New properties of convex functions in the Heisenberg group

We prove some new properties of the weakly -convex functions recently introduced by Danielli, Garofalo and Nhieu. As an interesting application of our results we prove a theorem of Busemann-Feller-Alexandrov type in the Heisenberg groups , .

     

Exactly quantized dynamics of classical incommensurate sliders

We report peculiar velocity quantization phenomena in the classical motion of an idealized 1D solid lubricant, consisting of a harmonic chain interposed between two periodic sliders. The ratio upsilon(c.m.)/upsilon(ext) of the chain center-of-mass velocity to the externally imposed relative velocity of the sliders stays pinned to exact "plateau" values for wide ranges of parameters, such as slider corrugation amplitudes, external velocity, chain stiffness, and dissipation, and is strictly determined by the commensurability ratios alone. The phenomenon is explained by one slider rigidly dragging the kinks that the chain forms with the other slider. Possible consequences of these results for some real systems are discussed.     

Density functional theory in transition-metal chemistry: a self-consistent Hubbard U approach

Transition-metal centers are the active sites for a broad variety of biological and inorganic chemical reactions. Notwithstanding this central importance, density-functional theory calculations based on generalized-gradient approximations often fail to describe energetics, multiplet structures, reaction barriers, and geometries around the active sites. We suggest here an alternative approach, derived from the Hubbard U correction to solid-state problems, that provides an excellent agreement with correlated-electron quantum chemistry calculations in test cases that range from the ground state of Fe2 and Fe2- to the addition elimination of molecular hydrogen on FeO+. The Hubbard U is determined with a novel self-consistent procedure based on a linear-response approach.     

A Synthetic Fluorescent Mitochondria‐Targeted Sensor for Ratiometric Imaging of Calcium in Live Cells

Ca²⁺ handling by mitochondria is crucial for cell life and the direct measure of mitochondrial Ca²⁺ concentration in living cells is of pivotal interest. Genetically‐encoded indicators greatly facilitated this task, however they require demanding delivery procedures. On the other hand, existing mitochondria‐targeted synthetic Ca²⁺ indicators are plagued by several drawbacks, for example, non‐specific localization, leakage, toxicity. Here we report the synthesis and characterization of a new fluorescent Ca²⁺ sensor, named mt‐fura‐2, obtained by coupling two triphenylphosphonium cations to the molecular backbone of the ratiometric Ca²⁺ indicator fura‐2. Mt‐fura‐2 binds Ca²⁺ with a dissociation constant of ≈1.5 μm in vitro. When loaded in different cell types as acetoxymethyl ester, the probe shows proper mitochondrial localization and accurately measures matrix [Ca²⁺] variations, proving its superiority over available dyes. We describe the synthesis, characterization and application of mt‐fura‐2 to cell types where the delivery of genetically‐encoded indicators is troublesome.     

Tight Xenon Confinement in a Crystalline Sandwich‐like Hydrogen‐Bonded Dimeric Capsule of a Cyclic Peptide

A cyclic hexapeptide with three pyridyl moieties connected to its backbone forms a hydrogen‐bonded dimer, which tightly encapsulates a single xenon atom, like a pearl in its shell. The dimer imprints its shape and symmetry to the captured xenon atom, as demonstrated by ¹²⁹Xe NMR spectroscopy, single‐crystal X‐ray diffraction, and computational studies. The dimers self‐assemble hierarchically into tubular structures to form a porous supramolecular architecture, whose cavities are filled by small molecules and gases.     

Cosmological Horizons and Reconstruction of Quantum Field Theories

As a starting point, we state some relevant geometrical properties enjoyed by the cosmological horizon of a certain class of Friedmann-Robertson-Walker backgrounds. Those properties are generalised to a larger class of expanding spacetimes M admitting a geodesically complete cosmological horizon common to all co-moving observers. This structure is later exploited in order to recast, in a cosmological background, some recent results for a linear scalar quantum field theory in spacetimes asymptotically flat at null infinity. Under suitable hypotheses on M, encompassing both the cosmological de Sitter background and a large class of other FRW spacetimes, the algebra of observables for a Klein-Gordon field is mapped into a subalgebra of the algebra of observables constructed on the cosmological horizon. There is exactly one pure quasifree state λ on which fulfills a suitable energy-positivity condition with respect to a generator related with the cosmological time displacements. Furthermore λ induces a preferred physically meaningful quantum state λ _M for the quantum theory in the bulk. If M admits a timelike Killing generator preserving , then the associated self-adjoint generator in the GNS representation of λ _M has positive spectrum (i.e., energy). Moreover λ _M turns out to be invariant under every symmetry of the bulk metric which preserves the cosmological horizon. In the case of an expanding de Sitter spacetime, λ _M coincides with the Euclidean (Bunch-Davies) vacuum state, hence being Hadamard in this case. Remarks on the validity of the Hadamard property for λ _M in more general spacetimes are presented. Dedicated to Professor Klaus Fredenhagen on the occasion of his 60th birthday.     

Lévy processes and Schrödinger equation

We analyze the extension of the well known relation between Brownian motion and the Schrödinger equation to the family of the Lévy processes. We consider a Lévy-Schrödinger equation where the usual kinetic energy operator-the Laplacian-is generalized by means of a selfadjoint, pseudodifferential operator whose symbol is the logarithmic characteristic of an infinitely divisible law. The Lévy-Khintchin formula shows then how to write down this operator in an integro-differential form. When the underlying Lévy process is stable we recover as a particular case the fractional Schrödinger equation. A few examples are finally given and we find that there are physically relevant models-such as a form of the relativistic Schrödinger equation-that are in the domain of the non stable Lévy-Schrödinger equations.     

Evidence of structural strain in epitaxial graphene layers on 6H-SiC(0001)

The early stages of epitaxial graphene layer growth on the Si-terminated 6H-SiC (0001) are investigated by Auger electron spectroscopy (AES) and depolarized Raman spectroscopy. The selection of the depolarized component of the scattered light results in a significant increase in the C-C bond signal over the second order SiC Raman signal, which allows us to resolve submonolayer growth, including individual, localized C=C dimers in a diamondlike carbon matrix for AES C/Si ratio of approximately 3, and a strained graphene layer with delocalized electrons and Dirac single-band dispersion for AES C/Si ratio >6. The linear strain, measured at room temperature, is found to be compressive, which can be attributed to the large difference between the coefficients of thermal expansion of graphene and SiC. The magnitude of the compressive strain can be varied by adjusting the growth time at fixed annealing temperature.     

Diode-pumped Yb3+:KYF4 femtosecond laser

Passive mode locking of a diode-pumped Yb(3+):KYF(4) laser is demonstrated using a semiconductor saturable absorber mirror. A high-stability, transform-limited pulse train with a repetition rate of 57 MHz is generated. Solitonlike pulses with maximum average output power of 250 mW, minimum pulse duration of 170 fs, and rms time jitter of 360 fs were obtained.     

Protecting entanglement via the quantum Zeno effect

We study the exact entanglement dynamics of two atoms in a lossy resonator. Besides discussing the steady-state entanglement, we show that in the strong coupling regime the system-reservoir correlations induce entanglement revivals and oscillations and propose a strategy to fight against the deterioration of the entanglement using the quantum Zeno effect.