Point interactions for 3D sub-Laplacians

In this paper we show that, for a sub-Laplacian Δ on a 3-dimensional manifold M, no point interaction centered at a point $q_0\in M$ exists. When M is complete w.r.t. the associated sub-Riemannian structure, this means that Δ acting on $C_0^{\infty }(M?\{q_0\})$ is essentially self-adjoint in $L^2(M)$. A particular example is the standard sub-Laplacian on the Heisenberg group. This is in stark contrast with what happens in a Riemannian manifold N, whose associated Laplace-Beltrami operator acting on $C_0^{\infty }(N?\{q_0\})$ is never essentially self-adjoint in $L^2(N)$, if $\dim ?N\le 3$. We then apply this result to the Schrödinger evolution of a thin molecule, i.e., with a vanishing moment of inertia, rotating around its center of mass.     

A Boundary Estimate for Degenerate Parabolic Diffusion Equations

Potential Analysis - We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to degenerate parabolic equations of p-laplacian type....     

Monitoring the Light-induced Isomerisation of the Prototypical Polycyclic Aromatic Hydrocarbons C10H8+ through Ion-Molecule Reactions

Structural rearrangements in ions are essential for understanding the composition and evolution of energetic and chemically active environments. This study explores the interconversion routes for simple polycyclic aromatic hydrocarbons, namely naphthalene and azulene radical cations (C₁₀H₈⁺), by combining mass spectrometry and vacuum ultraviolet tunable synchrotron radiation through the chemical monitoring technique. Products of ion-molecule reactions are used to probe C₁₀H₈⁺ structures that are formed as a function of their internal energies. Isomerisation from azulene radical cation towards naphthalene radical cation in a timescale faster than 80 μs was monitored, whereas no reverse isomerisation was observed in the same time window. When energising C₁₀H₈⁺ with more than 6 eV, the reactivity of C₁₀H₈⁺ unveils the formation of a new isomeric group with a contrasted reactivity compared with naphthalene and azulene cations. We tentatively assigned these structures to phenylvinylacetylene cations.     

Complexes of Dichlorogermylene with Phosphine/Sulfoxide-Supported Carbone as Ligand

Due to their remarkable electronic features, recent years have witnessed the emergence of carbones L₂C, which consist in two donating L ligands coordinating a central carbon atom bearing two lone pairs. In this context, the phosphine/sulfoxide-supported carbone 4 exhibits a strong nucleophilic character, and here, we describe its ability to coordinate dichlorogermylene. Two original stable coordination complexes were obtained and fully characterized in solution and in the solid state by NMR spectroscopy and X-ray diffraction analysis, respectively. At 60 °C, in the presence of 4, the Ge(II)-complex 5 undergoes a slow isomerization that transforms the bis-ylide ligand into an yldiide.     

Electrical biosensing with synthetic nanopores and nanochannels

The integration of constriction structures such as nanopores and nanochannels into fluidic devices discloses powerful biosensing capabilities that can be tuned to a wide range of analytes through conceptually simple size calibrations. The practical implementation of this tuning requires a nontrivial manipulation of matter at nanoscale with further requirements for low complexity and low-cost procedures that may be adapted to industrial production. Here, we review the recent progress on the fabrication techniques of nanopores and nanochannels, together with the efforts to realize their full biosensing potential by understanding and amending the problems still afflicting the measurement performed during operation.     

Friction oscillator excited by moving base and colliding with a rigid or deformable obstacle

The dynamics of non-smooth oscillators has not yet sufficiently been investigated, when damping is simultaneously due to friction and impact. Because of the theoretical and practical interest of this type of systems, an effort is made in this paper to lighten the behaviour of a single-degree-of-freedom oscillator colliding with an obstacle and excited by a moving base, which transfers energy to the system via friction. The different nature of discontinuities arising in the combined problem of friction and impact has been recognized and discussed. Closed-form solutions are presented for both transient and steady-state response, assuming Coulomb's friction law and a rigid stop-limiting motion. Furthermore, a deformable (hysteretic) obstacle has been considered, and its influence on the response has been investigated.     

Entanglement and Non-Locality in Quantum Protocols with Identical Particles

We study the role of entanglement and non-locality in quantum protocols that make use of systems of identical particles. Unlike in the case of distinguishable particles, the notions of entanglement and non-locality for systems whose constituents cannot be distinguished and singly addressed are still debated. We clarify why the only approach that avoids incongruities and paradoxes is the one based on the second quantization formalism, whereby it is the entanglement of the modes that can be populated by the particles that really matters and not the particles themselves. Indeed, by means of a metrological and of a teleportation protocol, we show that inconsistencies arise in formulations that force entanglement and non-locality to be properties of the identical particles rather than of the modes they can occupy. The reason resides in the fact that orthogonal modes can always be addressed while identical particles cannot.     

Oxidation of α-Acetoxy Acetals with Trichloroisocyanuric Acid

α-Acetoxy acid methyl esters are prepared in excellent yields by treating aliphatic α-acetoxy dimethyl acetals with trichloroisocyanuric acid in DMF.