Maxwell speed distribution and analogue Hawking–Unruh temperature in an ontological model of a Harmonic oscillator ground state

Within an ontological (hidden variable) model of quantum fluctuation, one can discuss the actual   properties of a system regardless (independent) of measurement. Here we apply an ontological model proposed earlier to investigate a Harmonic oscillator in the quantum mechanical ground state. We first show that the actual speed of the oscillator fluctuates randomly following the Maxwell–Boltzmann distribution. On the other hand, the actual energy obeys a broad Gamma distribution with an average 3?ω/2$3?\omega /2$, where ω$\omega$ is the classical angular frequency, so that one may conclude that the outcome of a single energy measurement reveals the average of the actual energy. The distribution of actual speed (energy) thus formally resembles the distribution of speed (energy) of an ideal gas in thermal equilibrium of temperature T_g=?ω/2$T_g=?\omega /2$. We shall then argue that T_g$T_g$ can be written in a form analogous to the Hawking temperature for a Schwarzschild black hole in which the average distance of the oscillator from the origin plays the analogous role of the radius of the black hole event horizon. It can also be written in a form analogous to the Unruh temperature experienced by a body moving with a uniform acceleration. In the analogy, the oscillator suffers an effective acceleration which balances the attractive force of the trapping Harmonic potential, thus keeps its average position away from the origin.     

Narrowband solid state vuv coherent source for laser cooling of antihydrogen

We describe the design and performance of a solid-state pulsed source of narrowband (< 100 MHz) Lyman-α radiation designed for the purpose of laser cooling magnetically trapped antihydrogen. Our source utilizes an injection seeded Ti:Sapphire amplifier cavity to generate intense radiation at 729.4 nm, which is then sent through a frequency doubling stage and a frequency tripling stage to generate 121.56 nm light. Although the pulse energy at 121.56 nm is currently limited to 12 nJ with a repetition rate of 10 Hz, we expect to obtain greater than 0.1 μJ per pulse at 10 Hz by further optimizing the alignment of the pulse amplifier and the efficiency of the frequency tripling stage. Such a power will be sufficient for cooling a trapped antihydrogen atom from 500 mK to 20mK.     

High‐performance a‐Si1–xOx:H/c‐Si heterojunction solar cells realized by the a‐Si:H/a‐Si1–xOx:H stack buffer layer

We used amorphous silicon oxide (a‐Si_1–xO_x:H) and microcrystalline silicon oxide (µc‐Si_1–xO_x:H) as buffer layer and p‐type emitter layer, respectively, in n‐type silicon hetero‐junction (SHJ) solar cells. We proposed to insert a thin (2 nm) intrinsic amorphous silicon (a‐Si:H) thin film between the thin (2.5 nm) a‐Si_1–xO_x:H buffer layer and the p‐layer to form a stack buffer layer of a‐Si:H/a‐Si_1–xO_x:H. As a result, a high open‐circuit voltage (V_OC) and a high fill factor (FF) were obtained at the same time. Finally, a high efficiency of 19.0% (J_SC = 33.46 mA/cm², V_OC = 738 mV, FF = 77.0%) was achieved on a 100 μm thick polished wafer using the stack buffer layer.

     

Unexpected effect of catalyst concentration on photochemical CO2 reduction by trans(Cl)–Ru(bpy)(CO)2Cl2: new mechanistic insight into the CO/HCOO– selectivity

Photochemical CO₂ reduction catalysed by trans(Cl)–Ru(bpy)(CO)₂Cl₂ (bpy = 2,2′-bipyridine) efficiently produces carbon monoxide (CO) and formate (HCOO^–) in N,N-dimethylacetamide (DMA)/water containing [Ru(bpy)₃]²⁺ as a photosensitizer and 1-benzyl-1,4-dihydronicotinamide (BNAH) as an electron donor. We have unexpectedly found catalyst concentration dependence of the product ratio (CO/HCOO^–) in the photochemical CO₂ reduction: the ratio of CO/HCOO^– decreases with increasing catalyst concentration. The result has led us to propose a new mechanism in which HCOO^– is selectively produced by the formation of a Ru(i)–Ru(i) dimer as the catalyst intermediate. This reaction mechanism predicts that the Ru–Ru bond dissociates in the reaction of the dimer with CO₂, and that the insufficient electron supply to the catalyst results in the dominant formation of HCOO^–. The proposed mechanism is supported by the result that the time-course profiles of CO and HCOO^– in the photochemical CO₂ reduction catalysed by [Ru(bpy)(CO)₂Cl]₂ (0.05 mM) are very similar to those of the reduction catalysed by trans(Cl)–Ru(bpy)(CO)₂Cl₂ (0.10 mM), and that HCOO^– formation becomes dominant under low-intensity light. The kinetic analyses based on the proposed mechanism could excellently reproduce the unusual catalyst concentration effect on the product ratio. The catalyst concentration effect observed in the photochemical CO₂ reduction using [Ru(4dmbpy)₃]²⁺ (4dmbpy = 4,4′-dimethyl-2,2′-bipyridine) instead of [Ru(bpy)₃]²⁺ as the photosensitizer is also explained with the kinetic analyses, reflecting the smaller quenching rate constant of excited [Ru(4dmbpy)₃]²⁺ by BNAH than that of excited [Ru(bpy)₃]²⁺. We have further synthesized trans(Cl)–Ru(6Mes-bpy)(CO)₂Cl₂ (6Mes-bpy = 6,6′-dimesityl-2,2′-bipyridine), which bears bulky substituents at the 6,6′-positions in the 2,2′-bipyridyl ligand, so that the ruthenium complex cannot form the dimer due to the steric hindrance. We have found that this ruthenium complex selectively produces CO, which strongly supports the catalytic mechanism proposed in this work.     

Hexagonal Defect Array Formed under Steady Shear Flow in Water-in-Cholesteric Liquid Crystal Emulsions

The relation between the liquid crystalline textures and the steady shear viscosity has been investigated in cholesteric emulsions, composed of water, surfactants, and cholesteric liquid crystals. Both at the substrate surface and at the surfactant-coated droplet surface, a homeotropic anchoring is enforced to the adjacent liquid crystal. Under a steady shear flow with the shear rate below 100 s^–1, we observed that point defects spontaneously appear, and tend to adopt a regular hexagonal arrangement in the low shear-rate range of 1–20 s^–1. In viscosity measurements, the shear-thinning behavior was found, showing a clear correspondence to the texture change. We estimated the height of point defects in the hexagonal array from the viscosity increase in the shear-thinning, assuming that the shear-thinning behavior is caused by the reduction of the effective gap between cone and plate, owing to the presence of the hexagonal array anchored on the plate. The relation between the estimated height and the measured lateral size of point defects agreed with that of the quadrilateral array, which is formed after termination of the shear. This agreement informs that the shape of a point defect is preserved in both defect arrays, independently of shearing conditions.     

Classical provability of uniform versions and intuitionistic provability

Along the line of Hirst‐Mummert 9 and Dorais 4 , we analyze the relationship between the classical provability of uniform versions Uni(S) of Π₂‐statements S with respect to higher order reverse mathematics and the intuitionistic provability of S. Our main theorem states that (in particular) for every Π₂‐statement S of some syntactical form, if its uniform version derives the uniform variant of over a classical system of arithmetic in all finite types with weak extensionality, then S is not provable in strong semi‐intuitionistic systems including bar induction in all finite types but also nonconstructive principles such as K?nig's lemma and uniform weak K?nig's lemma . Our result is applicable to many mathematical principles whose sequential versions imply .     

Self-accumulation of aromatics at the oil-water interface through weak hydrogen bonding

It is well-known that the amphiphilic solutes are surface-active and can accumulate at the oil-water interface. Here, we have investigated the water and a light-oil model interface by using molecular dynamic simulations. It was found that aromatics concentrated in the interfacial region, whereas the other hydrocarbons were uniformly distributed throughout the oil phase. Similar to previous studies, such concentrations were not observed at pure aromatics-water interfaces. We show that the self-accumulation of aromatics at the oil-water interface is driven by differences in the interfacial tension, which is lower for aromatics-water than between the others. The weak hydrogen bonding between the aromatic rings and the water protons provides the mechanism for lowering the interfacial tension.     

Optimization of silica surface with nanosize holes for immobilization of biomolecules and analysis of their interactions

An evanescent-field-coupled waveguide-mode sensor of the Kretschmann configuration with a silica waveguide having nanoscale holes is an ideal tool for detection of bimolecular reactions. In the present research, an optimized surface of the sensor with cylindrical nanoscale holes was modified with sodium (1-{[6-(2,5-dioxo-2,5-dihydro-1H-pyrrol-1-yl)hexanoyl]oxy}-2,5-dioxopyrrolidine-3-sulfonate) (Sulfo-EMCS) to facilitate the attachment of biomolecules; the resulting surface could be cleaned for reuse simply by changing the pH of the buffering solution. The modification is expected to be useful for wide range of molecular detection.     

Photocatalytic degradation of dichloroacetyl chloride adsorbed on TiO<Subscript>2</Subscript>

Dichloroacetyl chloride (DCAC) attracted our attention as an intermediate product of the photocatalytic degradation of trichloroethylene (TCE). The adsorption and photocatalytic reaction of DCAC on TiO₂ have been investigated by FTIR spectroscopy. The influence of the surface structure of several TiO₂s on the reaction mechanism was discussed in order to understand the complete degradation mechanism of TCE as well as DCAC. DCAC was transformed into dichloroacetic acid (DCAA) on the relatively hydrophobic TiO₂ surface by the small amount of the water molecules weakly adsorbed on the surface. This DCAA was degraded to phosgene, CO₂, and CO during UV irradiation. For the hydrophilic TiO₂, DCAC was mainly transformed into the dichloroacetate anion. UV irradiation allowed this species to produce chloroform in addition to phosgene, CO₂, and CO. It is suggested that DCAC easily reacts with the Ti–OH group on the hydrophilic TiO₂ and forms the bidentate titanium chelate of dichloroacetate, which efficiently degrades into chloroform.