Comparison of Spaces of Hardy Type for the Ornstein–Uhlenbeck Operator

Denote by γ the Gauss measure on ℝ ⁿ and by ${\mathcal{L}}${\mathcal{L}} the Ornstein–Uhlenbeck operator. In this paper we introduce a Hardy space \mathfrakh¹g{{\mathfrak{h}}^1}{{\rm \gamma}} of Goldberg type and show that for each u in ℝ ∖ {0} and r > 0 the operator (rI+L)^iu(r{\mathcal{I}}+{\mathcal{L}})^{iu} is unbounded from \mathfrakh¹g{{\mathfrak{h}}^1}{{\rm \gamma}} to L ¹γ. This result is in sharp contrast both with the fact that (rI+L)^iu(r{\mathcal{I}}+{\mathcal{L}})^{iu} is bounded from H ¹γ to L ¹γ, where H ¹γ denotes the Hardy type space introduced in Mauceri and Meda (J Funct Anal 252:278–313, 2007), and with the fact that in the Euclidean case (rI-D)^iu(r{\mathcal{I}}-\Delta)^{iu} is bounded from the Goldberg space \mathfrakh¹\mathbbRⁿ{{\mathfrak{h}}^1}{{\mathbb{R}}^n} to L ¹ℝ ⁿ . We consider also the case of Riemannian manifolds M with Riemannian measure μ. We prove that, under certain geometric assumptions on M, an operator T{\mathcal{T}}, bounded on L ² μ, and with a kernel satisfying certain analytic assumptions, is bounded from H ¹ μ to L ¹ μ if and only if it is bounded from \mathfrakh¹m{{\mathfrak{h}}^1}{\mu} to L ¹ μ. Here H ¹ μ denotes the Hardy space introduced in Carbonaro et al. (Ann Sc Norm Super Pisa, 2009), and \mathfrakh¹m{{\mathfrak{h}}^1}{\mu} is defined in Section 4, and is equivalent to a space recently introduced by M. Taylor (J Geom Anal 19(1):137–190, 2009). The case of translation invariant operators on homogeneous trees is also considered.     

Spectral Structure and Doublon Dissociation in the Two-Particle Non-Hermitian Hubbard Model

Strongly-correlated systems in non-Hermitian models are an emergent area of research. Herein, a non-Hermitian Hubbard model is considered, where the single-particle hopping amplitudes on the lattice are not reciprocal, and provide exact analytical results of the spectral structure in the two-particle sector of Hilbert space under different boundary conditions. The analysis unveils some interesting spectral and dynamical effects of purely non-Hermitian nature and that deviate from the usual scenario found in the single-particle regime. Specifically, a spectral phase transition of the Mott-Hubbard band on the infinite lattice is predicted as the interaction energy is increased above a critical value, from an open to a closed loop in complex energy plane, and the dynamical dissociation of doublons, i.e., instability of two-particle bound states, in the bulk of the lattice, with a sudden revival of the doublon state when the two particles reach the lattice edge. Particle dissociation observed in the bulk of the lattice is a clear manifestation of non-Hermitian dynamics arising from the different lifetimes of single-particle and two-particle states, whereas the sudden revival of the doublon state at the boundaries is a striking burst edge dynamical effect peculiar to non-Hermitian systems with boundary-dependent energy spectra, here predicted for the first time for correlated particles.     

A Note on Fick’s Law with Phase Transitions

Journal of Statistical Physics - We characterize the non equilibrium stationary states in two classes of systems where phase transitions are present. We prove that the interface in the limit is a...     

A Novel [OSSO]-Type Chromium(III) Complex as a Versatile Catalyst for Copolymerization of Carbon Dioxide with Epoxides

A new chromium(III) complex, bearing a bis-thioether-diphenolate [OSSO]-type ligand, was found to be an efficient catalyst in the copolymerization of CO₂ and epoxides to achieve poly(propylene carbonate), poly(cyclohexene carbonate), poly(hexene carbonate) and poly(styrene carbonate), as well as poly(propylene carbonate)(cyclohexene carbonate) and poly(propylene carbonate)(hexene carbonate) terpolymers.     

Reversibility in Infinite Hamiltonian Systems with Conservative Noise

The set of stationary measures of an infinite Hamiltonian system with noise is investigated. The model consists of particles moving in with bounded velocities and subject to a noise that does not violate the classical laws of conservation, see [OVY]. Following [LO] we assume that the noise has also a finite radius of interaction, and prove that translation invariant stationary states of finite specific entropy are reversible with respect to the stochastic component of the evolution. Therefore the results of [LO] imply that such invariant measures are superpositions of Gibbs states. Received: 26 September 1996 / Accepted: 3 January 1997     

Complex Geometry and Dirac Equation

Complex geometry represents a fundamentalingredient in the formulation of the Dirac equation bythe Clifford algebra. The choice of appropriate complexgeometries is strictly related to the geometricinterpretation of the complex imaginary unit . We discuss two possibilities which appearin the multivector algebra approach: the₁₂₃ and ₂₁ complexgeometries. Our formalism provides a set of rules which allows an immediate translation between thecomplex standard Dirac theory and its version withingeometric algebra. The problem concerning a doublegeometric interpretation for the complex imaginary unit is also discussed.     

Cosmological dark energy effects from entanglement

The thorny issue of relating information theory to cosmology is here addressed by assuming a possible connection between quantum entanglement measures and observable universe. In particular, we propose a cosmological toy model, where the equation of state of the cosmological fluid, which drives the today observed cosmic acceleration, can be inferred from quantum entanglement between different cosmological epochs. In such a way the dynamical dark energy results as byproduct of quantum entanglement.     

Electrochemical behavior of active surface layers in AA8xxx aluminum alloys

AA8xxx alloys employed in the HVAC&R sector (heating, ventilating, air conditioning, and refrigerating) were investigated to highlight the effect of active surface layers in heat-exchanger fins. The local behavior of the surface and the bulk of the alloy sheets was studied by means of an electrochemical microcell in combination with glow-discharge optical-emission spectrometry. Surface layers strongly enhance the electrochemical activity of the fin material. This is related to the segregation of Mg and other elements (Sn) strongly impairing the protective behavior of the oxide film generated during thermomechanical processing.     

Speciation of phytate ion in aqueous solution. Cadmium(II) interactions in aqueous NaCl at different ionic strengths

Interactions between myo-inositol 1,2,3,4,5,6-hexakis(dihydrogen phosphate) (phytic acid) and cadmium(II) were studied by using potentiometry (at 25 °C with the ISE-H⁺ glass electrode) in different metal to ligand (Phy) ratios (1:1≤Cd²⁺:Phy≤4:1) in NaCl_aq at different ionic strengths (0.1≤I/mol L⁻¹≤1). Nine Cd_iH_jPhy^{(12−2i−j)−} species are formed with i=1 and 2 and 4≤j≤7; and trinuclear Cd₃H₄Phy²⁻. Dependence of complex formation constants on ionic strength was modeled by using Specific ion Interaction Theory (SIT) equations. Phytate and cadmium speciation are also dependent on the metal to ligand ratio. Stability of Cd_iH_jPhy^{(12−2i−j)−} species was modeled as a function of both the ligand protonation step (j) and the number of metal cations bound to phytate (i), and relationships found were used for the prediction of species other than those experimentally determined (mainly di- and tri-protonated complexes), allowing the possibility of modeling Phy and Cd(II) behavior in natural waters and biological fluids. A critical evaluation of phytate sequestering ability toward cadmium(II) has been made under several experimental conditions, and the determination of an empirical parameter has been proposed for an objective “quantification” of this ability. A thorough analysis of literature data on phytate–cadmium(II) complexes has been performed. Previous contributions to this series: [1–8]     

Defining the nucleotide binding sites of P2Y receptors using rhodopsin-based homology modeling

Ongoing efforts to model P2Y receptors for extracellular nucleotides, i.e., endogenous ADP, ATP, UDP, UTP, and UDP-glucose, were summarized and correlated for the eight known subtypes. The rhodopsin-based homology modeling of the P2Y receptors is supported by a growing body of site-directed mutagenesis data, mainly for P2Y₁ receptors. By comparing molecular models of the P2Y receptors, it was concluded that nucleotide binding could occur in the upper part of the helical bundle, with the ribose moiety accommodated between transmembrane domain (TM) 3 and TM7. The nucleobase was oriented towards TM1, TM2, and TM7, in the direction of the extracellular side of the receptor. The phosphate chain was oriented towards TM6, in the direction of the extracellular loops (ELs), and was coordinated by three critical cationic residues. In particular, in the P2Y₁, P2Y₂, P2Y₄, and P2Y₆ receptors the nucleotide ligands had very similar positions. ADP in the P2Y₁₂ receptor was located deeper inside the receptor in comparison to other subtypes, and the uridine moiety of UDP-glucose in the P2Y₁₄ receptor was located even deeper and shifted toward TM7. In general, these findings are in agreement with the proposed binding site of small molecules to other class A GPCRs.