-printed micro lens-in-lens for in vivo multimodal microendoscopy

Published online: March 1, 2022Multimodal microendoscopes enable co-located structural and molecular measurements in vivo, thus providing useful insights into the pathological changes associated with disease. However, different optical imaging modalities often have conflicting optical requirements for optimal lens design. For example, a high numerical aperture (NA) lens is needed to realize high-sensitivity fluorescence measurements. In contrast, optical coherence tomography (OCT) demands a low NA to achieve a large depth of focus. These competing requirements present a significant challenge in the design and fabrication of miniaturized imaging probes that are capable of supporting high-quality multiple modalities simultaneously. An optical design is demonstrated which uses two-photon 3D printing to create a miniaturized lens that is simultaneously optimized for these conflicting imaging modalities. The lens-in-lens design contains distinct but connected optical surfaces that separately address the needs of both fluorescence and OCT imaging within a lens of 330 µm diameter. This design shows an improvement in fluorescence sensitivity of >10x in contrast to more conventional fiber-optic design approaches. This lens-in-lens is then integrated into an intravascular catheter probe with a diameter of 520 µm. The first simultaneous intravascular OCT and fluorescence imaging of a mouse artery in vivo is reported.Jiawen Li, Simon Thiele, Rodney W. Kirk, Bryden C. Quirk, Ayla Hoogendoorn, Yung Chih Chen, Karlheinz Peter, Stephen J. Nicholls, Johan W. Verjans, Peter J. Psaltis, Christina Bursill, Alois M. Herkommer, Harald Giessen, and Robert A. McLaughli

ELABORATION OF AMORPHOUS METALS AND GLASS TRANSITIONFORMATION AND CHARACTERIZATION OF AMORPHOUS METALS

This review deals with the definition of amorphous and glassy metals ; the principal methods for their preparation by atom-by-atom deposition, rapid liquid quenching and particle bombardment ; criteria for their formation, especially ready glass formation (RGF) and its alloy chemical foundations ; and their classification. This is followed by a discussion of their elastic and plastic properties (Young's modulus and microhardness) and thermal stability (glass transition and crystallization temperatures), with emphasis on the correlation and composition dependence of these properties and without special reference to technically important glassy alloys

Electronic and magnetic properties of amorphous and crystalline Zr\u3csub\u3e40\u3c/sub\u3eCu\u3csub\u3e60-x\u3c/sub\u3eFe\u3csub\u3ex\u3c/sub\u3e alloys

Electronic states and localized magnetic moments and their interactions were studied in amorphous and crystalline Zr40Cu60-xFex alloys for 0≤x≤12. Electrical resistivity, magnetic susceptibility, and high-field magnetization measurements were performed. In the dilute crystalline alloys Curie-Weiss behavior is seen in the susceptibility and is associated with localized moments (μeff≈3μB) on the iron atoms. At higher iron concentrations ferromagnetism is observed. Curie-Weiss behavior also is seen in the susceptibility of the dilute (0eff≈0.7μB). There is some evidence that the local environment of the Fe atoms is important and may depend sensitively on the quench rate used in making the samples or, perhaps, on room-temperature ageing effects in the samples. The dilute amorphous alloys exhibit a negative dρ/d T from 1.4 to 300 K. This is not to be associated with Kondo spin-flip scattering but it is consistent with several other mechanisms including localized-spin-fluctuation scattering, s-d scattering in a nonmagnetic model, scattering from tunneling states in the amorphous alloy, or quasi-liquidmetal-pseudopotential scattering. A recent theory due to Nagel and Tauc on the nearly-free-electron approach to metallic glass alloys is shown to be consistent with this last idea and also is used to account for other features exhibited by the amorphous Zr-Cu system. In the concentrated (x\u3e6) amorphous alloys, resistance maxima and magnetic hysteresis are seen at low temperatures. For x=12 a random ferromagnetic state develops with T0=30 K, which is some five times smaller than T0 for the corresponding crystalline alloy. The saturation moment in the amorphous alloy is also considerably smaller than in the crystalline case. This behavior is similar to other systems in which the crystalline-to-amorphous transition greatly weakens the magnetism