The Existence and Stability of Noncommutative Scalar Solitons

 We establish existence and stability results for solitons in noncommutative scalar field theories in even space dimension 2d. In particular, for any finite rank spectral projection P of the number operator 𝒩 of the d-dimensional harmonic oscillator and sufficiently large noncommutativity parameter θ we prove the existence of a rotationally invariant soliton which depends smoothly on θ and converges to a multiple of P as θ→∞. In the two-dimensional case we prove that these solitons are stable at large θ, if P=P _N , where P _N projects onto the space spanned by the N+1 lowest eigenstates of 𝒩, and otherwise they are unstable. We also discuss the generalisation of the stability results to higher dimensions. In particular, we prove stability of the soliton corresponding to P=P ₀ for all θ in its domain of existence. Finally, for arbitrary d and small values of θ, we prove without assuming rotational invariance that there do not exist any solitons depending smoothly on θ. Received: 13 July 2001 / Accepted: 9 July 2002 Published online: 10 January 2003     

Josephson effect in superconducting constrictions with hybrid SF electrodes: Peculiar properties determined by the misorientation of magnetizations

Josephson current in SFcFS junctions with arbitrary transparency of the constriction (c) is investigated. The emphasis is on the analysis of the supercurrent dependencies on the misorientation angle θ between the in-plane magnetizations of diffusive ferromagnetic layers (F). It is found that the current-phase relation I(φ) may be radically modified with the θ variation: the harmonic I ₁ sin φ vanishes for a definite value of θ provided that, for an identical orientation of the magnetizations (θ = 0), the junction is in the “π” state. The Josephson current may exhibit a nonmonotonic dependence on the misorientation angle both for realization of the “0” and “π” state at θ = 0. We also analyze the effect of the exchange field induced enhancement of the critical current, which may occur in a definite range of θ. The text was submitted by the author in English.     

| m | Partial wave treatment for two-dimensional Coulomb-scattering and Regge pole

The symmetry and |m| partial-wave analysis for two-dimensional (2D) Coulomb-scattering is investigated. As a function of energyE, the |m| partial-wave scattering amplitudef _|m|(θ) is analytically continuated to the, negativeE (complexk) plane, and it is found that the bound state energy eigenvalues (E<0) are just located at the poles off _|m|(θ) on the positive imaginaryk axis as is expected. In addition, as a function of |m|,f _|m|(θ) is analytically continuated to the complex |m| plane, the bound state energy eigenvalues are just located at the poles off _|m|(θ) on the positive real |m| axis.     

The S-D mixing and dielectron widths of higher charmonium 1−− states

The dielectron widths of ψ(4040), ψ(4160), and ψ(4415), and their ratios are shown to be in good agreement with experiment, if in all cases the S-D mixing with a large mixing angle θ ≅ 34° is taken. Arguments are presented why continuum states give small contributions to the wave functions at the origin. We find that the Y (4360) resonance, considered as a pure 3 ³ D ₁ state, would have very small dielectron width, Γ _ee (Y (4360)) = 0.060 keV. On the contrary, for large mixing between the 4 ³ S ₁ and 3 ³ D ₁ states with the mixing angle θ = 34.8°, Γ _ee (ψ(4415)) = 0.57 keV coincides with the experimental number, while a second physical resonance, probably Y (4360), has also a rather large Γ _ee (Y (∼4400)) = 0.61 keV. For the higher Y (4660) resonance, considered as a pure 5 ³ S ₁ state, we predict the dielectron width Γ _ee (Y (4660)) = 0.70 keV, but it becomes significantly smaller, namely 0.31 keV, if the mixing angle between the 5 ³ S ₁ and 4 ³ D ₁ states has the characteristic value θ = 34°. The mass and dielectron width of the 6 ³ S ₁ charmonium state are calculated. The text was submitted by the authors in English.     

A Generalized Hadamard-Fresnel Complementary Transformation Derived by Virtue of New Coherent-Entangled State

The new coherent-entangled state |z,x;θ〉 is proposed in the two-mode Fock space, which exhibits both the properties of coherent and entangled states. The completeness relation of |z,x;θ〉 is proved by virtue of the technique of integral within an ordered product of operators. A generalized Hadamard-Fresnel complementary transformation derived by virtue of the coherent-entangled state |z,x;θ〉, which is unitary. The new unitary operator plays the role of both Hadamard transformation for ([^(a)]₁sinq-[^(a)]₂cosq)(\hat{a}_{1}\sin\theta -\hat{a}_{2}\cos\theta) and Fresnel transformation for ([^(a)]₁cosq+[^(a)]₂sinq)(\hat{a}_{1}\cos\theta +\hat{a}_{2}\sin\theta), respectively.     

Large Deviations for a Stochastic Model of Heat Flow

We investigate a one-dimensional chain of 2N harmonic oscillators in which neighboring sites have their energies redistributed randomly. The sites −N and N are in contact with thermal reservoirs at different temperature τ₋ and τ₊. Kipnis et al. (J. Statist. Phys., 27:65–74 (1982).) proved that this model satisfies Fourier’s law and that in the hydrodynamical scaling limit, when N → ∞, the stationary state has a linear energy density profile , u ∈[−1,1]. We derive the large deviation function S(θ(u)) for the probability of finding, in the stationary state, a profile θ(u) different from . The function S(θ) has striking similarities to, but also large differences from, the corresponding one of the symmetric exclusion process. Like the latter it is nonlocal and satisfies a variational equation. Unlike the latter it is not convex and the Gaussian normal fluctuations are enhanced rather than suppressed compared to the local equilibrium state. We also briefly discuss more general models and find the features common in these two and other models whose S(θ) is known.     

Mixing angles of quarks and leptons in quantum field theory

Arguments coming from Quantum Field Theory are supplemented with a 1-loop perturbative calculation to settle the non-unitarity of mixing matrices linking renormalized mass eigenstates to bare flavor states for non-degenerate coupled fermions. We simultaneously diagonalize the kinetic and mass terms and counterterms in the renormalized Lagrangian. SU(2) _L gauge invariance constrains the mixing matrix in charged currents of renormalized mass states, for example the Cabibbo matrix, to stay unitary. Leaving aside CP violation, we observe that the mixing angles exhibit, within experimental uncertainty, a very simple breaking pattern of SU(2) _f horizontal symmetry linked to the algebra of weak neutral currents, the origin of which presumably lies beyond the Standard Model. It concerns on the one hand the three quark mixing angles; on the other hand a neutrino-like pattern in which θ ₂₃ is maximal and tan (2θ ₁₂)=2. The Cabibbo angle fulfills the condition tan (2θ _c )=1/2 and θ ₁₂ for neutrinos satisfies accordingly the “quark–lepton complementarity condition” θ _c +θ ₁₂=π/4. θ ₁₃=±5.7⋅10⁻³ are the only values obtained for the third neutrino mixing angle that lie within present experimental bounds. Flavor symmetries, their breaking by a non-degenerate mass spectrum, and their entanglement with the gauge symmetry, are scrutinized; the special role of flavor rotations as a very mildly broken symmetry of the Standard Model is outlined.     

Angular spread of Gaussian Schell-model array beams propagating through atmospheric turbulence

The closed-form expression for the angular spread of Gaussian Schell-model (GSM) array beams propagating through atmospheric turbulence is derived. It is shown that the angular spread θ _sp of GSM array beams for the superposition of the cross-spectral density function is smaller than of those for the superposition of the intensity. However, the θ _sp of GSM array beams for the superposition of the intensity is less sensitive to turbulence than that for the superposition of the cross-spectral density function. For the superposition of the cross-spectral density function, θ _sp of GSM array beams with smaller coherence length σ ₀, smaller waist width w ₀, smaller beam number N, and larger separation distance x _d are less affected by turbulence than of those with larger σ ₀,w ₀,N, and smaller x _d ; while, for the superposition of the intensity, the effect of turbulence on θ _sp is independent of N and x _d . In addition, the angular spread is nearly the same for the two types of superposition when σ ₀ or w ₀ is small enough, or x _d is large enough. On the other hand, it is found that there exist equivalent GSM array beams for the two types of superposition which may have the same directionality as the corresponding fully coherent Gaussian beam in free space and also in turbulence.     

Deviation from tri-bimaximal mixings through flavour twisters in inverted and normal hierarchical neutrino mass models

We explore a novel possibility for lowering the solar mixing angle (θ ₁₂) from tri-bimaximal mixings, without sacrificing the predictions of maximal atmospheric mixing angle (θ ₂₃ = 45°) and zero reactor angle (θ ₁₃ = 0°) in the inverted and normal hierarchical neutrino mass models having 2–3 symmetry. This can be done through the identification of a flavour twister term in the texture of neutrino mass matrix and the variation of such term leads to lowering of solar mixing angle. For the observed ranges of Δm ₂₁² and Δm ₂₃², we calculate the predictions on tan² θ ₁₂ = 0.5, 0.45, 0.35 for different input values of the parameters in the neutrino mass matrix. We also observe a possible transition from inverted hierarchical model having even CP parity (Type-IHA) to inverted hierarchical model having odd CP parity (Type-IHB) in the first two mass eigenvalues, when there is a change in input values of parameters in the same mass matrix. The present work differs from the conventional approaches for the deviations from tri-bimaximal mixing, where the 2–3 symmetry is broken, leading to θ ₂₃ ≠ 45° and θ ₁₃ ≠ 0°.      

Spin-Hall Effect with Quantum Group Symmetries

We construct a model of spin-Hall effect on a noncommutative four sphere S ⁴ _Θ with isospin degrees of freedom, coming from a noncommutative instanton, and invariance under a quantum group SO _θ. The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state; there are both integer and fractional excitations. Similar models exist on higher dimensional spheres S _Θ ^N and projective spaces . Dedicated to Rafael Sorkin with friendship and respect.     

Metastable Behavior for Bootstrap Percolation on Regular Trees

We examine bootstrap percolation on a regular (b+1)-ary tree with initial law given by Bernoulli(p). The sites are updated according to the usual rule: a vacant site becomes occupied if it has at least θ occupied neighbors, occupied sites remain occupied forever. It is known that, when b>θ≥2, the limiting density q=q(p) of occupied sites exhibits a jump at some p _T=p _T(b,θ)∈(0,1) from q _T:=q(p _T)<1 to q(p)=1 when p>p _T. We investigate the metastable behavior associated with this transition. Explicitly, we pick p=p _T+h with h>0 and show that, as h ↓0, the system lingers around the “critical” state for time order h ^−1/2 and then passes to fully occupied state in time O(1). The law of the entire configuration observed when the occupation density is q∈(q _T,1) converges, as h ↓0, to a well-defined measure.     

Dense Coding with Extended GHZ-W State via Local Measurements

Two schemes, with entanglement concentration and via generalized measurement, for dense coding are investigated by using a extended four-qubit GHZ-W state, where the supervisors (David and Cliff) can control the average amount of information transmitted from the sender (Alice) to the receiver (Bob) by adjusting the measurement angles θ ₃ and θ ₄. We show that the results for the average amounts of information are unique from the different two schemes.     

Dense Coding with Cluster State Via Local Measurements

Two schemes, introducing generalized measurement and entanglement concentration respectively, for dense coding are investigated by using a one-dimensional four-particle cluster state, where the supervisors (Cliff and David) can control the average amount of information transmitted from the sender (Alice) to the receiver (Bob) by adjusting the local measurement angles θ ₃ and θ ₄. It is shown that the results for the average amounts of information are unique from the different two schemes.     

Vortex–antivortex states in nanostructured superconductor–ferromagnet hybrids

The formation of vortex–antivortex states in a superconducting film with a square array of magnetic dipoles magnetized perpendicularly to the film is investigated in the framework of the time-dependent Ginzburg–Landau equations. It is shown that a possible route to obtain equilibrium states is obtained following an experimentally realizable field-cooling procedure. The states thus obtained demonstrate a rich variety of phases, depending on magnetic moment intensity and dipole array-to-superconducting film distance. For instance, in the region of the phase diagram where each dipoles is able to generate N = 2 vortex–antivortex pairs, the antivortices induced by the negative stray fields of the dipoles undergo two transitions before ultimately merging into doubly-quantized giant antivortices. For N = 4, a state consisting on a three-quanta giant vortex below each dipole and an interstitial vortex–antivortex molecule was observed. Such state is thermodynamically stable and is induced by the fourfold symmetry of the dipole array, similar to symmetry-induced vortex–antivortex molecules found in mesoscopic superconductors.     

Accurate method for determining tilt bias angles in thin films of nematic liquid crystals

We have developed a new method for measuring tilt bias angles in spatially uniform and nonuniform thin films of nematic liquid crystals. The method employs modulation ellipsometry, based on the use of an exponentially decaying light wave to probe the boundary layer. Oscillations of the director of the liquid crystal, which are induced by the flexoelectric torque, are excited with an external periodic field. A periodic variation of the ellipticity of the light wave reflected from the interface is detected at both the first and second harmonics of the exciting electric field. When these two Fourier components of the electrooptic response are known, it is possible to calculate both the tilt bias angle θ₀ of the director and the dynamic deviation δ₀ of the tilt bias angle. The angles θ₀ and δ₀ measured by this method on the surface of an electrode (ITO) and on the surface of a ferroelectric film (a copolymer of vinylidene fluoride and trifluoroethylene), oriented in a corona discharge, were equal to θ ₀=5.1°, δθ=0.5° and θ₀=89°, δθ=0.06°, respectively. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 6, 387–392 (25 March 1998)     

Role of <Superscript>8</Superscript>Be heavy stripping mechanism in the <Emphasis Type="Italic">α</Emphasis> + <Superscript>12</Superscript>C inelastic scattering to the near-3<Emphasis Type="Italic">α</Emphasis>-threshold states in <Superscript>12</Superscript>C

The angular distributions of α + ¹²C elastic and inelastic (to the 4.44 MeV, 2⁺; 7.65MeV, 0⁺; and 9.64MeV, 3⁻ states) scattering at 110 MeV are characterized by pronounced enhancement and strong oscillations at large angles. We performed calculations of the differential cross sections of these reactions assuming a potential scattering in the forward hemisphere and the direct transfer of ⁸Be cluster θ _c.m. > 90°. We showed that the α + ⁸Be cluster configuration with relative angular momentum L = 0 dominates in the Hoyle state being 4.4 times larger than that in the ground state. This result also contributes to the verification of αBEC hypothesis and is consistent with the conjecture of a dilute 3α structure of the Hoyle state. In the 9.64 MeV, 3⁻ state, a positive interference of all allowed α + ⁸Be configurations with a dominance of the p-orbital (49%) α-⁸Be relative motion is found. This finding manifests the exotic 3α, but hardly condensed structure of the 9.64-MeV 3⁻ state in ¹²C.     

Phase and frequency shifts of two nonlinearly coupled oscillators

We analyze two nonlinearly phase coupled oscillators with eigenfrequencies ω₁and ω₂, where n\gw₁=m\gw₂+\gp, with integern andm. For \gh=0 there are up to four stable synchronized states which differ from each other only by the difference of the oscillators\rs phases. The number of different synchronized states depends on the coupling constants. If \gh does not vanish phase shifts and frequency shifts may occur givig rise to stable synchronized states which also differ from each other due to the frequencies. By means of the center manifold theorem we calculate these shifts explicitely. Different coupling constants are investigated: symmetrical, homogenously asymmetrical and arbitrary coupling constants. Our results point out the decisive influence of the symmetry of the coupling constants upon the frequency and phase shifts. Moreover the local stability of the unperturbed synchronized state (i.e. for \gh=0) determines the magnitude of the frequency and phase shifts.     

Electrical conductivity and magnetic properties of La1 ? xCaxMn1 ? yFeyO3 ceramic samples (x = 0.67, y = 0, 0.05)

The temperature dependences of the magnetic susceptibility χ(T) and the electrical resistivity ρ(T) of ceramic samples of La_{1 − x} Ca _x MnO₃ with x = 0.67 (LCMO) and La_{1 − x} Ca _x Mn_{1 − y} Fe _y O₃ with x = 0.67 and y = 0.05 (LCMFO) are investigated in magnetic fields B = 50–10⁵ G and the temperature range T = 4.2–400 K. Both samples undergo a transition from the paramagnetic state to a state with charge (orbital) ordering (CO) at temperatures T _CO ≈ 272 K for LCMO and T _CO ≈ 222 K for LCMFO. The behavior of the paramagnetic phase in the temperature range 320–400 K for LCMO and 260–400 K for LCMFO is described by the Curie-Weiss law with effective Bohr magneton numbers p _eff = 4.83 μ_B (LCMO) and 4.77 μ_B (LCMFO), respectively. The disagreement between the observed positive Weiss temperatures (θ ≈ 175 K (LCMO) and θ ≈ 134 K (LCMFO)) and negative Weiss temperatures required for the antiferromagnetic ground state can be explained by the phase separation and transition to the charge-ordered state. The magnetic irreversibility for T < T _CO is accounted for by the existence of a mixture of the ferromagnetic and antiferromagnetic phases, as well as the cluster glass phase. At low temperatures, doping with iron enhances the frustration of the system, which manifests itself in a more regular behavior of the decay rate of the remanent magnetization with time. The temperature dependence of the electrical resistivity in the range of the charge-ordered phase conforms to the variable-range hopping model. The behavior of the electrical resistivity is governed by the complex structure of the density of localized states near the Fermi level, which includes a soft Coulomb gap Δ = 0.464 eV for LCMO and 0.446 eV for LCMFO. It is established that the ratio between the localization radii of charge carriers a for LCMFO and a _und for LCMO is a/a _und = 0.88. Original Russian Text ? V.S. Zakhvalinskiĭ, R. Laiho, T.S. Orlova, A.V. Khokhulin, 2008, published in Fizika Tverdogo Tela, 2008, Vol. 50, No. 1, pp. 61–68.     

Calculation of the photoionization with deexcitation cross sections of He and helium-like ions

We discuss the results of the calculation of the photoionization with deexcitation of excited He and helium-like ions Li⁺ and B³⁺ at high but nonrelativistic photon energies θ. Several lower ¹ S and ³ S states are considered. We present and analyze the ratios R _d ⁺ * of the cross sections of photoionization with deexcitation, σ _(d) ⁺ *(θ), and of the photoionization with excitation, σ⁺*(θ). The dependence of R _d ⁺ * on the excitation of the target object and the charge of its nucleus is presented. In addition to theoretical interest, the results obtained can be verified using long-lived excited states such as 2³ S of He. The text was submitted by authors in English.