The semi-classical limit with a delta-prime potential

We consider the quantum evolution $e^{-i\frac{t}{\hbar}H_{\beta}} \psi_{\xi}^{\hbar}$ of a Gaussian coherent state $\psi_{\xi}^{\hbar}\in L^{2}(\mathbb{R})$ localized close to the classical state $\xi \equiv (q,p) \in \mathbb{R}^{2}$, where $H_{\beta}$ denotes a self-adjoint realization of the formal Hamiltonian $-\frac{\hbar^{2}}{2m}\,\frac{d^{2}\,}{dx^{2}} + \beta\,\delta'_{0}$, with $\delta'_{0}$ the derivative of Dirac's delta distribution at $x = 0$ and $\beta$ a real parameter. We show that in the semi-classical limit such a quantum evolution can be approximated (w.r.t. the $L^{2}(\mathbb{R})$-norm, uniformly for any $t \in \mathbb{R}$ away from the collision time) by $e^{\frac{i}{\hbar} A_{t}} e^{it L_{B}} \phi^{\hbar}_{x}$, where $A_{t} = \frac{p^{2}t}{2m}$, $\phi_{x}^{\hbar}(\xi) := \psi^{\hbar}_{\xi}(x)$ and $L_{B}$ is a suitable self-adjoint extension of the restriction to $\mathcal{C}^{\infty}_{c}({\mathscr M}_{0})$, ${\mathscr M}_{0} := \{(q,p) \in \mathbb{R}^{2}\,|\,q \neq 0\}$, of ($-i$ times) the generator of the free classical dynamics. While the operator $L_{B}$ here utilized is similar to the one appearing in our previous work [C. Cacciapuoti, D. Fermi, A. Posilicano, The semi-classical limit with a delta potential, Annali di Matematica Pura e Applicata (2020)] regarding the semi-classical limit with a delta potential, in the present case the approximation gives a smaller error: it is of order $\hbar^{7/2-\lambda}$, $0 < \lambda < 1/2$, whereas it turns out to be of order $\hbar^{3/2-\lambda}$, $0 < \lambda < 3/2$, for the delta potential. We also provide similar approximation results for both the wave and scattering operators.Comment: 24 pages. arXiv admin note: text overlap with arXiv:1907.0580

Scattering from local deformations of a semitransparent plane

We study scattering for the couple $(A_{F},A_{0})$ of Schr\"odinger operators in $L^2(\mathbb{R}^3)$ formally defined as $A_0 = -\Delta + \alpha\, \delta_{\pi_0}$ and $A_F = -\Delta + \alpha\, \delta_{\pi_F}$, $\alpha >0$, where $\delta_{\pi_F}$ is the Dirac $\delta$-distribution supported on the deformed plane given by the graph of the compactly supported, Lipschitz continuous function $F:\mathbb{R}^{2}\to\mathbb{R}$ and $\pi_{0}$ is the undeformed plane corresponding to the choice $F\equiv 0$. We provide a Limiting Absorption Principle, show asymptotic completeness of the wave operators and give a representation formula for the corresponding Scattering Matrix $S_{F}(\lambda)$. Moreover we show that, as $F\to 0$, $\|S_{F}(\lambda)-\mathsf 1\|^{2}_{\mathfrak{B}(L^{2}({\mathbb S}^{2}))}={\mathcal O}\!\left(\int_{\mathbb{R}^{2}}d\textbf{x}|F(\textbf{x})|^{\gamma}\right)$, $0<\gamma<1$. We correct a minor mistake in the computation of the scattering matrix, occurring in the published version of this paper (see J. Math. Anal. Appl. 473(1) (2019), pp. 215-257). The mistake was in Section 7, and affected the statement of Corollary 7.2, specifically, Eq. (7.8). Regrettably the formula for $S_F$ in the Corrigendum J. Math. Anal. Appl. 482(1) (2020), 123554, still contains a misprint, the correct expression is the one given here.Comment: We corrected a minor mistake in the computation of the scattering matri

One-Way Functions Imply Secure Computation in a Quantum World

We prove that quantum-hard one-way functions imply simulation-secure quantum oblivious transfer (QOT), which is known to suffice for secure computation of arbitrary quantum functionalities. Furthermore, our construction only makes black-box use of the quantum-hard one-way function. Our primary technical contribution is a construction of extractable and equivocal quantum bit commitments from quantum-hard one-way functions in the standard model. Instantiating the Bennet-Brassard-Cr\'epeau-Skubiszewska (CRYPTO 91) framework with these commitments yields simulation-secure quantum oblivious transfer

Kerr metric, static observers and Fermi coordinates

The coordinate transformation which maps the Kerr metric written in standard Boyer-Lindquist coordinates to its corresponding form adapted to the natural local coordinates of an observer at rest at a fixed position in the equatorial plane, i.e., Fermi coordinates for the neighborhood of a static observer world line, is derived and discussed in a way which extends to any uniformly circularly orbiting observer there.Comment: 15 page latex iopart class documen

Benzothiazolium-functionalized NU-1000 : a versatile material for carbon dioxide adsorption and cyanide luminescence sensing

The benzothiazolium-decorated NU-1000-BzTz MOF is a versatile material for carbon dioxide storage and cyanide luminescence sensing in aqueous solutions

Dual Photoredox and Nickel Catalysed Reductive Coupling of Alkynes and Aldehydes

A regioselective vinylation of aromatic and aliphatic aldehydes promoted by the merging of photoredox and nickel catalysis is here reported. A comprehensive investigation on the reaction conditions allowed the disclosure of a valid and reproducible protocol based on a nickel-mediated reductive coupling approach under visible light irradiation. The employment of 3CzClIPN (2,4,6-tris(carbazol-9-yl)-5-chloro-isophthalonitrile) as the photocatalyst and Hantzsch's ester as the sacrificial organic reductant replace the use of boron-, silicon- or zinc-based reducing agents, making this method a worthy alternative to the already known protocols. The developed mild reaction conditions allow the access to a wide range of substituents decorating both the aldehyde and the alkyne. Moreover, careful photophysical investigations shed light on the mechanism of the reaction

Dual photosensitizer cycles working synergistically in a C(sp)-C(sp3) cross-coupling reaction

Funding: Authors thank the University of St Andrews, Syngenta and the EPSRC Centre for Doctoral Training in Critical Resource Catalysis (CRITICAT) for financial support [Ph.D. studentship to “M.B.”; Grant code: EP/L016419/1]. We thank Umicore AG for the gift of materials. E.Z.-C. and P.C. acknowledge the European Union H2020 research and innovation program under the Marie Skłodowska Curie Grant Agreement (PhotoReAct, No 956324).To assess the value and reactivity of new photocatalysts (PCs), their performance should be evaluated in one or more established reactions and benchmarked against the performance using known PCs. Here, we evaluated our recently developed PC, pDTCz- DPmS, in a C(sp)-C(sp3) cross-coupling reaction that had been documented in the literature. Previous findings indicated this reaction could not proceed in the absence of PC; however, under our conditions this was not the case. Without PC, a moderate product yield was obtained, while this yield increased significantly upon addition of pDTCz-DPmS. UV-Vis absorption studies indicated that the Hantzsch ester (HE) additive was acting as a competitive absorber of the light from the excitation source, and quenching studies confirmed that the HE was quenched by the radical precursor, N-(acyloxy)phthalimide. Mechanistic investigations established that two parallel photosensitization pathways were in operation; a reductive quenching photocatalytic pathway (using pDTCz-DPmS) and a sacrificial photoreductant pathway (employing HE). These pathways work synergistically to enhance the yield of target product.Publisher PDFPeer reviewe

Light-Induced Access to Carbazole-1,3-dicarbonitrile: A Thermally Activated Delayed Fluorescent (TADF) Photocatalyst for Cobalt-Mediated Allylations

The stability of a photocatalyst under irradiation is important in photoredox applications. In this work, we investigated the stability of a thermally activated delayed fluorescence (TADF) photocatalyst {3DPAFIPN [2,4,6-tris(diphenylamino)-5-fluoroisophthalonitrile]}, recently employed in photoredox-mediated processes, discovering that in the absence of quenchers the chromophore is unstable and is efficiently converted by irradiation with visible light into another species based on the carbazole-1,3-dicarbonitrile moiety. The new species obtained is itself a TADF emitter and finds useful applications in photoredox transformations. At the excited state, it is a strong reductant and was efficiently applied to cobalt-mediated allylation of aldehydes, whereas other TADFs (4CzIPN and 3DPAFIPN) failed to promote efficient photocatalytic cycles