Interaction of a parabolic-shaped pulse pair in a passively mode-locked Yb-doped fiber laser

We numerically investigate the formation and interaction of a parabolic-shaped pulse pair in a passively mode-locked Yb-doped fiber laser. Based on a lumped model, the parabolic-shaped pulse pair is obtained by controlling the intercavity average dispersion and gain saturation energy, Moreover, pulse repulsive and attractive motion are also achieved with different pulse separations. Simulation results show that the phase shift plays an important role in pulse interaction, and the interaction is determined by the inter-cavity average dispersion and gain saturation energy, i.e., the strength of the interaction is proportional to the gain saturation energy, a stronger gain saturation energy will result in a higher interaction intensity. On the contrary, the increase of the inter-cavity dispersion will counterbalance some interaction force. The results also show that the interaction of a parabolic-shaped pulse pair has a larger interaction distance compared to conventional solitons.     

Interaction of parabolic-shaped pulse pair in a passively mode-locked Yb-doped fiber laser

We numerically investigate the formation and interaction of parabolic-shaped pulse pair in a passively mode-locked Yb-doped fiber laser. Based on a lumped model, the parabolic-shaped pulse pair is obtained by controlling the inter-cavity average dispersion and gain saturation energy, Moreover, pulse repulsive and attractive motion are also achieved with different pulse separations. Simulation results show that the phase shift plays an important role in pulse interaction, and the interaction is determined by the inter-cavity average dispersion and gain saturation energy, i.e., the strength of the interaction is proportional to the gain saturation energy, the stronger gain saturation energy will result in higher interaction intensity. On the contrary, the increase of the inter-cavity dispersion will counterbalance some interaction force. The results also show that the interaction of a parabolic-shaped pulse pair has a larger interaction distance compare to the conventional solitons.     

Influence of the interaction volume on the kinetic energy resolution of a velocity map imaging spectrometer

We investigate the influence of the interaction volume on the energy resolution of a velocity map imaging spectrometer.The simulation results show that the axial interaction size has a significant influence on the resolution. This influence is increased for a higher kinetic energy. We further show that the radial interaction size has a minor influence on the energy resolution for the electron or ion with medium energy, but it is crucial for the resolution of the electron or ion with low kinetic energy. By tracing the flight trajectories we show how the electron or ion energy resolution is influenced by the interaction size.     

Elastic interaction between a dislocation and a near-by inclusion

The study of elastic interaction between a dislocation and an inclusion (i.e., a region transformed without change of elastic constants) in an elastic continuum is extended to the cases when the singular dislocation line intersects or touches the inclusion or is situated inside it. The interaction energy is shown to be a finite and continuous function of position of the inclusion. The interaction of an edge dislocation with a dilatation sphere and of a screw dislocation with a sphere transformed into ellipsoid in isotropic continuum are studied in detail. The spherical inclusion which is considered as a rough model of a point defect (e.g. of carbon atom in iron) has a maximum and minimum energy position near the dislocation line so that the binding energy can be calculated in a consistent way.     

Elastic interaction between a point defect and a step

The elastic interaction energy between a point defect or an adatom and a step is calculated. The defect is represented by a localized dipole force while the presence of the step is modelled by a distribution of dipole forces on half of the surface plane. The interaction energy changes sign when the defect goes through the plane perpendicular to the surface and containing the edge of the step. For an adatom, this energy behaves like the inverse of its distance to the edge of the step ; it is attracted to the step on one terrace and repelled from it on the other terrace.     

Energy of a Polaron in a Wurtzite Nitride Finite Parabolic Quantum Well

The effects of electron-phonon interaction on energy levels of a polaron in a wurtzite nitride finite parabolic quantum well （PQW） are studied by using a modified Lee-Low-Pines variational method. The ground state, first excited state, and transition energy of the polaron in the GaN/Al0.3Ga0.7N wurtzite PQW are calculated by taking account of the influence of confined LO（TO）-like phonon modes and the half-spaee LO（TO）-like phonon modes and considering the anisotropy of all kinds of phonon modes. The numerical results are given and discussed. The results show that the electron-phonon interaction strongly affects the energy levels of the polaron, and the contributions from phonons to the energy of a polaron in a wurtzite nitride PQW are greater than that in an A1GaAs PQW. This indicates that ehe electron-phonon interaction in a wurtzite nitride PQW is not negligible.     

Infrared catastrophe in a two-quasiparticle collision integral

Relaxation of a nonequilibrium state in a disordered metal with a spin-dependent electron energy distribution is considered. The collision integral due to the electron-electron interaction is computed within the approximation of a two-quasiparticle scattering. It is shown that the spin-flip scattering processes with a small energy transfer may lead to the divergence of the collision integral for a quasi one-dimensional wire. This divergence is present only for a spin-dependent electron energy distribution that corresponds to the total electron spin magnetization M = 0 and only for nonzero interaction in the triplet channel. In this case, a nonperturbative treatment of the electron-electron interaction is needed to provide an effective infrared cutoff.     

Exciton eigenstates and biexciton interaction energies in a spherical core/shell semiconductor hetero-nano structure

The exciton eigenstates and biexciton interaction energies in a spherical core–shell hetero-nano structure in the type II and the quasi-type II carrier localization regimes have been analyzed. For the analysis, we have evaluated the electron–hole overlap integral, the binding energy of exciton ground state, and the interaction energy of bi-exciton ground state in the structure. In the evaluation, the first order perturbation approach has been employed, where the direct Coulomb interaction energy, the surface polarization energy and the dielectric solvation energy are included. Our results show that the exciton eigenenergies and exciton–exciton interaction energy strongly depend on the choice of materials on which both the dielectric constants and the electron and hole effective masses rely.     

The van der Waals interaction energy between a void and a metal surface

The plasmon part of the van der Waals interaction energy between a void and a metal surface is calculated. In the limit of large z₀ (distance between the void and the surface), the interaction energy is shown to be proportional to z^-3₀ and 2 to 5 times larger than the elastic energy for copper.     

Energy of a wedge-shaped nanotwin calculated in terms of a dislocation mesoscopic model

The total energy of a wedge-shaped micro- and nanotwin is calculated in terms of a dislocation mesoscopic model. The total energy of the twin is represented as a sum of the elastic energy, energy of interaction between twinning dislocations, and stacking-fault energy of partial dislocations of the wedge-shaped twin. It is found that the evolution of the twin is controlled by the energy of interaction between twinning dislocations: in the case of a microtwin, it is five orders of magnitude higher than the elastic energy and six orders of magnitude higher than the stacking-fault energy. In the case of a nanotwin with the number of twinning dislocations at the twin boundary less than 20, all the three energies listed above are of the same order of magnitude. Therefore, all the components of the total energy contribute to the origination of a wedge-shaped twin. As the length of the twin increases with its width and the number of twinning dislocations at twin boundaries fixed, the total energy modulo grows although the density of twinning dislocations at twin boundaries decreases. This indicates that long-range stress fields due to twinning dislocations play an important part in the evolution of a wedge-shaped twin.     

Inelastic scattering and trapping of an atom on a cold,simple-cubic lattice

We report numerical calculations on the inelastic scattering of an incident atom with a simple-cubic harmonic lattice with the collision restricted to the head-on orientation. These calculations represent the first systematic investigation of the behavior of the energy accommodation coefficient and critical trapping energy as the interaction well depth, interaction range, incident energy, and incident mass are varied over significant ranges. These exact results provide a new, substantial “data base” for interpreting experimental results and for testing approximate theories. The incident atom is assumed to collide head-on with only one lattice surface atom. A Morse interaction is used, so that the dynamical effects of both an attractive and a repulsive interaction are included. The lattice is initially cold and classical mechanics is used throughout; the lattice dynamics are treated exactly by means of the response function for the Rosenstock-Newell lattice. We find that long range, soft interactions characteristic of physisorbed species display a broad minimum in energy accommodation at an incident energy near the dissociation energy of the adatom-surface interaction for adatom to lattice atom mass ratios of order one and greater. Stiffer interactions characteristic of chemisorbed species display a pronounced maximum in energy accommodation for mass ratios near 0.7. This is associated with a maximum in the critical trapping energy at the same mass ratio. The results are analyzed to confirm the validity of approximations based on both fast and slow collisions. In the high energy limit, the energy accommodation depends essentially only on the mass ratio, reflecting the pairwise binary collisions. In the slow collision limit, the collision dynamics are described by a newly derived adiabatic approximation for the lattice response.     

Infrared catastrophe in a two-quasiparticle collision integral

Relaxation of a nonequilibrium state in a disordered metal with a spin-dependent electron energy distribution is considered. The collision integral due to the electron-electron interaction is computed within the approximation of a two-quasiparticle scattering. It is shown that the spin-flip scattering processes with a small energy transfer may lead to the divergence of the collision integral for a quasi one-dimensional wire. This divergence is present only for a spin-dependent electron energy distribution that corresponds to the total electron spin magnetization M = 0 and only for nonzero interaction in the triplet channel. In this case, a nonperturbative treatment of the electron-electron interaction is needed to provide an effective infrared cutoff. The text was submitted by the authors in English. An erratum to this article is available at .     

Two Electron States in a Quantum Ring on a Sphere

Two electron states in a quantum ring on a spherical surface are discussed. The problem is discussed within the frameworks of Russell–Saunders coupling scheme, that is, the spin–orbit coupling is neglected. Treating Coulomb interaction as a perturbation, the energy correction for different states is calculated. The dependence of the Coulomb interaction energy on external polar boundary angle of quantum ring is obtained. In analogue with the helium atom the concept of states exchange time is introduced, and its dependence on geometrical parameters of the ring is shown.     

Magneto-elastic phase transition in a linear chain within the double and super-exchange model

In this work a magneto-elastic phase transition in a linear chain was obtained due the interplay between magnetism and lattice distortion in a double and super-exchange model. We consider a linear chain consisting of classical localized spins interacting with itinerant electrons. Due to the double exchange interaction, localized spins align ferromagnetically. This ferromagnetic tendency is expected to be frustrated by the anti-ferromagnetic super-exchange interaction between neighbor localized spins. Additionally, the lattice parameter is allowed to have small changes, which contributes harmonically to the energy of the system. The phase diagram is obtained as a function of the electron density and the super-exchange interaction using a Monte Carlo minimization. At low super-exchange interaction energy phase transition between electron-full ferromagnetic distorted and electron-empty anti-ferromagnetic undistorted phases occurs. In this case all electrons and lattice distortions were found within the ferromagnetic domain. For high super-exchange interaction energy, phase transition between two site distorted periodic arrangement of independent magnetic polarons ordered anti-ferromagnetically and the electron-empty anti-ferromagnetic undistorted phase was found. For this high interaction energy, Wigner crystallization, lattice distortion and charge distribution inside two-site polarons were obtained.     

Coulomb interactions in a computer simulation of a system periodic in two directions

The integral representation of the gamma function and the Poisson summation formula are used to calculate the interaction energy of charged particles in a 3-dimensional system periodic in two directions. A parallelogram shape simulation box is considered. Calculations are carried out for interactions described by any inverse power, and analytical continuation of the energy function leads to the final expression for the Coulomb interaction energy. Summation over the simulation box replica along one or the other side of the box base is replaced by summation in reciprocal space. Therefore there are two equivalent formulas for the potential energy that offer the possibility of avoiding slowly convergent series. The energy expressions are identical to those obtained from the Lekner method. The special case is considered where the functions defining the energy are infinite, i.e. when two charges lie on a line parallel to the simulation box side that was chosen to convert real space summation into reciprocal space.     

Diffusion of a Brownian walker in a bidimensional disordered medium constituted by adsorbing spheres suspended in a solvent

This paper reports on studies of the behaviour of a Brownian walker that diffuses in a bidimensional non-homogeneous medium constituted by immobile spherical adsorbing obstacles residing in a continuous solvent. Results show that the probability that the random walker is adsorbed, for a given adsorbing interaction potential between the walker and the surface, depends only on the full adsorbing surface S in the reaction medium, and does not show any appreciable dependence on the size of the adsorbing obstacles. Also, the diffusion coefficient of the random walker depends only on the value of S (for a given adsorbed interaction) if the adsorption energy is large enough. In contrast, when the adsorption energy between the walker and the surface of the adsorbing obstacles is zero, the diffusion coefficient decays exponentially with the volume fraction occupied for the obstacles. The efficiency of the walker to visit all obstacles in the simulation cell depends strongly on the concentration of obstacles and on the adsorbing interaction energy, decreasing quickly to zero with an increase in these parameters.     

On the validity of the triple-dipole interaction as a representation of non-additive intermolecular forces

A complete partial wave analysis of the non-expanded non-additive coulomb interaction energy for three non-degenerate S-state atoms is given through third-order in the interatomic potential energy function. Pseudo state techniques are used to evaluate various partial wave components of the non-expanded second and third-order non-additive interaction energies for various isosceles triangular configurations of three interacting ground-state hydrogen atoms. These second and third-order non-expanded coulomb results are used, in conjunction with Heitler-London results for the first-order non-additive energies for the quartet spin state of the H(1s)-H(1s)-H(1s) interaction, to discuss the relative importance of various parts of the non-additive energy as a function of the geometrical configuration of the atoms, and the validity of both the non-expanded triple-dipole energy and the expanded Axilrod-Teller-Muto triple-dipole result as a representation of non-additive coulomb energies. For example, in the non-bonded interaction of three S-state atoms it appears that representing the non-additive energy by the non-additive coulomb energy is not reliable until the interatomic separations are somewhat larger than R*, the interatomic distance associated with the van der Waals minimum in the corresponding non-bonded dimer interaction. Further, the use of the triple-dipole interaction energy, with or without charge overlap corrections, to represent the non-additive coulomb energy is of doubtful validity until the interatomic separations are considerably greater than R*.     

Bound polaron in a spherical quantum dot under an electric field

A variational approach is used to study the ground state of a bound polaron in a spherical quantum dot under an external electric field. The binding energy of the hydrogenic impurity state is calculated by taking the interaction of an electron with both the confined longitudinal optical phonons and the surface optical phonons into account. The interaction between impurity and longitudinal optical phonons has also been considered to obtain the binding energy of a bound polaron. It shows that the polaron effects give significant corrections to the binding energy and its Stark energy shift. The external electric field increases the phonon contributions to the binding energy.     

Realization of a resonant Fermi gas with a large effective range

We have measured the interaction energy and three-body recombination rate for a two-component Fermi gas near a narrow Feshbach resonance and found both to be strongly energy dependent. Even for de Broglie wavelengths greatly exceeding the van der Waals length scale, the behavior of the interaction energy as a function of temperature cannot be described by atoms interacting via a contact potential. Rather, energy-dependent corrections beyond the scattering length approximation are required, indicating a resonance with an anomalously large effective range. For fields where the molecular state is above threshold, the rate of three-body recombination is enhanced by a sharp, two-body resonance arising from the closed-channel molecular state which can be magnetically tuned through the continuum. This narrow resonance can be used to study strongly correlated Fermi gases that simultaneously have a sizable effective range and a large scattering length.     

Two Electron States in a Thin Spherical Nanolayer: Reduction to the Model of Two Electrons on a Sphere

Two electron states in a thin spherical nanolayer are discussed. Adiabatic approach is used to divide the system to fast (radial) and slow (angular) subsystems. This leads the Coulomb interaction to be dependent on angular variables, more precisely, on the relative angle between electrons. Approximated Coulomb interaction potential is discussed. Analytical solutions for angular part of Schrödinger equation as well as for energy spectrum for the case of harmonic approximation are obtained. Also the first order of correction energy is discussed by using perturbation theory. For the ground state an analytical expression for the first order correction energy dependent on effective radius of the nanolayer is obtained. Obtained results are compared with exact Coulomb interaction model presented by Loos and Gill.