Quantum oscillations in confined and degenerate Fermi gases. II. The phase diagram and applications of half-vicinity model

For part I see DOI: 10.1016/j.physleta.2018.02.006. Size and density dependent quantum oscillations appear in Fermi gases under strong confinement and degeneracy conditions. We provide a universal recipe that explicitly separates oscillatory regime from non-oscillatory (stationary) one. A phase diagram representing stationary and oscillatory regimes on degeneracy-confinement space is proposed. Analytical expressions of phase transition interfaces are derived. The critical point, which separates entirely stationary and oscillatory regions, is determined and its dependencies on aspect ratios are examined for anisometric domains. Accuracy of the half-vicinity model and the phase diagram are verified through the quantum oscillations in electronic heat capacity and its ratio to entropy.     

Ultrafast photonic crystal lasers

We describe recent progress in photonic crystal nanocavity lasers with an emphasis on our recent results on ultrafast pulse generation. These lasers produce pulses on the picosecond scale, corresponding to only hundreds of optical cycles. We describe laser dynamics in optically pumped single cavities and in coupled cavity arrays, at low and room temperature. Such ultrafast, efficient, and compact lasers show great promise for applications in high‐speed communications, information processing, and on‐chip optical interconnects.     

Detecting the long-distance structure of the X(3872)

Several investigations show that in a very small length scale there exist corrections to the entropy of black hole horizon. Due to fluctuations of the background metric and the external fields the action incorporates corrections. In the low energy regime, the one-loop effective action in four dimensions leads to trace anomaly. We start from the Noether current corresponding to the Einstein–Hilbert plus the one-loop effective action to calculate the charge for the diffeomorphisms which preserve the Killing horizon structure. Then a bracket for the charges is calculated. We show that the Fourier modes of the bracket are exactly similar to the Virasoro algebra. Then using the Cardy formula the entropy is evaluated. Finally, the explicit terms of the entropy expression is calculated for a classical background. It turns out that the usual expression for the entropy; i.e. the Bekenstein–Hawking form, is not modified.     

Exact Solutions of the Morse-like Potential,Step-Up and Step-Down Operators via Laplace Transform Approach

We intend to realize the step-up and step-down operators of the potential V (x) = V1 e 2βx+V2 e βx. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the eigenvalues of the potential by using the Laplace transform approach to study the Lie algebra satisfied the ladder operators of the potential under consideration. Our results are similar to the ones obtained for the Morse potential (β→β).     

Quantum shape effects and novel thermodynamic behaviors at nanoscale

Thermodynamic properties of confined systems depend on sizes of the confinement domain due to quantum nature of particles. Here we show that shape also enters as a control parameter on thermodynamic state functions. By considering specially designed confinement domains, we demonstrate how shape effects alone modify Helmholtz free energy, entropy and internal energy of a confined system. We propose an overlapped quantum boundary layer method to analytically predict quantum shape effects without even solving Schrödinger equation or invoking any other mathematical tools. Thereby we reduce a thermodynamic problem into a simple geometric one and reveal the profound link between geometry and thermodynamics. We report also a torque due to quantum shape effects. Furthermore, we introduce isoformal, shape preserving, process which opens the possibility of a new generation of thermodynamic cycles operating at nanoscale with unique features.     

Least-squares spectral element solution of incompressible Navier–Stokes equations with adaptive refinement

Least-squares spectral element solution of steady, two-dimensional, incompressible flows are obtained by approximating velocity, pressure and vorticity variable set on Gauss–Lobatto–Legendre nodes. Constrained Approximation Method is used for h- and p-type nonconforming interfaces of quadrilateral elements. Adaptive solutions are obtained using a posteriori error estimates based on least squares functional and spectral coefficient. Effective use of p-refinement to overcome poor mass conservation drawback of least-squares formulation and successful use of h- and p-refinement together to solve problems with geometric singularities are demonstrated. Capabilities and limitations of the developed code are presented using Kovasznay flow, flow past a circular cylinder in a channel and backward facing step flow.     

Metasurface‐Based Molecular Biosensing Aided by Artificial Intelligence

Molecular spectroscopy provides unique information on the internal structure of biological materials by detecting the characteristic vibrational signatures of their constituent chemical bonds at infrared frequencies. Nanophotonic antennas and metasurfaces have driven this concept towards few‐molecule sensitivity by confining incident light into intense hot spots of the electromagnetic fields, providing strongly enhanced light‐matter interaction. In this Minireview, recently developed molecular biosensing approaches based on the combination of dielectric metasurfaces and imaging detection are highlighted in comparison to traditional plasmonic geometries, and the unique potential of artificial intelligence techniques for nanophotonic sensor design and data analysis is emphasized. Because of their spectrometer‐less operation principle, such imaging‐based approaches hold great promise for miniaturized biosensors in practical point‐of‐care or field‐deployable applications.     

Quantum oscillations in confined and degenerate Fermi gases. I. Half-vicinity model

We propose an analytical model for the prediction and accurate calculation of size and density dependent quantum oscillations in thermodynamic and transport properties of confined and degenerate Fermi gases. Our model considers only half-vicinity states of Fermi level. We show that the half-vicinity model quite accurately estimates quantum oscillations depending on confinement and degeneracy. Periods of quantum oscillations are even analytically expressed for one-dimensional case. Furthermore, similarities between functional behaviors of total occupancy variance and conventional density of states functions at Fermi level are discussed.     

Enzymatic oxidative polymerization of para‐imine functionalized phenol catalyzed by horseradish peroxidase

Enzymatic oxidative polymerization of a new para‐imine functionalized phenol derivative, 4‐(4‐hydroxybenzylideneamino)benzoic acid (HBBA), using horseradish peroxidase enzyme and hydrogen peroxide oxidizer has been investigated in an equivolume mixture of an organic solvent (acetone, methanol, ethanol, dimethylformamide, 1,4‐dioxane, and tetrahydrofuran) and phosphate buffer (pH = 5.0, 6.0, 6.8, 7.0, 7.2, 8.0, and 9.0) at different temperatures under air for 24 h. The resulting oligomer, oligo(4‐(4‐hydroxybenzylideneamino)benzoic acid) [oligo(HBBA)], was characterized using ultraviolet–visible, Fourier transform infrared (FT‐IR), ¹H nuclear magnetic resonance (NMR), cyclic voltammetry, size exclusion chromatography, differential scanning calorimetry, and thermogravimetric analyses. Polymerization involved carbon dioxide and hydrogen elimination from the monomer, and terminal units of the oligomer structure consisted of phenolic hydroxyl (–OH) groups at the ends. The polymer is mainly composed of a mixture of phenylene and oxyphenylene units according to ¹H NMR and FT‐IR analyses. Effects of solvent system, temperature and buffer pH on the polymerization have been investigated in respect to the yield and molecular weight (M_n) of the product. The best condition in terms of the highest molecular weight (M_n = 3000 g/mol, DP ~ 15) was achieved in an equivolume mixture of 1,4‐dioxane/pH 5.0 phosphate buffer condition at 35°C. Electrochemical characterization of oligo(HBBA) was investigated at different scan rates. The resulting oligomer has also shown relatively high thermal stability according to thermogravimetric analysis. Copyright © 2015 John Wiley & Sons, Ltd.