Theory of laser noise in the phase locking region

We start from quantum mechanical laser equations which were derived in a previous paper for an inhomogeneously broadened laser and which contain in particular the noise sources due to cavity losses, vacuum fluctuations, interaction with phonons and nonlasing photons and the pump. For the example of frequency locking caused by the nonlinear polarization we derive a quantum mechanical Langevin equation for the relative phase angleψ=2ψ ₂ —ψ ₁-ψ ₃, whereψ ₁,ψ ₂,ψ ₃, are the total phases of three axial modes which would be equally spaced in the unloaded cavity. In the resulting equation

$$\dot \psi = \delta - \beta \sin \psi + f(t)$$     

Determination of the region of existence of ferromagnetic nanostructures in the paraphase of La<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Ba<Subscript>x</Subscript>MnO<Subscript>3</Subscript> by the EPR method

In the paraphase of a number of La_1?x Ba_xMnO₃ single crystals with 0.1 ≤ x ≤ 0.2 below 340 K, signals of the ferromagnetic resonance are observed, which indicates the presence of magnetically ordered nanoscopic objects (ferrons). The region of the existence of ferrons on the Ba density-temperature phase diagram has an approximate triangular shape, which is characteristic of the Griffiths phase. Investigations of the angular and frequency dependences of the position of the ferromagnetic resonance line indicate that the nanostructures have a spherical shape. The parameters of their magnetic anisotropy are found to be H _a1 = 2500 Oe and H _a2 = ?700 Oe.     

Photoproduction of <Emphasis Type="Italic">J/ψ</Emphasis> mesons at high energies within the parton model and in the <Emphasis Type="Italic">k</Emphasis><Subscript>T</Subscript>-factorization approach

The photoproduction of J/ψ mesons is considered on the basis of the parton model and in the k_T-factorization approach in the leading order in α _s . It is shown that, at specific values of the charmed-quark mass and the J/ψ-meson wave function at the origin, the predictions of the two approaches for the total cross section and z spectra of J/ψ mesons nearly coincide and agree with experimental data obtained at the HERA ep collider. At the same time, the parton model and the theory of semihard processes predict significantly different p_T spectra of J/ψ mesons and significantly different transverse-momentum dependences of the ratio of the cross sections for the production of longitudinally and transversely polarized J/ψ mesons. It is expected that nontrivial effects of low-x physics will clearly manifest themselves in experimentally testing this fact.     

Quark-antiquark composite systems: The Bethe-Salpeter equation in the spectral-integration technique

The Bethe-Salpeter equations for the quark-antiquark composite systems, q\(\bar q\), are written in terms of spectral integrals. For the q\(\bar q\) mesons characterized by the mass M, spin J, and radial quantum number n, the equations are presented for the following (n, M²) trajectories: π _J , η _J , a _J , f _J , ρ _J , ω _J , h _J , and b _J .     

Gamow Vectors and Borel Summability in a Class of Quantum Systems

We analyze the detailed time dependence of the wave function ψ(x,t) for one dimensional Hamiltonians \(H=-\partial_{x}^{2}+V(x)\) where V (for example modeling barriers or wells) and ψ(x,0) are compactly supported.We show that the dispersive part of ψ(x,t) is the Borel sum of its asymptotic series in powers of t ^?1/2, t→∞. The remainder, the difference between ψ and the Borel sum, i.e., the exponential part of the transseries of ψ, is a convergent expansion of the form \(\sum_{k=0}^{\infty}g_{k}\Gamma_{k}(x)e^{-\gamma_{k} t}\), where Γ _k are the Gamow vectors of H, and iγ _k are the associated resonances; generically, all g _k are nonzero. For large k, γ _k ～const?klog?k+k ² π ² i/4. The effect of the Gamow vectors is visible when time is not very large, and the decomposition defines rigorously resonances and Gamow vectors in a nonperturbative regime, in a physically relevant way.The decomposition allows for calculating ψ for moderate and large t, to any prescribed exponential accuracy, using optimal truncation of power series plus finitely many Gamow vectors contributions.The analytic structure of ψ is perhaps surprising: in general (even in simple examples such as square wells), ψ(x,t) turns out to be C ^∞ in t but nowhere analytic on ?⁺. In fact, ψ is t-analytic in a sector in the lower half plane and has the whole of ?⁺ a natural boundary. In the dual space, we analyze the resurgent structure of ψ.     

On the orientation effect of the neutron yield increase in <Emphasis Type="Italic">d</Emphasis>(<Emphasis Type="Italic">d,n</Emphasis>)<Superscript>3</Superscript>Hе reactions at an energy of 7–12 keV in TiD<Subscript>2</Subscript> crystals

The orientation dependence of the d(d, n)³He reaction probability in a TiD₂ crystal at a deuteron energy of 7–12 keV is investigated. The BCM-1.0 code developed for calculating the trajectories of channeled particles within classical mechanics is used to simulate deuteron trajectories at (200)-planar channeling in a 0.15-μm-thick Ti crystal with the angular divergence of the beam taken into account. The enhancement of the reaction probability in the computer experiments is 2.1 in the case of a parallel deuteron beam and near-zero crystal entry angles relative to the (200) planes. In the case of a deuteron beam with its angular divergence equal to 1/5 of the critical channeling angle, the maximum reaction-probability enhancement is 1.5. The results of calculations agree qualitatively with recent experiments performed at Tomsk Polytechnic University.     

Angular distributions in the decays of the triplet <Emphasis Type="Italic">D</Emphasis><Subscript>2</Subscript> state of charmonium directly produced in polarized proton–antiproton collisions

Using the helicity formalism, we calculate the combined angular distribution function of the two gamma photons and the electron in the cascade process \({\bar{p}p}\to{}^{3}{D}_{2}\to\chi_{J}+\gamma_{1}\to(\psi +\gamma_{2})+\gamma_{1}\to({e}^{+}+{e}^{-})+\gamma_{1}+\gamma_{2}\) (J=0,1,2), when \({\bar{p}}\) and p are arbitrarily polarized. We also present the partially integrated angular distribution functions in six different cases. Our results show that by measuring the two-particle angular distribution of γ ₁ and γ ₂ and that of γ ₁ and e ^?, one can determine the relative magnitudes as well as the relative phases of all the helicity amplitudes in the two radiative decay processes ³ D ₂→χ _J +γ ₁ and χ _J →ψ+γ ₂.     

Estimating of CP-violation in <Emphasis Type="Italic">B</Emphasis><Superscript>0</Superscript>→ψ(2<Emphasis Type="Italic">S</Emphasis>)π<Superscript>0</Superscript> decay

I present estimates of CP-violating asymmetries in the non-leptonic charmonium two-body B⁰→ψ(2S)π⁰ decay and the same decays of B⁺→ψ(2S)π⁺ and B⁺→ψ(2S)K⁺ These estimates are based on QCD and improved QCD factorization approach making use of next-to-leading order (NLO) contributions. The CP-violating asymmetry for B⁰→ψ(2S)π⁰ decay is not available, according to the same calculations, it is expected if it can be measured in the future its value will be S_ψ(2S)π0(B⁰ → ψ(2S)π⁰)= 0.662 ± 0.197 and C_ψ(2S)π0(B⁰ → ψ(2S)π⁰)= 0.024 ± 0.007.     

Microscopic theory of second-order and third-order elastic constants for an NaCl crystal

Relations between the second-order and third-order symmetry-independent elastic constants and the energy of interatomic interactions dependent on the mutual arrangement of pairs and triplets of atoms are obtained for crystals belonging to the crystal class O _h. The derived relations and experimental data on the elastic constants are used to calculate four third-order elastic constants and the temperature dependence of the elastic anisotropy factor a(T) for an NaCl crystal. The calculated dependence a(T) is in qualitative agreement with the experimental dependence a _exp(T).     

Crystallographic and dynamic characteristics of K<Subscript>1 − <Emphasis Type="Italic">x</Emphasis></Subscript>Rb<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript>TiOPO<Subscript>4</Subscript> solid solutions in the low-temperature ranges

The unit cell parameters a and c of K_{1 ? x} Rb _x TiOPO₄ (x= 0, 0.3, and 0.5) crystals are investigated using x-ray diffraction in the temperature range 90–320 K. The thermal expansion coefficients along the principal crystallographic axes of the crystals are determined from the obtained temperature dependences of the unit cell parameters. It is found that the parameter a increases with increasing temperature, while the parameter c decreases. For the crystals under investigation, the elastic moduli c ₁₁ and c ₃₃ along the [100] and [001] directions are determined by the ultrasonic pulse-echo technique in the temperature range 100–350 K. It is shown that c ₃₃ > c ₁₁. The anomalies revealed in the temperature dependences of the crystallographic and dynamic characteristics of the samples at a temperature T ≈ 280 K indicate the occurrence of a phase transition. The temperature of the phase transition is found to increase with increasing rubidium content x.     

Proc ess es e+ e− → cccc and e+ e− → J/ψ + gg at $$\sqrt s = 10.59 G eV$$

Experimental data obtained by the BELLE Collaboration for inclusive J/ψ production in the processes e⁺e^? → J/ψ + gg and e⁺e^? → J/ψ + cc are discussed. These data are compared with the predictions of perturbative QCD that were obtained by two methods, that which employs information about the J/ψ wave function and that which relies on the hypothesis of quark-hadron duality exclusively. Both computational methods yield results that disagree with the experimental data considerably. The dependence of the cross section for the process e⁺e^? → J/ψ + gg on the effective gluon mass is studied. The cross section for the production of doubly charmed baryons Ξ _cc ^* is estimated.     

Analytic Structure of Many-Body Coulombic Wave Functions

We investigate the analytic structure of solutions of non-relativistic Schrödinger equations describing Coulombic many-particle systems. We prove the following: Let ψ(x) with \({{\bf x} = (x_{1},\dots, x_{N})\in \mathbb {R}^{3N}}\) denote an N-electron wavefunction of such a system with one nucleus fixed at the origin. Then in a neighbourhood of a coalescence point, for which x ₁ = 0 and the other electron coordinates do not coincide, and differ from 0, ψ can be represented locally as ψ(x) = ψ ⁽¹⁾(x) + |x ₁|ψ ⁽²⁾(x) with ψ ⁽¹⁾, ψ ⁽²⁾ real analytic. A similar representation holds near two-electron coalescence points. The Kustaanheimo-Stiefel transform and analytic hypoellipticity play an essential role in the proof.     

Investigation of the Balitsky-Fadin-Kuraev-Lipatov dynamics of gluon distributions in the inelastic production of <Emphasis Type="Italic">J/ψ</Emphasis> mesons at the HERA collider

The inelastic photo-and electroproduction of J/ψ mesons at the HERA collider are considered within the semihard (k _T -factorization) QCD approach and the color-singlet model. The total, differential, and double-differential cross sections for the inelastic production of J/ψ mesons are investigated versus the Pomeron intercept Δ, which is the basic parameter of low-x physics; also studied here is the spin alignment parameter α versus the square of the transverse momentum, p _ψT ² , and the variable z. The theoretical results obtained in the present study are compared with the latest experimental data of the H1 and ZEUS Collaborations. It is shown that experimental investigations of the polarization properties of J/ψ mesons at the HERA collider for Q²<1 GeV² may provide an additional test of the Balitsky-Fadin-Kuraev-Lipatov dynamics of gluon distributions.     

Polarized angular distributions in the decays of the singlet D2 state of charmonium originating from $\bar{p}p$ collisions

Using the helicity formalism, we calculate the combined angular distribution function of the neutral pion (π ⁰) and the polarized electron (e ^?) and photon (γ) produced in the triple cascade process \(\bar{p}+p\rightarrow{}^{1}D_{2}\rightarrow{}^{1}P_{1}+\gamma\rightarrow(\psi +\pi^{0})+\gamma \rightarrow(e^{-}+e^{+})+\pi^{0}+\gamma\), when \(\bar{p}\) and p are unpolarized. We also present the partially integrated angular distribution functions in three different cases where the combined angular distribution function of the three particles is integrated over the direction of one of the particles. Our results show that by measuring the two-particle angular distribution of the electron and the photon with the polarization of either particle, one can determine the relative magnitudes as well as the relative phases of all the angular-momentum helicity amplitudes in the two decay processes ¹ D ₂→¹ P ₁+γ and ¹ P ₁→ψ+π ⁰.     

Quantifying Correlations via the Wigner-Yanase-Dyson Skew Information

In this paper, based on a discussion about the Wigner-Yanase-Dyson (WYD) skew information, the measure F_a,α(ρ_ab) for correlations in terms of the WYD skew information is introduced and discussed. The following conclusions are obtained. For a classical-quantum state ρ_ab, F_a,α(ρ_ab)=0 if and only if ρ_ab is a product state; F_a,α(ρ_ab) is locally unitary invariant and convex on the set of states with the fixed marginal ρ_a; F_a,α(ρ_ab) decreases under local random unitary operation on H_b; For a quantum-classical state ρ_ab, F_a,α(ρ_ab) decreases under local operation on H_b; Lastly, F_a,α(ρ_ab) is computed for the pure states and the Bell-diagonal states, respectively.     

Critical current in S-FNF-S Josephson structures with the noncollinear magnetization vectors of ferromagnetic films

The critical current I _C of S-FNF-S Josephson junctions, which are ferromagnet (F)-normal metal (N)-ferromagnet multilayer structures whose ends are in contact with the superconducting (S) electrodes, has been calculated. It has been shown that both the magnitude and sign of I _C depends significantly on the misorientation angle α of the magnetization vectors M _{1, 2} of the ferromagnetic films and the distance L between the superconducting electrodes. The effect of the triplet superconducting component ～〈ψ↑ψ↑〉 ～〈ψ↓ψ↓〉 appearing in the structure on I _C(α) has been analyzed. It has been proven that a new type of the π junction exists, appearing due to the superposition of two contributions to I _C that decrease monotonically with L and are damped at lengths about the coherence length of the normal metal. It has been shown that the effective control over the magnitude and sign of I _C of the structure is achieved at a small deflection of the vectors M _{1, 2} from the antiferromagnetic (M ₁ ↑↓ M ₂) configuration.     

Coulomb Problem for <Emphasis Type="Italic">Z</Emphasis> &gt; Z<Subscript>cr</Subscript> in Doped Graphene

The dynamics of charge carriers in doped graphene, i.e., graphene with a gap in the energy spectrum depending on the substrate, in the presence of a Coulomb impurity with charge Z is considered within the effective two-dimensional Dirac equation. The wave functions of carriers with conserved angular momentum J = M + 1/2 are determined for a Coulomb potential modified at small distances. This case, just as any two-dimensional physical system, admits both integer and half-integer quantization of the orbital angular momentum in plane, M = 0, ±1, ±2, …. For J = 0, ±1/2, ±1, critical values of the effective charge Z_cr(J, n) are calculated for which a level with angular momentum J and radial quantum numbers n = 0 and n = 1 reaches the upper boundary of the valence band. For Z < Z_cr (J, n = 0), the energy of a level is presented as a function of charge Z for the lowest values of orbital angular momentum M, the level with J = 0 being the first to descend to the band edge. For Z>Z_cr (J, n = 0), scattering phases are calculated as a function of hole energy for several values of supercriticality, as well as the positions ε₀ and widths γ of quasistationary states as a function of supercriticality. The values of ε₀* and width γ* are pointed out for which quasidiscrete levels may show up as Breit–Wigner resonances in the scattering of holes by a supercritical impurity. Since the phases are real, the partial scattering matrix is unitary, so that the radial Dirac equation is consistent even for Z > Z_cr. In this single-particle approximation, there is no spontaneous creation of electron–hole pairs, and the impurity charge cannot be screened by this mechanism.     

Intermediate phases in [111]- and [001]-oriented PbMg<Subscript>1/3</Subscript>Nb<Subscript>2/3</Subscript>O<Subscript>3</Subscript>–29PbTiO<Subscript>3</Subscript> single crystals

Phase transformations in [111]- and [001]-oriented PbMg_1/3Nb_2/3O₃–29PbTiO₃ single crystals have been studied using dielectric and optical measurements before and after applying an electric field. It is shown that the subsequence of phase transitions rhombohedral (R)—tetragonal (T)—cubic (C) phases is observed in nonpolarized samples of both orientations as temperature increases. In the [111]-oriented crystal, an additional intermediate monoclinic phase (it is possible, M _a ) is induced after preliminary polarization at room temperature and the R–M _a –T–C phase transitions are observed on heating. In the [001]-oriented crystal, after its polarization, the monoclinic phase forms instead of the rhombohedral phase even at room temperature and the M _a –T–C transitions occur on heating. The results are discussed from the point of view of the existence polar nanoregions with different local symmetries in a glasslike matrix.     

Breit-Wigner parameters of the <Emphasis Type="Italic">S</Emphasis><Subscript>11</Subscript>(1535) nucleon resonance

The results of a partial-wave analysis of the angular distributions for the process γp → ηp over the energy range up to 2 GeV are presented. Reliable estimates of the Breit-Wigner parameters of the S₁₁(1535) resonance, as well as the energy dependence of the real and imaginary parts of the electric dipole amplitude E₀₊ and its phase, are derived from the energy dependence of the regression coefficient a₀(W).