Level -1/2 Realization of Quantum N-Toroidal Algebra in Type Cn

We construct a level -1/2 vertex representation of the quantum [Formula: see text]-toroidal algebra of type [Formula: see text], which is a natural generalization of the usual quantum toroidal algebra. The construction also provides a vertex representation of the quantum toroidal algebra for type [Formula: see text] as a by-product.

Contextual Inferences, Nonlocality, and the Incompleteness of Quantum Mechanics

It is known that “quantum non locality”, leading to the violation of Bell’s inequality and more generally of classical local realism, can be attributed to the conjunction of two properties, which we call here elementary locality and predictive completeness. Taking this point of view, we show again that quantum mechanics violates predictive completeness, allowing the making of contextual inferences, which can, in turn, explain why quantum non locality does not contradict relativistic causality. An important question remains: if the usual quantum state ψ is predictively incomplete, how do we complete it? We give here a set of new arguments to show that ψ should be completed indeed, not by looking for any “hidden variables”, but rather by specifying the measurement context, which is required to define actual probabilities over a set of mutually exclusive physical events.

Tunneling Quantum Dynamics in Ammonia

Ammonia is a well-known example of a two-state system and must be described in quantum-mechanical terms. In this article, we will explain the tunneling phenomenon that occurs in ammonia molecules from the perspective of trajectory-based quantum dynamics, rather than the usual quantum probability perspective. The tunneling of the nitrogen atom through the potential barrier in ammonia is not merely a probability problem; there are underlying reasons and mechanisms explaining why and how the tunneling in ammonia can happen. Under the framework of quantum Hamilton mechanics, the tunneling motion of the nitrogen atom in ammonia can be described deterministically in terms of the quantum trajectories of the nitrogen atom and the quantum forces applied. The vibrations of the nitrogen atom about its two equilibrium positions are analyzed in terms of its quantum trajectories, which are solved from the Hamilton equations of motion. The vibration periods are then computed by the quantum trajectories and compared with the experimental measurements.

Marginal metallic state at a fractional filling of ’8/5’ and ’4/3’ of Landau levels in the GaAs/AlGaAs 2D electron system

A metallic state with a vanishing activation gap, at a filling factor $$\nu = 8/5$$ ν = 8 / 5 in the untilted specimen with $$n= 2 \times 10^{11} cm^{-2}$$ n = 2 × 10 11 c m - 2 , and at $$\nu = 4/3$$ ν = 4 / 3 at $$n=1.2 \times 10^{11} cm^{-2}$$ n = 1.2 × 10 11 c m - 2 under a $$\theta = 66^{0}$$ θ = 66 0 tilted magnetic field, is examined through a microwave photo-excited transport study of the GaAs/AlGaAs 2 dimensional electron system (2DES). The results presented here suggest, remarkably, that at the possible degeneracy point of states with different spin polarization, where the 8/5 or 4/3 FQHE vanish, there occurs a peculiar marginal metallic state that differs qualitatively from a quantum Hall insulating state and the usual quantum Hall metallic state. Such a marginal metallic state occurs most prominently at $$\nu =8/5$$ ν = 8 / 5 , and at $$\nu =4/3$$ ν = 4 / 3 under tilt as mentioned above, over the interval $$1 \le \nu \le 2$$ 1 ≤ ν ≤ 2 , that also includes the $$\nu = 3/2$$ ν = 3 / 2 state, which appears perceptibly gapped in the first instance.

Dissipationless zero energy epigraphene edge state for nanoelectronics

The graphene edge state is essential for graphene electronics and fundamental in graphene theory, however it is not observed in deposited graphene. Here we report the discovery of the epigraphene edge state (EGES) in conventionally patterned epigraphene using plasma-based lithography that stabilizes and passivates the edges probably by fusing the graphene edges to the non-polar silicon carbide substrate, as expected. Transport involves a single, essentially dissipationless conductance channel at zero energy up to room temperature. The Fermi level is pinned at zero energy. The EGES does not generate a Hall voltage and the usual quantum Hall effect is observed only after subtraction of the EGES current. EGES transport is highly protected and apparently mediated by an unconventional zero-energy fermion that is half electron and half hole. Interconnected networks involving only the EGES can be patterned, opening the door to a new graphene nanoelectronics paradigm that is relevant for quantum computing.

Bivariate continuous q-Hermite polynomials and deformed quantum Serre relations

We introduce bivariate versions of the continuous [Formula: see text]-Hermite polynomials. We obtain algebraic properties for them (generating function, explicit expressions in terms of the univariate ones, backward difference equations and recurrence relations) and analytic properties (determining the orthogonality measure). We find a direct link between bivariate continuous [Formula: see text]-Hermite polynomials and the star product method of [S. Kolb and M. Yakimov, Symmetric pairs for Nichols algebras of diagonal type via star products, Adv. Math. 365 (2020), Article ID: 107042, 69 pp.] for quantum symmetric pairs to establish deformed quantum Serre relations for quasi-split quantum symmetric pairs of Kac–Moody type. We prove that these defining relations are obtained from the usual quantum Serre relations by replacing all monomials by multivariate orthogonal polynomials.

On the Importance of Catalysis in Photocatalysis: Triggering of Photocatalysis at Well-Defined Anatase TiO2 Crystals Through Facet-Specific Deposition of Oxygen Reduction Cocatalyst

Well-defined anatase TiO₂ crystals with co-exposed {101} and {001} facets represent a promising platform for fundamental studies in photocatalysis and for the development of novel photocatalytic systems exhibiting higher than usual quantum efficiencies. Herein, we present protocols enabling the photoreductive deposition of Pt nanoparticles onto anatase TiO₂ micro-sized (1-3 mm) crystals prepared by hydrothermal growth in fluoride-containing solutions to be carried out either facet-selectively (on {101} facets only) or facet non-selectively (on both {101} and {001} facets). The photocatalytic behavior of resulting photocatalysts is studied using investigations of oxidative photodegradation of a test pollutant (4-chlorophenol, 4-CP), photocurrent measurements, and kinetic analysis of the open-circuit photopotential decay. We demonstrate that the deposition of Pt nanoparticles effectively triggers the photocatalytic degradation of 4-CP at anatase crystals which are otherwise completely inactive. The role of Pt in triggering the photocatalysis is demonstrated to consist chiefly in the catalytic enhancement of the reaction rate of oxygen reduction by photogenerated electrons. Only platinized {101} facets contribute to photocatalysis, whereas the {001} facets, in the literature often referred to as “highly reactive”, are even after platinization completely inactive, most likely due to (1 × 4) surface reconstruction upon the heat treatment necessary to decrease the amount of surface fluorides. Based on our results, we highlight the eminent role of efficient surface catalysis for effective charge separation, and provide specific design rules for further development of photocatalysts with high quantum efficiencies.

On the Importance of Catalysis in Photocatalysis: Triggering of Photocatalysis at Well-Defined Anatase TiO2 Crystals Through Facet-Specific Deposition of Oxygen Reduction Cocatalyst

Well-defined anatase TiO₂ crystals with co-exposed {101} and {001} facets represent a promising platform for fundamental studies in photocatalysis and for the development of novel photocatalytic systems exhibiting higher than usual quantum efficiencies. Herein, we present protocols enabling the photoreductive deposition of Pt nanoparticles onto anatase TiO₂ micro-sized (1-3 mm) crystals prepared by hydrothermal growth in fluoride-containing solutions to be carried out either facet-selectively (on {101} facets only) or facet non-selectively (on both {101} and {001} facets). The photocatalytic behavior of resulting photocatalysts is studied using investigations of oxidative photodegradation of a test pollutant (4-chlorophenol, 4-CP), photocurrent measurements, and kinetic analysis of the open-circuit photopotential decay. We demonstrate that the deposition of Pt nanoparticles effectively triggers the photocatalytic degradation of 4-CP at anatase crystals which are otherwise completely inactive. The role of Pt in triggering the photocatalysis is demonstrated to consist chiefly in the catalytic enhancement of the reaction rate of oxygen reduction by photogenerated electrons. Only platinized {101} facets contribute to photocatalysis, whereas the {001} facets, in the literature often referred to as “highly reactive”, are even after platinization completely inactive, most likely due to (1 × 4) surface reconstruction upon the heat treatment necessary to decrease the amount of surface fluorides. Based on our results, we highlight the eminent role of efficient surface catalysis for effective charge separation, and provide specific design rules for further development of photocatalysts with high quantum efficiencies.

On the Importance of Catalysis in Photocatalysis: Triggering of Photocatalysis at Well-Defined Anatase TiO2 Crystals Through Facet-Specific Deposition of Oxygen Reduction Cocatalyst

Well-defined anatase TiO₂ crystals with co-exposed {101} and {001} facets represent a promising platform for fundamental studies in photocatalysis and for the development of novel photocatalytic systems exhibiting higher than usual quantum efficiencies. Herein, we present protocols enabling the photoreductive deposition of Pt nanoparticles onto anatase TiO₂ micro-sized (1-3 mm) crystals prepared by hydrothermal growth in fluoride-containing solutions to be carried out either facet-selectively (on {101} facets only) or facet non-selectively (on both {101} and {001} facets). The photocatalytic behavior of resulting photocatalysts is studied using investigations of oxidative photodegradation of a test pollutant (4-chlorophenol, 4-CP), photocurrent measurements, and kinetic analysis of the open-circuit photopotential decay. We demonstrate that the deposition of Pt nanoparticles effectively triggers the photocatalytic degradation of 4-CP at anatase crystals which are otherwise completely inactive. The role of Pt in triggering the photocatalysis is demonstrated to consist chiefly in the catalytic enhancement of the reaction rate of oxygen reduction by photogenerated electrons. Only platinized {101} facets contribute to photocatalysis, whereas the {001} facets, in the literature often referred to as “highly reactive”, are even after platinization completely inactive, most likely due to (1 × 4) surface reconstruction upon the heat treatment necessary to decrease the amount of surface fluorides. Based on our results, we highlight the eminent role of efficient surface catalysis for effective charge separation, and provide specific design rules for further development of photocatalysts with high quantum efficiencies.

On the Importance of Catalysis in Photocatalysis: Triggering of Photocatalysis at Well-Defined Anatase TiO2 Crystals Through Facet-Specific Deposition of Oxygen Reduction Cocatalyst

Well-defined anatase TiO₂ crystals with co-exposed {101} and {001} facets represent a promising platform for fundamental studies in photocatalysis and for the development of novel photocatalytic systems exhibiting higher than usual quantum efficiencies. Herein, we present protocols enabling the photoreductive deposition of Pt nanoparticles onto anatase TiO₂ micro-sized (1-3 mm) crystals prepared by hydrothermal growth in fluoride-containing solutions to be carried out either facet-selectively (on {101} facets only) or facet non-selectively (on both {101} and {001} facets). The photocatalytic behavior of resulting photocatalysts is studied using investigations of oxidative photodegradation of a test pollutant (4-chlorophenol, 4-CP), photocurrent measurements, and kinetic analysis of the open-circuit photopotential decay. We demonstrate that the deposition of Pt nanoparticles effectively triggers the photocatalytic degradation of 4-CP at anatase crystals which are otherwise completely inactive. The role of Pt in triggering the photocatalysis is demonstrated to consist chiefly in the catalytic enhancement of the reaction rate of oxygen reduction by photogenerated electrons. Only platinized {101} facets contribute to photocatalysis, whereas the {001} facets, in the literature often referred to as “highly reactive”, are even after platinization completely inactive, most likely due to (1 × 4) surface reconstruction upon the heat treatment necessary to decrease the amount of surface fluorides. Based on our results, we highlight the eminent role of efficient surface catalysis for effective charge separation, and provide specific design rules for further development of photocatalysts with high quantum efficiencies.