(1 + 2)-Dimensional sub-strongly nonlocal spatial optical solitons: Perturbation method

By extending the (1 + 1)-dimensional [(1 + 1)-D] perturbation method suggested by Ouyang et al. [S. Ouyang, Q. Guo, W. Hu, Phys. Rev. E. 74 (2006) 036622] to the (1 + 2)-D case, we obtain a fundamental soliton solution to the (1 + 2)-D nonlocal nonlinear Schrödinger equation (NNLSE) with a Gaussian-type response function for the sub-strongly nonlocal case. Numerical simulations show that the soliton solution obtained in this paper can describe the soliton states in both the sub-strongly nonlocal case and the strongly nonlocal case. It is found that the phase constant and the power of the (1 + 2)-D strongly nonlocal spatial optical soliton with a Gaussian-type response function are both in inverse proportion to the 4th power of its beam width.     

A quantum exactly solvable non-linear oscillator with quasi-harmonic behaviour

The quantum version of a non-linear oscillator, previously analyzed at the classical level, is studied. This is a problem of quantization of a system with position-dependent mass of the form m = (1 + λx²)⁻¹ and with a λ-dependent non-polynomial rational potential. This λ-dependent system can be considered as a deformation of the harmonic oscillator in the sense that for λ → 0 all the characteristics of the linear oscillator are recovered. First, the λ-dependent Schrödinger equation is exactly solved as a Sturm-Liouville problem, and the λ-dependent eigenenergies and eigenfunctions are obtained for both λ > 0 and λ < 0. The λ-dependent wave functions appear as related with a family of orthogonal polynomials that can be considered as λ-deformations of the standard Hermite polynomials. In the second part, the λ-dependent Schrödinger equation is solved by using the Schrödinger factorization method, the theory of intertwined Hamiltonians, and the property of shape invariance as an approach. Finally, the new family of orthogonal polynomials is studied. We prove the existence of a λ-dependent Rodrigues formula, a generating function and λ-dependent recursion relations between polynomials of different orders.     

An ab initio-based approach to phase diagram calculations for GaAs(0 0 1)-(2 × 4)γ surfaces

Surface phase diagram of recently proposed GaAs(0 0 1)-(2 × 4)γ is systematically investigated by using our ab initio-based approach. We focus on the (4 × 7) domain consisting of c(4 × 4)-like and (2 × 4)-like regions to clarify surface dimer constituents as functions of temperature T and As (As₂ and As₄) pressure p_As by comparing chemical potentials of surface dimers in the vapor phase with that on the surface. The calculated results under As₄ imply that Ga dimers in the c(4 × 4)-like region tend to become stable with increase of temperature and appear at the conventional growth condition such as T ∼ 800 K and p_As ∼ 10⁻⁶ Torr, while the (2 × 4)-like region favors As dimers. This is consistent with temperature dependence of change in surface dimer constituents on the c(4 × 4) and (2 × 4)β2 clarified in our previous study. Furthermore, the surface phase transition from the c(4 × 4) to (2 × 4)β2 via (2 × 4)γ is discussed on the basis of the phase diagram obtained in this study.     

Deconfined criticality, runaway flow in the two-component scalar electrodynamics and weak first-order superfluid-solid transitions

We perform a comparative Monte Carlo study of the easy-plane deconfined critical point (DCP) action and its short-range counterpart to reveal close similarities between the two models for intermediate and strong coupling regimes. For weak coupling, the structure of the phase diagram depends on the interaction range: while the short-range model features a tricritical point and a continuous U(1) × U(1) transition, the long-range DCP action is characterized by the runaway renormalization flow of coupling into a first (I) order phase transition. We develop a “numerical flowgram” method for high precision studies of the runaway effect, weakly I-order transitions, and polycritical points. We prove that the easy-plane DCP action is the field theory of a weakly I-order phase transition between the valence bond solid and the easy-plane antiferromagnet (or superfluid, in particle language) for any value of the weak coupling strength. Our analysis also solves the long standing problem of what is the ultimate fate of the runaway flow to strong coupling in the theory of scalar electrodynamics in three dimensions with U(1) × U(1) symmetry of quartic interactions.     

Experimental constraints on the phase diagram of elemental zirconium

The phase diagram of zirconium metal has been studied using synchrotron X-ray diffraction and time-of-flight neutron scattering at temperatures and pressures up to 1273 K and 17 GPa. The equilibrium phase boundary of the α-ω transition has a dT/dP slope of 473 K/GPa, and the extrapolated transition pressure at ambient temperature is located at 3.4 GPa. For the ω-β transition, the phase boundary has a negative dT/dP slope of 15.5 K/GPa between 6.4 and 15.3 GPa, which is substantially smaller than a previously reported value of −39±5 K/GPa in the pressure range of 32-35 GPa. This difference indicates a significant curvature of the phase boundary between 15.3 and 35 GPa. The α-ω-β triple point was estimated to be at 4.9 GPa and 953 K, which is comparable to previous results obtained from a differential thermal analysis. Except for the three known crystalline forms, the β phase of zirconium metal was found to possess an extraordinary glass forming ability at pressures between 6.4 and 8.6 GPa. This transformation leads to a limited stability field for the β phase in the pressure range of 6-16 GPa and to complications of high-temperature portion of phase diagram for zirconium metal.     

Bose-Einstein solitons in time-dependent linear potential

In this paper, Bose-Einstein soliton solutions of the nonlinear Schrödinger equation with time-dependent linear potential are considered. Based on the F-expansion method, we present a number of Jacobian elliptic function solutions. Particular cases of these solutions, where the elliptic function modulus equals 1 and 0, are various localized solutions and trigonometric functions, respectively. Specially, for V_ext = ZF(T) = Z[mg + Hcos (ω₁T)], we discussed the Bose-Einstein condensate trapped in the coupling external field with considering the effect of gravity; for F(T) = constant, it describes the wave (Langmuir or electromagnetic) in a linearly inhomogeneous plasma with cubic nonlinearly.     

Analysis on generation schemes of Schrödinger cat-like states under experimental imperfections

An analysis and a comparison of two generation schemes of Schrödinger cat-like state including experimental imperfections are presented. Under practical conditions, a scheme using a squeezed vacuum and a photon subtraction will generate a cat-like state with its fidelity to the Schrödinger cat state F = 0.815 and value of its Wigner function at the origin of the phase space W(0,0) = −0.203, and then turned out to be more feasible than the scheme using squeezed single-photon state. The non-classicality of these cat-like states is governed only by non-classical photon number statistics. The criteria for ensuring W(0,0) < 0 are also presented in terms of imperfection parameter diagrams.     

Phase transitions in CsHSO4 up to 2.5 GPa: Impedance spectroscopy under pressure

Phase transitions in CsHSO₄ at pressures up to 2.5 GPa have been studied with the help of electrical impedance measurements. The phase boundaries have been identified with the help of calculated activation energies of electrical conductivity and dielectric relaxation time. The derived temperatures of phase transition from the low conductive phase II into super ionic phase I at pressure less than 1 GPa confirm the previous results of Ponyatovski? et al. (1985) [4] and Friesel et al. (1989) [27]. The phase diagram derived in this study for pressure larger than 1 GPa differs from the data of Ponyatovski? et al. (1985) [4]. The phase transitions IV-VI and VI-I occur at higher temperatures having significantly larger Clapeyron slope. The phase VII was not identified from heating cycle and appears only under cooling between phases I and VI. The phase VIII was detected at 2.5 GPa at T<350 K and only during heating.     

Synthesis and characterization of the xZnO-(1−x)α-Fe2O3 nanoparticles system

The xZnO-(1−x)α-Fe₂O₃ nanoparticles system has been obtained by mechanochemical activation for x=0.1, 0.3 and 0.5 and for ball milling times ranging from 2 to 24 h. Structural and morphological characteristics of the zinc-doped hematite system were investigated by X-ray diffraction (XRD) and Mössbauer spectroscopy. The Rietveld structure of the XRD spectra yielded the dependence of the particle size and lattice constant on the amount x of Zn substitutions and as function of the ball milling time. The x=0.1 XRD spectra are consistent with line broadening as Zn substitutes Fe in the hematite structure and the appearance of the zinc ferrite phase at milling times longer than 4 h. Similar results were obtained for x=0.3, while for x=0.5 the zinc ferrite phase occurred at 2 h and entirely dominated the spectrum at 24 h milling time. The Mössbauer spectra corresponding to x=0.1 exhibit line broadening as the ball milling time increases, in agreement with the model of local atomic environment. Because of this reason, the Mössbauer spectrum for 12 h of milling had to be fitted with two sextets. For x=0.3 and 12 milling hours, the Mössbauer spectrum reveals the occurrence of a quadrupole-split doublet, with the hyperfine parameters characteristic to zinc ferrite, ZnFe₂O₄. This doublet clearly dominates the Mössbauer spectrum for x=0.5 and 24 h of milling, demonstrating that the entire system of nanoparticles consists finally of zinc ferrite. As ZnO is not soluble in hematite in the bulk form, the present study clearly demonstrates that the solubility limits of an immiscible system can be extended beyond the limits in the solid state by mechanochemical activation. Moreover, this synthesis route allowed us to reach nanometric particle dimensions, which would make the materials very important for gas sensing applications.     

Ni/Ni3Al interface: A density functional theory study

The optimal geometries, mechanical and thermal properties, and electronic structures of the three low index (0 0 1), (1 1 0), (1 1 1) Ni/Ni₃Al thin film were studied using first principle calculations. Simulated results indicated that Ni and Al atoms in γ^′ phase preferred to place in the hollow site of Ni atoms in γ phase. In hollow site models, electronic states affected by interface localize within 2 atomic layers. While the top site model, electronic states localize within 3 atomic layers. It is also found that hollow site (1 1 0) interface has the best mechanical properties. Hollow site (0 0 1) interface is the most easily formed interface, which has the best thermodynamic properties.     

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping δ away from half-filling, finite-system density-matrix renormalization-group (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/δ and 1/δ, respectively, corresponding to ordering wavevectors 2k_F and 4k_F for the currents and densities, where 2k_F = π (1 − δ). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/δ, the DMRG results are consistent with a true long-range order scenario for the currents and densities.     

Phase structure and critical behavior of multi-Higgs U(1) lattice gauge theory in three dimensions

We study the three-dimensional (3D) compact U(1) lattice gauge theory coupled with N-flavor Higgs fields by means of the Monte Carlo simulations. This model is relevant to multi-component superconductors, antiferromagnetic spin systems in easy plane, inflational cosmology, etc. It is known that there is no phase transition in the N = 1 model. For N = 2, we found that the system has a second-order phase transition line in the c₂ (gauge coupling)-c₁ (Higgs coupling) plane, which separates the confinement phase and the Higgs phase. Numerical results suggest that the phase transition belongs to the universality class of the 3D XY model as the previous works by Babaev et al. and Smiseth et al. suggested. For N = 3, we found that there exists a critical line similar to that in the N = 2 model, but the critical line is separated into two parts; one for c₂<c_2tc=2.4±0.1 with first-order transitions, and the other for c_2tc<c₂ with second-order transitions, indicating the existence of a tricritical point. We verified that similar phase diagram appears for the N = 4 and N = 5 systems. We also studied the case of anistropic Higgs coupling in the N = 3 model and found that there appear two second-order phase transitions or a single second-order transition and a crossover depending on the values of the anisotropic Higgs couplings. This result indicates that an “enhancement” of phase transition occurs when multiple phase transitions coincide at a certain point in the parameter space.     

Canonical quantization of Galilean covariant field theories

The Galilean-invariant field theories are quantized by using the canonical method and the five-dimensional Lorentz-like covariant expressions of non-relativistic field equations. This method is motivated by the fact that the extended Galilei group in 3 + 1 dimensions is a subgroup of the inhomogeneous Lorentz group in 4 + 1 dimensions. First, we consider complex scalar fields, where the Schrödinger field follows from a reduction of the Klein-Gordon equation in the extended space. The underlying discrete symmetries are discussed, and we calculate the scattering cross-sections for the Coulomb interaction and for the self-interacting term λΦ⁴. Then, we turn to the Dirac equation, which, upon dimensional reduction, leads to the Lévy-Leblond equations. Like its relativistic analogue, the model allows for the existence of antiparticles. Scattering amplitudes and cross-sections are calculated for the Coulomb interaction, the electron-electron and the electron-positron scattering. These examples show that the so-called ‘non-relativistic’ approximations, obtained in low-velocity limits, must be treated with great care to be Galilei-invariant. The non-relativistic Proca field is discussed briefly.     

High-pressure X-ray diffraction study of 1T-TaS2

We present a room temperature high-pressure X-ray diffraction study of the layered compound 1T-TaS₂ up to 20 GPa. This material is known to exhibit a variety of structural phase transitions that are ascribed to the stabilization of charge density wave states. It has been recently shown that at pressures larger than 3 GPa and up to 25 GPa, 1T-TaS₂ becomes superconductor below about 5 K. It was suggested that this superconductivity coexists with different CDW states, an hypothesis that can be tested by X-ray diffraction. Our first results at room temperature show that at around 1.9 GPa, the nearly-commensurate (NCCDW) phase transforms into a phase similar to the high temperature incommensurate phase (ICCDW). Above 9 GPa, we show the existence of another IC phase, still discernable up to 20 GPa despite the pressure-induced crystal damage above 13 GPa. These results are consistent with resistivity measurements, but call for a complete exploration of the P–T phase diagram of 1T-TaS₂.     

Structure and magnetic properties of (Nd,Dy)16(Fe,Co)76−xTixB8 powders prepared by mechanical alloying

Nanocrystalline (Nd,Dy)₁₆(Fe,Co)_76−xTi_xB₈ magnets were prepared by mechanical alloying and respective heat treatment at 973–1073 K/30–60 min. An addition of 0.5 at % of Ti results in an increase of coercivity from 796 to 1115 kA m⁻¹. Partial substitution of Nd by Dy results in an additional increase of coercivity up to 1234 kA m⁻¹. Mössbauer investigations shows that for x?1 the (Nd,Dy)₁₆(Fe,Co)_76−xTi_xB₈ powders are single phase. For higher Ti contents (x>1) the mechanically alloyed powders heat treated at 973 K are no more single phase, and the coercivity decreases due to the presence of an amorphous phase. A heat treatment at a higher temperature (1073 K) for longer time (1 h) results in the full recrystallisation of powders. The mean hyperfine field of the Nd₂Fe₁₄B phase decreases for titanium contents of 0?x?1, and remains constant for x>1. This indicates that the Ti content in the Nd₂Fe₁₄B phase reaches its maximum value.     

Pressure-induced structural phase transition in ReO3

We have investigated the pressure-induced structural phase transition in ReO₃ by neutron diffraction on a single crystal. We collected neutron diffraction intensities from the ambient and high pressure phases at P=7 kbar and refined the crystal structures. We have determined the stability of the high pressure phase as a function temperature down to T=2 K and have constructed the (P-T) phase diagram. The critical pressure is P_c=5.2 kbar at T=300 K and decreases almost linearly with decreasing temperature to become P_c=2.5 kbar at T=50 K. The phase transition is driven by the softening of the M₃ phonon mode. The high pressure phase is formed by the rigid rotation of almost undistorted ReO₆ octahedra and the Re-O-Re angle deviates from 180°. We do not see any evidence for the existence of the tetragonal (P4/mbm) intermediate pressure phase reported earlier.     

Two-temperature relaxation and melting after absorption of femtosecond laser pulse

The theory and experiments concerned with the electron-ion thermal relaxation and melting of overheated crystal lattice constitute the subject of this paper. The physical model includes two-temperature (2T) equation of state, many-body interatomic potential, the electron-ion energy exchange, electron thermal conductivity, and optical properties of solid, liquid, and two phase solid-liquid mixture. Two-temperature hydrodynamics and molecular dynamics codes are used. An experimental setup with pump-probe technique is used to follow evolution of an irradiated target with a short time step 100 fs between the probe femtosecond laser pulses. Accuracy of measurements of reflection coefficient and phase of reflected probe light are 1% and ∼1 nm, respectively. It is found that, firstly, the electron-electron collisions make a minor contribution to a light absorption in solid Al at moderate intensities; secondly, the phase shift of a reflected probe results from heating of ion subsystem and kinetics of melting of Al crystal during  ps, where t is time delay between the pump and probe pulses measured from the maximum of the pump; thirdly, the optical response of Au to a pump shows a marked contrast to that of Al on account of excitation of d-electrons.     

ZnO:Ag film growth on Si substrate with ZnO buffer layer by rf sputtering

ZnO buffer layers were deposited on n-Si (1 0 0) substrate by rf magnetron sputtering at a lower power of 40 W. Then Ag-doped ZnO (SZO) films were deposited on buffered and non-buffered Si at a higher sputtering power of 100 W. The effects of buffer layer on the structural, electrical and optical properties of SZO films were investigated. The three-dimensional island growth process of ZnO buffer layer was discussed. The energy band diagram of p-SZO/n-Si heterojunction was constructed based on Anderson's model. Results show the ZnO buffer layer leads to better properties of SZO film, including larger grain size, smoother surface, higher carrier mobility, better rectifying behavior, lower interface state density, and weaker deep-level emission. It is because the ZnO buffer layer effectively relaxes the partial stress induced by the large lattice mismatch between SZO and Si.     

Phase behavior of unsymmetrical dimers on a square lattice

Monte Carlo simulations in the grand canonical ensemble have been carried out to study phase transitions in monolayers formed by heterogeneous dimers, composed of segments A and B, on a square lattice. The unsymmetrical segment-segment interactions are assumed (u_AA ≠ u_BB). The systems with u_AB = u_BB = −1 and different AA-interactions studied in our previous work [W. R?ysko, M. Borówko, Surf. Sci. 520 (2002) 151] are reconsidered. The structural phase transitions at high temperatures are investigated. It is shown that topology of a phase diagram depends on the energy u_AA. For repulsive AA-interactions a triple point is found and the system belongs to the universality class of a tricritical point. When u_AA < 0 the critical line of the order-disorder transition terminates at a critical end point and the system belongs to the universality class of the 2D Ising model.     

Swift ion irradiations of Fe/Fe/Si trilayers

We report here on changes in magnetism and microstructure when implanting, at 92 or 300 K, up to 5 × 10¹⁵ Au²⁶⁺-ions cm⁻² of 350 MeV into ^natFe(45 nm)/⁵⁷Fe(20 nm)/Si trilayers. This choice of ions and energy allowed to test the irradiation effects in the regime of pure electronic stopping. The samples were analysed before and after irradiation by Rutherford back-scattering spectroscopy, X-ray diffraction, conversion electron Mössbauer spectroscopy, and magneto-optical Kerr effect. Up to 1 × 10¹⁵ ions cm⁻², there was interface broadening at a mixing rate of Δσ²/Φ = 55(5) nm⁴, followed by full Fe-Si inter-diffusion. The Mössbauer spectra revealed fractions of α-Fe and amorphous ferromagnetic and paramagnetic iron silicides, but no crystalline Fe-Si phase. The magnetic remanence in the as-deposited Fe-layer showed small components of uniaxial and four-fold magnetization. For increasing ion fluence, the component with four-fold symmetry grew at the expense of the uniaxial component. For the highest fluences, an isotropic magnetization was found.