Optical solitons in (1 + 1) and (2 + 1) dimensions

This paper addresses the nonlinear Schrödinger's equation that serves as the model to study the propagation of optical solitons through nonlinear optical fibers. The main focus of this paper is the aspect of integrability. There are a couple of integration tools that are employed to obtain the exact solutions to the model. Fan's F-expansion approach is applied to extract several forms of solutions to the model. This integration mechanism displays cnoidal waves, snoidal waves and several other solutions; needless to mention that these solutions, in the limiting case, leads to bright, dark and singular soliton solutions. The study then rolls over to the (2 + 1)-dimensions where, in addition, the semi-inverse variational principle is applied to extract a bright soliton solution, along with the necessary constraint conditions. There is also a display of several numerical simulations.     

Rate coefficients measurement for the energy-pooling collisions Cs(5D) + Cs(5D) → Cs(6S) + Cs(nl = 9D, 11S, 7F)

We report experimental rate coefficients for the energy-pooling collisions Cs(5D) + Cs(5D) → Cs(6S) + Cs(nl = 9D, 11S, 7F). In the experiment the Cs(5D) state was populated via photodissociation of Cs₂ molecules using an argon-ion laser at wavelength 488.0 nm. We also consider the competing process 6P_1/2 + 7S → 6S + (nl = 9D, 11S, 7F) that might also populate 9D, 11S and 7F. An intermodulation technique was used to select the fluorescence contributions due only to the process 6P_1/2 + 7S → 6S + (nl = 9D, 11S, 7F). The excited atom (nl_J) density and spatial distribution were mapped by monitoring the absorption of a counterpropagating probe laser beam tuned to various transitions. The measured excited atom densities are combined with measured fluorescence ratios to yield rate coefficients for the energy-pooling collisions Cs(5D) + Cs(5D) → Cs(6S) + Cs(nl = 9D, 11S, 7F). The rate coefficients for nl = 9D, 11S, 7F are (4.1 ± 2.0) × 10⁻¹⁰ cm³ s⁻¹, (1.6 ± 0.8) × 10⁻¹⁰ cm³ s⁻¹ and (3.6 ± 1.8) × 10⁻¹⁰ cm³ s⁻¹, respectively. The contributions to the rate coefficients from other energy transfer processes are also discussed.     

Quasiclassical studies of Eley-Rideal and hot-atom reactions on a surface at 94 K: H(D) → D(H) + Cu(1 1 1)

Reactions and reaction dynamics of gas-phase H(or D) atoms with D(or H) atoms adsorbed onto a Cu(1 1 1) surface have been investigated by the quasi-classical molecular dynamics method. To simulate the H(D) → D(H) + Cu(1 1 1) system at a 94 K surface temperature, D(or H) adsorbates were disseminated arbitrarily on the surface of Cu(1 1 1) to form 0.50, 0.28 and 0.18 ML of coverages. The interaction of hydrogen atoms and the surface system is worked out by an LEPS function. LEPS parameters have been determined by using the total energy values which were calculated by a density functional theory (DFT) method and the generalized gradient approximation (GGA) for the exchange-correlation energy for various configurations of one and two hydrogen atoms on the Cu(1 1 1) surface. The Cu(1 1 1) surface, imitated by an embedded-atom method which is a many-body potential parameterized by Voter-Chen, is formed as a multilayer slab. The slab atoms are permitted to move. Various processes, trapping onto the surface, inelastic reflection of the incident projectile and penetration of the adsorbate or projectile atom into the slab, are examined. The dependence of these mechanisms on isotopic replacement has also been analyzed. Considerable contributions of the hot-atom pathways for the product formations are consequently observed. The rate of subsurface penetrations is obtained to be larger than the sticking rate onto the surface.     

Quantum states of hydrogen (H, D, T) atoms on Cu(1 0 0) and (1 1 0) surfaces

We investigate the quantum mechanical behavior of adsorbed hydrogen (H, D, T) on Cu(1 0 0) and (1 1 0) surfaces. We construct potential energy surfaces (PESs) for the motion of the hydrogen H atom on Cu(1 0 0) and (1 1 0) surfaces within the framework of density functional theory. The potential energy takes a minimum value on the hollow site of Cu(1 0 0) and on the short bridge site of Cu(1 1 0). Moreover, we calculate the quantum states of hydrogen atom motion on these calculated PESs. The ground state wave function of the hydrogen atom motion is strongly localized around the hollow site on the Cu(1 0 0) surface. On the other hand, the ground state wave function of the hydrogen atom motion on Cu(1 1 0) is distributed from the short bridge site to two neighboring pseudo-threefold sites. We finally show isotope effects on the quantum states of the motion of hydrogen on both surfaces.     

Structure and stability of Sb/Au(1 1 0)-c(2 × 2) surface phase

Adsorption of 0.5 monolayers (ML) of Sb on the Au(1 1 0) surface resulted in the formation of a c(2 × 2) surface reconstruction. Analysis of surface X-ray diffraction data by a direct method revealed the existence of an ordered substitutional surface alloy, with every other hollow site occupied by Au and Sb atoms. Quantitative conventional χ² refinement showed a contraction of 0.12 ± 0.03 Å in the spacing of the first Au layer to the second, an expansion of 0.13 ± 0.03 Å in the second-to-third layer distance, and an inward Sb displacement (rumpling) of 0.21 ± 0.04 Å. This surface phase proved to be extremely robust, with the long-range order of this arrangement remaining up to substrate temperatures of 900 K.     

Transformation to soluble model for structural phase transition from (4 × 1) to (8 × “2”) of In-adsorbed Si(1 1 1) surface

The Ising model proposed previously for the structural phase transition from (4 × 1) to (8 × “2”) of In-adsorbed Si(1 1 1) surface, Hamiltonian of which is consisting of a two-spin interaction as well as a four-spin interaction is shown to be equivalent in thermodynamic properties to a soluble Ising model with two-spin interactions. Temperature dependence of the long range order and the transition temperature can now be determined from the exact formulae. Comparison between the simulation results and those from the exact formulae is made to see accuracy of the simulation.     

A spectro-microscopic study of the reactive phase separation of Au + Pd and O on Rh(1 1 0)

Reorganization of Au + Pd submonolayers on a Rh(1 1 0) surface occurring during the water formation reaction has been observed and characterized by low energy electron microscopy (LEEM) and X-ray photoemission electron microscopy (XPEEM). The results demonstrate segregation of Au + Pd and oxygen into separate surface phases, the morphology and size of the O and Au + Pd patterns being governed by the reaction parameters and adsorbate coverage. At moderate Au + Pd coverages and temperatures in the range 760-860 K, lamellar periodic Au + Pd/O micro-structures are generated. The results are interpreted in terms of kinetic and thermodynamic considerations.     

Assignment of surface IR absorption spectra observed in the oxidation reactions: 2H + H2O/Si(1 0 0) and H2O + H/Si(1 0 0)

Infrared reflection absorption spectroscopy that used buried metal layer substrates (BML-IRRAS) and density functional cluster calculations were employed to investigate the water related oxidation reactions of 2H + H₂O/Si(1 0 0)-(2 × 1), 2D + H₂O/Si(1 0 0)-(2 × 1), and H₂O + H/Si(1 0 0)-(2 × 1). In addition to the oxygen inserted coupled monohydrides, which were previously reported in the former reaction system, we report several other oxidized Si hydride species in our BML-IRRAS experiments. Three new pairs of vibrational bands are identified between 900 and 1000 cm⁻¹. These vibrational frequencies were calculated using Si9 and Si10 cluster models that included all possible structures from zero to five oxygen insertions into the top layer silicon atoms using a B3LYP gradient corrected density functional method with a polarized 6-31G** basis set for all atoms. The three pairs of vibrational modes are assigned to the scissoring modes of adjacent and isolated SiH₂ with zero, one, and two oxygen atoms inserted into the Si back bonds. All the other newly observed vibrational peaks related to Si oxidation are also assigned in this study. The Si-O stretching bands observed in the reaction 2D + H₂O/Si(1 0 0)-(2 × 1) show an isotope effect, which suggests that in the system 2H + H₂O/Si(1 0 0)-(2 × 1) also, hydrogen atom tunneling plays an important role for the insertion of oxygen atoms into Si back bonds that form oxidized adjacent dihydrides.     

Spatiotemporal self-similar nonlinear tunneling effects in the (3 + 1)-dimensional inhomogeneous nonlinear medium with the linear and nonlinear gain

With the help of two kinds of similarity transformations connected with the elliptic equation, at first we analytically derive spatiotemporal self-similar solutions of the (3 + 1)-dimensional inhomogeneous nonlinear Schrödinger equation with the linear and nonlinear gain. Then we give out the mutually exclusive parameter domains for bright and dark similaritons. Finally, we discuss nonlinear tunneling effects for spatiotemporal similaritons passing through the nonlinear barrier or well. Results show that bright and dark similaritons in the normal and anomalous dispersion regions have opposite dynamic behaviors.     

High resolution analysis of the rotational levels of the (0 0 0), (0 1 0), (1 0 0), (0 0 1), (0 2 0), (1 1 0) and (0 1 1) vibrational states of SO2

A high resolution (0.0018 cm⁻¹) Fourier transform instrument has been used to record the spectrum of an enriched ³⁴S (95.3%) sample of sulfur dioxide. A thorough analysis of the ν₂, 2ν₂ − ν₂, ν₁, ν₁ + ν₂ − ν₂, ν₃, ν₂ + ν₃ − ν₂, ν₁ + ν₂ and ν₂ + ν₃ bands has been carried out leading to a large set of assigned lines. From these lines ground state combination differences were obtained and fit together with the existing microwave, millimeter, and terahertz rotational lines. An improved set of ground state rotational constants were obtained. Next, the upper state rotational levels were fit. For the (0 1 0), (1 1 0) and (0 1 1) states, a simple Watson-type Hamiltonian sufficed. However, it was necessary to include explicitly interacting terms in the Hamiltonian matrix in order to fit the rotational levels of the (0 2 0), (1 0 0) and (1 0 1) states to within their experimental accuracy. More explicitly, it was necessary to use a ΔK = 2 term to model the Fermi interaction between the (0 2 0) and (1 0 0) levels and a ΔK = 3 term to model the Coriolis interaction between the (1 0 0) and (0 0 1) levels. Precise Hamiltonian constants were derived for the (0 0 0), (0 1 0), (1 0 0), (0 0 1), (0 2 0), (1 1 0) and (0 1 1) vibrational states.     

Surface phase transition and electronic structure of c(5√2 × √2)R45°-Pb/Cu(1 0 0)

The c(5√2 × √2)R45°-Pb/Cu(1 0 0) surface phase is investigated by means of angle resolved ultraviolet photoemission and low energy electron diffraction in the temperature range between 300 and 550 K. We identify and characterize a temperature-induced surface phase transition at 440 K from the room temperature c(5√2 × √2) R45° phase to a (√2 × √2)R45° structure with split superstructure spots. The phase transition is fully reversible and takes place before the two-dimensional melting of the structure at 520 K. The electronic structure of the split (√2 × √2)R45° phase is characterized by a metallic free-electron like surface band. This surface band is backfolded with c(5√2 × √2)R45° periodicity phase at room temperature, giving rise to a surface band gap at the Fermi energy. We propose that a gain in electronic energy explains in part the stability of the c(5√2 × √2)R45° phase.     

Lateral interactions and nonequilibrium in adsorption and desorption. Part 1. Experimental results for (2 × 2)-(3O + NO)/Ru(0 0 1)

Extending earlier vibrational spectroscopy and thermal desorption measurements on this system, its geometrical structure and its adsorption/desorption kinetics have been investigated in detail. The adsorption and desorption of NO proceed, with little influence on the 3O template, on its (2 × 2) lattice of empty hcp sites. The desorption kinetics, with splitting of the TPD spectra into two peaks, are far from the expected behavior for independent sites. Also, the vibrational band structure shows dispersion beyond dipole-dipole interactions. So, despite the quite large NO-NO distance and their screening by the O atoms, there is clear evidence for static and dynamic lateral interactions which should be extractable from the data. A qualitative analysis suggests that these interactions are due to elastic coupling between the positions and vibrations, respectively, of the O and NO adsorbates. However, quantitative conclusions cannot be drawn directly as the kinetic data cannot be interpreted in a quasiequilibrium approach, as would be the normal procedure, due to the presence of strong nonequilibrium effects. The lack of internal equilibration is presumably caused by slow diffusion. The results are sufficiently complete and detailed to justify the effort of theoretical modeling with the aim to quantitatively describe both the lateral interactions and the nonequilibrium effects.     

Soft X-ray appearance potential spectroscopy (SXAPS) study of TiO2(1 1 0)-1 × 2 and (0 0 1)-1 × 1 surfaces

A soft X-ray appearance potential spectroscopy (SXAPS) apparatus with high sensitivity was built to measure non-derivative spectra. SXAPS spectra (non-derivative) of Ti 2p and O 1s for TiO₂(1 1 0)-1 × 2 and (0 0 1)-1 × 1 surfaces have been measured using low incident currents (about 10 μA/cm²) and a photon counting mode. Density of empty states on Ti and O sites are deduced by self-deconvoluting the spectra. The self-deconvoluted SXAPS spectra are qualitatively similar to those measured by X-ray absorption spectroscopy (XAS). The Ti 2p_3/2 spectrum shows two strong peaks which correspond to t_2g and e_g states. For the O 1s spectrum two strong peaks near the threshold are also found which can be ascribed to O 2pπ and O 2pσ states. These results suggest that the spectra almost obey the dipole selection rule, so-called the “approximate dipole selection rule”. The SXAPS spectra of Ti 2p and O 1s for the (1 1 0) and (0 0 1) surfaces resemble qualitatively, which is consistent with the XAS results. The spectra measured on the (1 1 0)-1 × 2 surface at an incident angle of 45° off normal to the surface and on the (1 1 0) surface sputtered by Ar ions indicate that SXAPS is very sensitive to the surface electronic states.     

Formation and hydrogenation of p(2 × 2)-N on Pt(1 1 1)

The formation of a well-ordered p(2 × 2) overlayer of atomic nitrogen on the Pt(1 1 1) surface and its reaction with hydrogen were characterized with reflection absorption infrared spectroscopy (RAIRS), temperature programmed desorption (TPD), low energy electron diffraction (LEED), Auger electron spectroscopy (AES), and X-ray photoelectron spectroscopy (XPS). The p(2 × 2)-N overlayer is formed by exposure of ammonia to a surface at 85 K that is covered with 0.44 monolayer (ML) of molecular oxygen and then heating to 400 K. The reaction between ammonia and oxygen produces water, which desorbs below 400 K. The only desorption product observed above 400 K is molecular nitrogen, which has a peak desorption temperature of 453 K. The absence of oxygen after the 400 K anneal is confirmed with AES. Although atomic nitrogen can also be produced on the surface through the reaction of ammonia with an atomic, rather than molecular, oxygen overlayer at a saturation coverage of 0.25 ML, the yield of surface nitrogen is significantly less, as indicated by the N₂ TPD peak area. Atomic nitrogen readily reacts with hydrogen to produce the NH species, which is characterized with RAIRS by an intense and narrow (FWHM ∼ 4 cm⁻¹) peak at 3322 cm⁻¹. The areas of the H₂ TPD peak associated with NH dissociation and the XPS N 1s peak associated with the NH species indicate that not all of the surface N atoms can be converted to NH by the methods used here.     

O2 dissociation on Pd(2 1 1) and Cu(2 1 1) surfaces

We have performed ab initio Density Functional Theory (DFT) based calculations to observe the reactivity of the Pd(2 1 1) and Cu(2 1 1) surfaces towards O₂. In order to properly address the adsorption dynamics, the static potential energy surface calculations have been complemented with first principles molecular dynamics calculations, which reveal interesting steering effects that complicate the dissociation dynamics. We have found that on both surfaces the step microfacets are very reactive and the dissociation of the O₂ molecule at room temperature occurs mostly on those sites.     

para-Sexiphenyl thin film growth on Cu(1 1 0) and Cu(1 1 0)-(2 × 1)O surfaces

We present a reflectance difference spectroscopy (RDS) study of para-sexiphenyl (p-6P) thin film growth on Cu(1 1 0) and Cu(1 1 0)-(2 × 1)O substrates. The RDS spectra show pronounced anisotropies for p-6P films formed on both substrates at room temperature, demonstrating that the molecules are uniaxially aligned within the films. Based on the RD spectra and the evolution of the optical transitions with p-6P coverage the growth mode on both substrates could be identified. From the dominating RDS feature, assigned to the lowest energy HOMO-LUMO transition, the orientation of the molecular chain can be determined. On Cu(1 1 0), the p-6P molecular chains align in the direction, i.e., along the Cu atomic rows, whereas on the Cu(1 1 0)-(2 × 1)O surface, the molecules are oriented in the orthogonal [0 0 1] direction, i.e., along the “added” Cu-O rows of the Cu(1 1 0)-(2 × 1)O surface. The energetic position and line shape of the main RDS feature differs for the two substrates and varies with p-6P coverage. This fine structure is discussed in terms of different molecular conformations, adlayer structure and vibronic replicas.     

Duality in 2 + 1D quantum elasticity: superconductivity and quantum nematic order

Superfluidity and superconductivity are traditionally understood in terms of an adiabatic continuation from the Bose-gas limit. Here we demonstrate that at least in a 2 + 1D Bose system, superfluidity can arise in a strict quantum field-theoretic setting. Taking the theory of quantum elasticity (describing phonons) as a literal quantum field theory with a bosonic statistic, superfluidity and superconductivity (in the EM charged case) emerge automatically when the shear rigidity of the elastic state is destroyed by the proliferation of topological defects (quantum dislocations). Off-diagonal long range order in terms of the field operators of the constituent particles is not required. This is one of the outcomes of the broader pursuit presented in this paper. In essence, it amounts to the generalization of the well known theory of crystal melting in two dimensions by Nelson et al. [Phys. Rev. B 19 (1979) 2457; Phys. Rev. B 19 (1979) 1855], to the dynamical theory of bosonic states exhibiting quantum liquid-crystalline orders in 2 + 1 dimensions. We strongly rest on the field-theoretic formalism developed by Kleinert [Gauge fields in Condensed Matter, vol. II: Stresses and Defects, Differential Geometry, Crystal Defects, World Scientific, Singapore, 1989] for classical melting in 3D. Within this framework, the disordered states correspond to Bose condensates of the topological excitations, coupled to gauge fields describing the capacity of the elastic medium to propagate stresses. Our focus is primarily on the nematic states, corresponding with condensates of dislocations, under the topological condition that disclinations remain massive. The dislocations carry Burgers vectors as topological charges. Conventional nematic order, i.e., the breaking of space-rotations, corresponds in this field-theoretic duality framework with an ordering of the Burgers vectors. However, we also demonstrate that the Burgers vectors can quantum disorder despite the massive character of the disclinations. We identify the physical nature of the ‘Coulomb nematic’ suggested by Lammert et al. [Phys. Rev. Lett. 70 (1993) 1650; Phys. Rev. E 52 (1995) 1778] on gauge-theoretical grounds. The 2 + 1D quantum liquid crystals differ in fundamental regards from their 3D classical counterparts due to the presence of a dynamical constraint. This constraint is the glide principle, well known from metallurgy, which states that dislocations can only propagate in the direction of their Burgers vector. In the present framework this principle plays a central role. This constraint is necessary to decouple compression rigidity from the dislocation condensate. The shear rigidity is not protected, and as a result the shear modes acquire a Higgs mass in the dual condensate. This is the way the dictum that translational symmetry breaking goes hand in hand with shear rigidity emerges in the field theory. However, because of the glide principle compression stays massless, and the fluids are characterized by an isolated massless compression mode and are therefore superfluids. Glide also causes the shear Higgs mass to vanish at orientations perpendicular to the director in the ordered nematic, and the resulting state can be viewed as a quantum smectic of a novel kind. Our most spectacular result is a new hydrodynamical way of understanding the conventional electromagnetic Meissner state (superconducting state). Generalizing to the electromagnetically charged elastic medium (‘Wigner Crystal’) we find that the Higgs mass of the shear gauge fields, becoming finite in the nematic quantum fluids, automatically causes a Higgs mass in the electromagnetic sector by a novel mechanism.     

First-principles study of adsorption and diffusion on Ge/Si(0 0 1)-(2 × 8) and Ge/Si(1 0 5)-(1 × 2) surfaces

Using first-principles total-energy calculations, we have investigated the adsorption and diffusion of Si and Ge adatoms on Ge/Si(0 0 1)-(2 × 8) and Ge/Si(1 0 5)-(1 × 2) surfaces. The dimer vacancy lines on Ge/Si(0 0 1)-(2 × 8) and the alternate S_A and rebonded S_B steps on Ge/Si(1 0 5)-(1 × 2) are found to strongly influence the adatom kinetics. On Ge/Si(0 0 1)-(2 × 8) surface, the fast diffusion path is found to be along the dimer vacancy line (DVL), reversing the diffusion anisotropy on Si(0 0 1). Also, there exists a repulsion between the adatom and the DVL, which is expected to increase the adatom density and hence island nucleation rate in between the DVLs. On Ge/Si(1 0 5)-(1 × 2) surface, the overall diffusion barrier of Si(Ge) along direction is relative fast with a barrier of ∼0.83(0.61) eV, despite of the large surface undulation. This indicates that the adatoms can rapidly diffuse up and down the (1 0 5)-faceted Ge hut island. The diffusion is also almost isotropic along [0 1 0] and directions.