Study of spin-wave dynamics in Fe65Ni35 ferromagnetic via small-angle polarized-neutron scattering

The results of studying the spin dynamics of a classical Fe₆₅Ni₃₅ invar alloy are presented and analyzed. The investigations are performed via small-angle polarized-neutron scattering in the oblique geometry of a magnetic field at various temperatures (T < T _C). This approach is based on the analysis of left-right asymmetry in the magnetic scattering of polarized neutrons. The asymmetry effect arises when the magnetization direction of a sample is inclined with respect to the wave vector of the incident beam. The spin-wave scattering is concentrated within a range bounded by the cutoff angle θ_c determined by the magnetic field: θ _c ² (H) = θ ₀ ² ?(gμ_B H)θ₀/E, where \(\theta _0 = \hbar ^2 \frac{1} {{2Dm_n }}\) , H is the external magnetic field, E is the initial neutron energy, D is the spin-wave stiffness constant, and m _n is the neutron mass. The scattering is blurred by spinwave damping in the vicinity of the cutoff angle. The spin-wave stiffness constant can be obtained from a comparison of the asymmetric contribution to scattering and a model function. The temperature dependence D = D(T) is well defined by the expression D = D ₀ |τ| ^x , where \(\tau = 1 - \frac{T} {{T_C }}\) , x = 0.47 ± 0.01, D ₀ = 137 ± 3 meVŲ, and τ > 0.1 in the entire temperature range. The given method enables us to construct the temperature dependence of the spin-wave stiffness constant with a high accuracy and a small step.     

Quantum Curves for Hitchin Fibrations and the Eynard–Orantin Theory

We generalize the topological recursion of Eynard–Orantin (JHEP 0612:053, 2006; Commun Number Theory Phys 1:347–452, 2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle T*C of an arbitrary smooth base curve C. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal ${\hbar}$ -deformation family of D modules over an arbitrary projective algebraic curve C of genus greater than 1, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the ${SL(2,\mathbb{C})}$ -character variety of the fundamental group π₁(C). We show that the semi-classical limit through the WKB approximation of these ${\hbar}$ -deformed D modules recovers the initial family of Hitchin spectral curves.     

The Schrödinger Equation,the Zero-Point Electromagnetic Radiation,and the Photoelectric Effect

A Schrödinger type equation for a mathematical probability amplitude Ψ(x,t) is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M and charge e, moving in a potential V(x). The particle phase space probability density is denoted Q(x,p,t), and the entire system is immersed in the “vacuum” zero-point electromagnetic radiation. We show, in the first part of the paper, that the generalized Liouville equation is reduced to a simpler Liouville equation in the equilibrium limit where the small radiative corrections cancel each other approximately. This leads us to a simpler Liouville equation that will facilitate the calculations in the second part of the paper. Within this second part, we address ourselves to the following task: Since the Schrödinger equation depends on \(\hbar \), and the zero-point electromagnetic spectral distribution, given by \(\rho _{0}{(\omega )} = \hbar \omega ^{3}/2 \pi ^{2} c^{3}\), also depends on \(\hbar \), it is interesting to verify the possible dynamical connection between ρ₀(ω) and the Schrödinger equation. We shall prove that the Planck’s constant, present in the momentum operator of the Schrödinger equation, is deeply related with the ubiquitous zero-point electromagnetic radiation with spectral distribution ρ₀(ω). For simplicity, we do not use the hypothesis of the existence of the L. de Broglie matter-waves. The implications of our study for the standard interpretation of the photoelectric effect are discussed by considering the main characteristics of the phenomenon. We also mention, briefly, the effects of the zero-point radiation in the tunneling phenomenon and the Compton’s effect.     

A coupled-channel treatment of Cabibbo-angle favoured (D,D s + )→VP decays

We have performed a two-channel calculation of Cabibbo-angle favoured decays,D _s ⁺ →VP. We find a satisfactory fit toS _s ⁺ →φπ ⁺,ρ ⁰ π ⁺ andK ⁺ \(\bar K^{ * 0} \) data from ARGUS and E-691. We have also studied Cabbibo-angle favouredD→VP decays in a coupled channel formalism. We coupleD→K ^*π,K _? and \(\bar K^0 \phi \) channels inI=1/2 state, andK ^*π andK _? channels inI=3/2 state. We leave the two channels, \(\bar K^0 \omega \) and \(\bar K^{ * 0} \eta \) out of our unitarization scheme. Particular attention is paid to the role of the weak annihilation term in these decays.     

On quantum analogue of dynamical stabilisation of inverted harmonic oscillator by time periodical uniform field

Quantum analogue of stabilised forced oscillations around an unstable equilibrium position is explored by solving the non-stationary Schrödinger equation (NSE) of the inverted harmonic oscillator (IHO) driven periodically by spatial uniform field of frequency \(\Omega \), amplitude \(F_{0}\) and phase \(\phi \), i.e. the system with the Hamiltonian of \(\hat{{H}}=(\hat{{p}}^{2}/2m)-(m\omega ^{2}x^{2}/2)-F_0 x\sin \) \(\left( {\Omega t+\phi } \right) \). The NSE has been solved both analytically and numerically by Maple 15 in dimensionless variables \(\xi = x\sqrt{m\omega /\hbar }\hbox {, }f_0 =F_0 /\omega \sqrt{\hbar m\omega }\) and \(\tau =\omega t\). The initial condition (IC) has been specified by the wave function (w.f.) of a generalised Gaussian type which suits well the corresponding quantum IC operator. The solution obtained demonstrates the non-monotonous behaviour of the coordinate spreading \(\sigma \left( \tau \right) \hbox { =}\sqrt{\big ( {\overline{\Delta \xi ^{2}\big ( \tau \big )} } \big )}\) which decreases first from quite macroscopic values of \(\sigma _{0} =2^{12,\ldots ,25}\) to minimal one of \(\sim \!(1/\sqrt{2})\) at times \(\tau <\tau _0 =0.125\ln \!\left( {16\sigma _0^4 +1} \right) \) and then grows back unlimitedly. For certain phases \(\phi \) depending on the \(\Omega /\omega \) ratio and \(n=\log _2\!\sigma _0 \), the mass centre of the packet \(\xi _{\mathrm {av}}( \tau )= \overline{\hat{{x}}(\tau )} \cdot \sqrt{m\omega /\hbar }\) delays approximately two natural ‘periods’ \(\sim \!(4\pi /\omega )\) in the area of the stationary point and then escapes to ‘\(+\)’ or ‘?’ infinity in a bifurcating way.  For ‘resonant’ \(\Omega =\omega \), the bifurcation phases \(\phi \) fit well with the regression formula of Fermi–Dirac type of argument n with their asymptotic \(\phi ( {\Omega ,n\rightarrow \infty } )\) obeying the classical formula \(\phi _{\mathrm {cl}} ( \Omega )=-\hbox {arctg} \, \Omega \) for initial energy \(E = 0\) in the wide range of \(\Omega =2^{-4},...,2^{7}\).     

On Representations of Quantum Conjugacy Classes of GL(n)

Let O be a closed Poisson conjugacy class of the complex algebraic Poisson group GL(n) relative to the Drinfeld-Jimbo factorizable classical r-matrix. Denote by T the maximal torus of diagonal matrices in GL(n). With every ${a \in O \cap T}$ we associate a highest weight module M _a over the quantum group ${U_q \bigl(\mathfrak{g} \mathfrak{l}(n)\bigr)}$ and an equivariant quantization ${\mathbb{C}_{\hbar,a}[O]}$ of the polynomial ring ${\mathbb{C}[O]}$ realized by operators on M _a . All quantizations ${\mathbb{C}_{\hbar,a}[O]}$ are isomorphic and can be regarded as different exact representations of the same algebra, ${\mathbb{C}_{\hbar}[O]}$ . Similar results are obtained for semisimple adjoint orbits in ${\mathfrak{g} \mathfrak{l}(n)}$ equipped with the canonical GL(n)-invariant Poisson structure.     

Two-Neutron Alignment in <Superscript>127</Superscript>Xe

High spin states in ¹²⁷Xe have been investigated via ⁹Be induced fusion-evaporation reaction at 48 MeV. Spin and parity of excited states up to \( \sim \frac {47}{2} \hbar \) have been confirmed from angular correlation and linear polarization results. Rotational alignment of the second pair of h _11/2 neutrons has been observed at \(\hbar \omega \sim \) 0.44 MeV; beyond that, the band is associated with ν[h _11/2]³ configuration. The alignment phenomena has been discussed in comparison with the neighboring ^125,129Xe.     

Uniform boundedness of conditional gauge and Schrödinger equations

We prove that for a bounded domainD ?R ⁿ withC ² boundary and \(q \in K_n^{loc} (n \geqq 3) if E^x \exp \int\limits_0^{\tau _D } {q(x_t )dt} \mathop \ddag \limits_--- \infty \) inD, then $$\mathop {\sup }\limits_{\mathop {x \in D}\limits_{z \in \partial D} } E_z^x \exp \int\limits_0^{\tau _D } {q(x_t )dt}< + \infty $$ ({x _t : Brownian motion}) The important corollary of this result is that if the Schrödinger equation Δ/2u+qu=0 has a strictly positive solution onD, then for anyD ₀ ? ?D, there exists a constantC=C(n,q,D,D ₀) such that for anyf εL ¹(?D, σ), (σ: area measure on ?D) we have $$\mathop {\sup |}\limits_{x \in D_0 } u_f (x)| \mathop< \limits_ = C\int\limits_{\partial D} {|f(y)|\sigma (dy)} $$ whereu _f is the solution of the Schrödinger equation corresponding to the boundary valuef. To prove the main result we set up the following estimate inequalities on the Poisson kernelK(x,z) corresponding to the Laplace operator: $$C_1 \frac{{d(x,\partial D)}}{{|x - z|^n }}\mathop< \limits_ = K(x,z)\mathop< \limits_ = C_2 \frac{{d(x,\partial D)}}{{|x - z|^n }},x \in D,z \in \partial D$$ whereC ₁ andC ₂ are constants depending onn andD.     

A semi-classical trace formula for Schrödinger operators

LetS _?=??Δ+V, withV smooth. If 0<E ²V(x), the spectrum ofS _? nearE ² consists (for ? small) of finitely-many eigenvalues,λ _j (?). We study the asymptotic distribution of these eigenvalues aboutE ² as ?→0; we obtain semi-classical asymptotics for $$\sum\limits_j {f\left( {\frac{{\sqrt {\lambda _j (\hbar )} - E}}{\hbar }} \right)} $$ with \(\hat f \in C_0^\infty \) , in terms of the periodic classical trajectories on the energy surface \(B_E = \left\{ {\left| \xi \right|^2 + V(x) = E^2 } \right\}\) . This in turn gives Weyl-type estimates for the counting function \(\# \left\{ {j;\left| {\sqrt {\lambda _j (\hbar )} - E} \right| \leqq c\hbar } \right\}\) . We make a detailed analysis of the case when the flow onB _E is periodic.     

Dispersion dependence of two-photon absorption transition on frequency in Si PIN photodetector

The variation of two-photon absorption (TPA) coefficient \(\beta _{\mathrm{TPA}} (\omega )\) of Si excited at difference photon energy was investigated. The TPA coefficient was measured by using a picosecond pulsed laser with the wavelength could be tuned in a wide photon-energy range. An equivalent RC circuit model was adapted to derive the TPA coefficient \(\beta _{\mathrm{TPA}} (\omega )\) . The results showed that \(\beta _{\mathrm{TPA}} (\omega )\) varied from \(4.2 \times 10^{-4}\) to \(1.17 \times 10^{-3 }\)  cm/GW in the transparent wavelength region \(1.80<\lambda <1.36\,\upmu \) m of Si. The increasing tendency of \(\beta _{\mathrm{TPA}} (\omega )\) with the incident photon energy can be qualitatively interpreted as the photon energy increases from \(E_{\mathrm{ig}}/2\) to nearly \(E_{\mathrm{ig}}\) , the electrons excited from the valance band find an increasing availability of conduction band states. Comparing with the high-energy side transitions, the TPA coefficient in low-energy side is about 10 times too small. This can be attributed that the TPA transition in low-energy side is the process of photon-assisted electron transitions from valence to conduction band occurring between different points in k-space, while is direct transition in high-energy side.     

Collisional damping of transverse waves in a plasma

The effect of collisions on transverse waves in a homogeneous, field free plasma is investigated by means of Gross-Krook collision model. The dispersion relation is calculated by assuming the collision frequency to be small andKλ _D ?1. The damping rate ω _I is obtained as $$\omega _I = \frac{{\nu _{ei} }}{2}\frac{{\omega _p^2 }}{{\omega _0^2 }}\left[ {1 + \frac{{3K^2 \lambda _D^2 \omega _p^2 }}{{\omega _0^2 }} - \frac{{K^2 \lambda _D^2 \omega _p^4 }}{{\omega _0^4 }}} \right] + \frac{{\nu _{ee} }}{2}\frac{{\omega _p^2 }}{{\omega _0^2 }}\left( {\frac{{K^2 \lambda _D^2 \omega _p^2 }}{{\omega _0^2 }}} \right)$$ where ω ₀ ² =c ² K ²+ω ₂ ^p , andv _ei andv _ee are electron-ion and electron-electron collision frequency respectively.     

Continuous measures in one dimension

Families of unimodal maps satisfying

1. T _λ: [?1,1]?[?1,1] withT(±1)=?1 and |T _λ ^′ (1)|>1.
2. T _λ(x) isC ² inx ² and λ, and symmetric inx.
3. T ₀(0)=0,T ₁(0)=1 with \(\frac{d}{{d\lambda }}\) T _λ(0)>0

are considered. The results of Guckenheimer (1982) are extended to show that there is a positive measure of λ for whichT _λ has a finite absolutely continuous invariant measure. The appendix contains general theorems for the existence of such measures for some markov maps of the interval.     

Asymptotic inverse spectral problem for anharmonic oscillators

We study perturbationsL=A+B of the harmonic oscillatorA=1/2(??²+x ²?1) on ?, when potentialB(x) has a prescribed asymptotics at ∞,B(x)～|x|^?α V(x) with a trigonometric even functionV(x)=Σa _mcosω _m x. The eigenvalues ofL are shown to be λ _k =k+μ _k with small μ _k =O(k ^?γ), γ=1/2+1/4. The main result of the paper is an asymptotic formula for spectral fluctuations {μ _k }, $$\mu _k \sim k^{ - \gamma } \tilde V(\sqrt {2k} ) + c/\sqrt {2k} ask \to \infty ,$$ whose leading term \(\tilde V\) represents the so-called “Radon transform” ofV, $$\tilde V(x) = const\sum {\frac{{a_m }}{{\sqrt {\omega _m } }}\cos (\omega _m x - \pi /4)} .$$ as a consequence we are able to solve explicitly the inverse spectral problem, i.e., recover asymptotic part |x ^?α|V(x) ofB from asymptotics of {µ _k }. ₁ ^∞      

Generalized Sturm expansions of the Coulomb Green’s function and two-photon Gordon formulas

The radial component of the Coulomb Green’s function (CGF) is written in the form of a double series in Laguerre polynomials (Sturm’s functions in the Coulomb problem), which contains two free parameters α and α′. The obtained result is applicable both in the nonrelativistic case and for the CGF of the squared Dirac equation with a Coulomb potential. The CGF is decomposed into the resonance and potential components (the latter is a smooth function of energy) for α = α′. In the momentum representation, the CGF with the free parameters is written in the form of an expansion in four-dimensional spherical functions. The choice of the parameters α and α ′ in accordance with the specific features of the given problem radically simplifies the calculation of the composite matrix elements for electromagnetic transitions. Closed analytic expressions (in terms of hypergeometric functions) are obtained for the amplitudes of bound-bound and bound-free two-photon transitions in the hydrogen atom from an arbitrary initial state ¦nl〉, which generalize the known (one-photon) Gordon formulas. The dynamic polarizability tensor components α_nlm(ω) for an arbitrary n are expressed in terms of the hypergeometric function ₂ F ₁ depending only on l and $\tilde \omega $ and through the polynomial functions $f_{nl} (\tilde \omega )$ of frequency $\tilde \omega = {{\hbar \omega } \mathord{\left/ {\vphantom {{\hbar \omega } {\left| {E_n } \right|}}} \right. \kern-0em} {\left| {E_n } \right|}}$ . The Rydberg (n ? 1) and threshold (?ω ～ ¦ E _n¦) asymptotic forms of polarizabilities are investigated.     

35Cl NQR spectra of group 1 and silver dichloromethanesulfonates

The dichloromethanesulfonates of silver and other +1-charged cations, M ^?+?(Cl₂CHSO $_{3}^{-})$ (M = Ag, Tl, Li, Na, K, Rb, Cs) were synthesized and studied by ³⁵Cl NQR. Dichloromethanesulfonic acid was prepared by the methanolysis of dichloromethanesulfonyl chloride, and was then neutralized with the carbonates of the +1-charged cations to produce the corresponding dichloromethanesulfonate salt. This NQR study completed the investigation of the chloroacetates and chloromethanesulfonates of silver, Ag^?+?(Cl _x CH_3???x SO $_{3}^{-})$ and Ag^?+?(Cl _x CH_3???x CO $_{2}^{-})$ , and suggests (1) that the ability of organochlorine atoms to coordinate to silver decreases as the number of electron-withdrawing groups (Cl, SO $_{3}^{-}$ , CO $_{2}^{-})$ attached to the carbon atom increases; (2) that the unusually large NQR spectral width found among M ^?+?(Cl₂CHCO $_{2}^{-})$ salts is not present among M ^?+?(Cl₂CHSO $_{3}^{-})$ salts, and therefore is not generally characteristic of the dichloromethyl group in salts.     

Quantum Sphere {\mathbb{S}^4} as a Non-Levi Conjugacy Class

We construct a ${U_\hbar(\mathfrak{sp}(4))}$ -equivariant quantization of the four-dimensional complex sphere ${\mathbb{S}^4}$ regarded as a conjugacy class, Sp(4)/Sp(2) ×?Sp(2), of a simple complex group with non-Levi isotropy subgroup, through an operator realization of the quantum polynomial algebra ${\mathbb{C}_\hbar[\mathbb{S}^4]}$ on a highest weight module of ${U_\hbar(\mathfrak{sp}(4))}$ .     

Final state interaction effects in the B + → D + K 0 decay

The exclusive decay of B ⁺ → D ⁺ K ⁰ is calculated by the QCD factorization method (QCDF) and final state interaction (FSI). First, the B ⁺ → D ⁺ K ⁰ decay is calculated via QCDF method. The result that is found by using the QCDF method is less than the experimental result. So FSI is considered to solve the B ⁺ → D ⁺ K ⁰ decay. For this decay, the D _s ⁺ π⁰, D _s ⁺ *ρ⁰, D _s ⁺ *? via the exchange of \(\bar K^0\) , \(\bar K^{0*} \) , D ^?, and D ^?* mesons are chosen for the intermediate states. The above intermediate states are calculated by using the QCDF method. In the FSI effects, the results of our calculations depend on η as the phenomenological parameter. The range of this parameter is selected from 2 to 2.4. It is found that if η = 2.4 is selected, the numbers of the branching ratio are placed in the experimental range. The experimental branching ratio of this decay is less than 2.9 × 10^?6 and our results calculated by QCDF and FSI are (0.16 ± 0.04) × 10^?6 and (2.8 ± 0.09) × 10^?6, respectively.     

Electrical and magnetic properties of La0.67Ba0.33Mn1−x (Me) x O3 perovskite manganites: case of manganese substituted by trivalent (Me = Cr) and tetravalent (Me = Ti) elements

The effects of non-magnetic Ti⁴⁺ substitution on the structural, electrical and magnetic properties of La_0.67Ba_0.33Mn_1?x Ti _x O₃ (0≤x≤0.1) are investigated and compared to those existing in La_0.67Ba_0.33Mn_1?x Cr _x O₃ (magnetic Cr³⁺). The structural refinement by the Rietveld method revealed that Ti-doped samples crystallize in the cubic lattice with space group $\mathrm{Pm}\bar{3}\mathrm{m}$ , while samples with Cr crystallize in the hexagonal setting of the rhombohedral $\mathrm{R}\bar{3}\mathrm{C}$ space group for identical contents of dopant. The most relevant structural features are an increase of the lattice parameters, of the cell volume and of the inter-ionic distances with increasing Ti doping level. Both series of samples show a decrease of the paramagnetic–ferromagnetic transition temperature when the amount of chromium or titanium increases. Transport measurements show that when increasing the metal doping, the resistivity increases whereas the metallic behavior of the parent compound La_0.67Ba_0.33MnO₃ is destroyed. For a substitution higher than 5 at.% of Ti and 10 at.% of Cr, the samples exhibit a semiconducting behavior in the whole range of temperature, for which the electronic transport can be explained by variable range hopping and/or small polaron hopping models.