dc Josephson effect in metallic single-walled carbon nanotubes

The dc Josephson effect is investigated in a single-walled metallic carbon nanotube connected to two superconducting leads. In particular, by using the Luttinger liquid theory, we analyze the effects of the electron-electron interaction on the supercurrent. We find that in the long junction limit the strong electronic correlations of the nanotube, together with its peculiar band structure, induce oscillations in the critical current as a function of the junction length and/or the nanotube electron filling. These oscillations represent a signature of the Luttinger liquid physics of the nanotube, for they are absent if the interaction is vanishing. We show that this effect can be exploited to reverse the sign of the supercurrent, realizing a tunable π-junction.     

Airy beams from a microchip laser

It is theoretically shown that an end-pumped microchip laser formed by a thin laser crystal with plane-plane but slightly tilted facets can emit, under appropriate pumping conditions and near a crystal edge, a truncated self-accelerating Airy output beam.     

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.