All-optical phase-independent logic elements based on phase shiftinduced by coherent soliton collisions

We demonstrate, for the first time to our knowledge, that a fast coherent collision between two Kerr spatial solitons can give rise to a significant phase shift for both interacting beams. The maximal collision-induced phase shift ≈π rad takes place when the amplitudes of the solitons are equal (η₁=η₂) and the length of the interaction zone is comparable with a soliton phase period. Depending on the ratio η₂/η₁, and the collision angle between the solitons, the magnitude of the phase shift can be varied within a reasonable range, for example from 180° to 40°. The analysis of the effect performed by the finite-difference beam-propagation method has shown that it is insensitive to the initial phase difference between the incident beams (δ_i), even in the case when η ₁≠η₂. It has been demonstrated that the phenomenon can be used for all-optical three-soliton logic elements, which are capable of providing more than 3-dB signal amplification and possess bi -independent output characteristics     

Small carbon clusters doped with early transition metals: a theoretical study of ScCn, ScCn+, and ScCn- (n = 1-8) open-chain clusters

A theoretical study of the ScCn, ScCn+, and ScCn- (n = 1-8) open-chain clusters has been carried out. Predictions for their electronic energies, rotational constants, dipole moments and vibrational frequencies have been made using the B3LYP method with different basis set including effective core potentials, ECPs. For the ScCn open-chain clusters the lowest-lying states correspond to quartet states for n-odd members, whereas for n-even species the ground state is found to be a doublet. In the cationic and anionic species, the electronic ground state is found to be a singlet for even n and a triplet for odd n. An even-odd parity effect (n-even clusters being more stable than n-odd ones) is observed in neutral and charged clusters. Ionization energies and electron affinities also exhibit a clear parity alternation trend, with n-even clusters having higher values than n-odd ones.     

An alternative multipolar expansion for intermolecular potential functions

We have derived a new multipolar expansion for intermolecular potential-energy functions with applications in molecular physics, theoretical chemistry, and mathematical physics. The new formulation employs a separation of radial and angular terms with a simple index structure that leads to computational efficiency and ease of physical interpretation. For the case of the Coulomb interaction, we compare the present formulation with two conventional multipole expansions: the Cartesian tensor and the irreducible spherical tensor expansions. The new formalism leads to efficient numerical algorithms that are useful for general applications beyond intermolecular potentials. In addition to the electrostatic Coulomb interaction, we illustrate the formalism with applications to special function theory and a bipolar expansion involved in potential theory.     

Light scalars coupled to photons and non-newtonian forces

A particle phi coupling to two photons couples also radiatively to charged particles, like protons. If the particle is a light scalar, this induced coupling leads to spin-independent non-Newtonian forces. We show that the experimental constraints on exotic, fifth-type forces lead to stringent constraints on the phigammagamma coupling. We discuss the impact on the recent PVLAS results and the role of paraphoton models introduced to solve the PVLAS-CAST puzzle.     

Low-temperature series for renormalized operators: The ferromagnetic square-lattice Ising model

A method for computing low-temperature series for renormalized operators in the two-dimensional Ising model is proposed. These series are applied to the study of the properties of the truncated renormalized Hamiltonians when we start at very low temperature and zero field. The truncated Hamiltonians for majority rule, Kadanoff transformation, and decimation for 2×2 blocks depend on the how we approach the first-order phase-transition line. The renormalization group transformations are multivalued and discontinuous at this first-order transition line when restricted to some finite-dimensional interaction space.     

Rates of desorption from solid surfaces: Coverage dependence

The recently developed Classical Stochastic Diffusion Theory is applied to obtain the coverage dependence of desorption rates for Xe on W(111). Using the attractive Xe-Xe potential from gas phase experiments, we find a strong coverage dependence in the desorption rates and calculate Temperature Programmed Desorption Spectra (for a potential with reduced attractiveness) that are in excellent qualitative agreement with experimental results. We also investigated the effect of purely repulsive adsorbate-adsorbate interactions where we find, for some coverage ranges, that two different adsorption configurations can be stable (at different temperatures) leading to a marked change in the corresponding desorption rates and to distinct non-Arrhenius behavior.     

Dual disjoint hypercyclic operators

Let E be a separable Fréchet space. The operators T₁,…,Tm are disjoint hypercyclic if there exists x∈E such that the orbit of (x,…,x) under (T₁,…,Tm) is dense in E×?×E. We show that every separable Banach space E admits an m-tuple of bounded linear operators which are disjoint hypercyclic. If, in addition, its dual E^∗ is separable, then they can be constructed such that are also disjoint hypercyclic.     

Absence of phase transition for antiferromagnetic Potts models via the Dobrushin uniqueness theorem

We prove that theq-state Potts antiferromagnet on a lattice of maximum coordination numberr exhibits exponential decay of correlations uniformly at all temperatures (including zero temperature) wheneverq>2r. We also prove slightly better bounds for several two-dimensional lattices: square lattice (exponential decay forq7), triangular lattice (q11), hexagonal lattice (q4), and Kagomé lattice (q6). The proofs are based on the Dobrushin uniqueness theorem.     

A new approach for modelling the damped Helmholtz oscillator:applications to plasma physics and electronic circuits

In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.