Non-adiabatic transitions for random processes in a two-level system

Non-adiabatic transitions in two-level systems are investigated theoretically for a random time dependence of ?ω, the energy difference, between the levels. We assumed that ω = ω(x) and the coordinate x = x(t) is a random function of time. Diffusion and Poisson processes (both homogeneous and with a source) for x(t) were assumed. The cases of linear crossing terms (ω = γx) and non-linear terms (ω = ω _e exp (- αx) + ω₀) were considered. Values of the non-adiabatic transition probability per unit time were obtained by perturbation theory for ω₁τ _c ? 1 where τ _c is the correlation time and ω₁ is the off-diagonal matrix element.     

Spectroscopic properties of SbH

Relativistic configuration interaction calculations which include spin-orbit interaction are carried out for nine low-lying ω-ω states and four λ-s states. Spectroscopic properties of six bound ω-ω states are reported. These calculations not only enable assignment of the experimentally observed X₁, X₂, A₁, A₂, and B states but also predict the properties of other electronic states (0⁺(II), 0⁺(IV), 2, 2(II), 1(II), 0⁻) which are yet to be observed. The dissociation energy of SbH is predicted to be 2.7 ± 0.2 eV.     

Filamentation-assisted fourth-order nonlinear process in KTP crystal

We present an experimental investigation of a filamentation-assisted fourth-order nonlinear optical process in KTP crystals pumped by intense 1.53~eV (807~nm) femtosecond laser pulses. Femtosecond light pulses at 2.58~eV (480~nm) are generated by the fourth-order nonlinear polarization (P⁴(ω ₂ ) = χ ⁴(ω ₂ ,ω ,ω ,ω ,- ω ₁ )E³(ω )E^* (ω ₁ ), where E(ω ) corresponds to the pump frequency and E(ω ₁ ) to the supercontinuum generated through filamentation). If the system is seeded by a laser beam at ω ₁ or ω ₂ and there are spatial and temporal overlaps with the pump beam, E(ω ₁ ) and E(ω ₂ ) are simultaneously amplified. When the intensity of the seed laser beam exceeds a certain intensity threshold, the contribution of P⁴(ω ) = χ ⁴(ω ,ω ₁ ,ω ₂ ,-ω, - ω )E(ω ₁ )E(ω ₂ )(E^* (ω))² becomes non-negligible, and the amplification weakens. The conversion efficiency from the pump to the signal at 2.58~eV (480~nm) attains to 0.1%.     

Optimization of third harmonic generation for two coupled three-frequency interactions of waves with multiple frequencies in periodic crystals

Third harmonic generation with simultaneous excitation of degenerate two-frequency (2ω = ω + ω) and three-frequency (3ω = 2ω + ω) interactions of collinear waves in periodic crystals is considered. It is shown that the optimal condition for third harmonic generation, in this case, is determined by the ratio of the amplitudes of the fundamental and second harmonics at the entrance of the crystal. The optimal value of this ratio, for which the efficiency of the third harmonic generation may reach 96%, is found.     

Exact derivative interband dielectric function at Van Hove singularities

Interpretations of derivative spectra obtained by wavelength or thermal modulation have been based on universal lineshape functions that include only the resonant term, $\text{(ω}{}_{\mathrm{g}}\text{? ω ?iη)}{}^{\mathrm{<mtext>?1</mtext><mtext>2</mtext>}}$, obtained from differentiating ε(ω) with respect to ω or ω_g, and that neglect the (ω + iη)^?2 prefactor. We find the following differences between the approximate universal lineshape functions and the exact results obtained by including the nonresonant terms. dε/dω and dε₂/dω are no longer simply related to each other; two entirely different functions are obtained. Wavelength and temperature modulation no longer have identical lineshapes. Either dε₁/dω or dε₂/dω has a resonant derivative lineshape according to whether j is even or odd, respectively, in contrast to the approximate universal function, which has no zeros, dε₁/dω for a pure M₁ singularity has positive and negative peaks of approximately equal strength, which would agree with the experimental results without invoking hyperbolic excitons (admixtures of M_j and m_j+1 lineshapes). On the other hand, the nonexcitonic exact result fails to reproduce other experimental features. At the very least, our results call into question the extraction of numbers from detailed curve fits to the approximate functions.     

Decomposition of a solid solution in the ω phase of the Ti-Zr system under high pressure

Phase separation in the hexagonal ω modification of the Ti-Zr system was observed. The ω → ω₁ + ω₂ decomposition in an equiatomic TiZr alloy after prolonged thermal treatment at P = 5.5 ± 0.6 GPa and T = 440 ± 30°C was revealed using x-ray diffraction. It is found that the concentration dependence of the specific volume of the ω phase of Ti-Zr alloys deviates from the Vegard law to higher values. An isobaric section of the equilibrium P-T-x phase diagram of the Ti-Zr system is shown to have the shape of an eutectoid diagram at pressures higher than 8 GPa.     

Stability and Symmetry-Breaking Bifurcation for the Ground States of a NLS with a δ′ Interaction

We determine and study the ground states of a focusing Schrödinger equation in dimension one with a power nonlinearity |ψ|^2μ ψ and a strong inhomogeneity represented by a singular point perturbation, the so-called (attractive) δ′ interaction, located at the origin. The time-dependent problem turns out to be globally well posed in the subcritical regime, and locally well posed in the supercritical and critical regime in the appropriate energy space. The set of the (nonlinear) ground states is completely determined. For any value of the nonlinearity power, it exhibits a symmetry breaking bifurcation structure as a function of the frequency (i.e., the nonlinear eigenvalue) ω. More precisely, there exists a critical value ω* of the nonlinear eigenvalue ω, such that: if ω₀ <  ω <  ω*, then there is a single ground state and it is an odd function; if ω >  ω* then there exist two non-symmetric ground states. We prove that before bifurcation (i.e., for ω <  ω*) and for any subcritical power, every ground state is orbitally stable. After bifurcation (ω = ω^* + 0), ground states are stable if μ does not exceed a value ${\mu^\star}$ that lies between 2 and 2.5, and become unstable for μ > μ*. Finally, for μ >  2 and ${\omega \gg \omega^*}$ , all ground states are unstable. The branch of odd ground states for ω <  ω* can be continued at any ω >  ω*, obtaining a family of orbitally unstable stationary states. Existence of ground states is proved by variational techniques, and the stability properties of stationary states are investigated by means of the Grillakis-Shatah-Strauss framework, where some non-standard techniques have to be used to establish the needed properties of linearization operators.     

Trivelpiece-Gould-Modes in an Axial Inhomogeneous Plasma

Experiments on the propagation of TG-modes in a weakly inhomogeneous plasma are reported. The modes travel from the high density part (ω < ω_pe) to that of lower density (ω > ω_pe). The wavelength decreases as expected but an increase of the longitudinal fieldstrength predicted by collisionless theory could not be observed. Two nonlinear effects appear one after another with increasing wave amplitude. These are the sideband instability and a decay into the drift frequency range occuring in the whole plasma column. Neither the region ω ≈ ω_pe nor the very vicinity of the exciter antenna are distinguished. The second instability is accompanied by effective electron heating.     

Parametric Excitation of Plasma instabilities by two Monochromatic Pump waves

The dispersion characteristics of a plasma in a pump field ??(t) = ?? sub ω₀t + ??₁ sin ω₁t are considered. Firstly we assume, that the second wave is weak (|??₁| ? |??₀|) and the frequency ω₁ is near sω₀(ω₁ = sω₀ + Ω,Ω ? ω₀). We obtain the dispersion equation, describing the parametric coupling of the waves driven by the strong field ??₀ sin ω₀t under the resonance condition ω₀ ≈ ω_Le/P and derive the expressions for the growth rates (ω_Le is the electron LANGMUIR frequency; s, p are integers). In the second part it is shown, that a strong field ??₁ with a frequency ω₁ much larger than ω _Le(ω _Le ≈ pω₀) stabilizes the plasma; the growth rates are reduced and the frequency region of the parametric instability is contracted.     

Nonlinear susceptibility x;(3) in a direct gap semiconductor derived from coupled inter-and intraband equations of motion

A set of generalized Maxwell Bloch Equations describing a two band semiconductor as a system of interacting two level atoms is used to calculate the nonlinear dielectric susceptibility x;⁽³⁾ (ω, ? ω, ω). For near resonance conditions (ω ≈ ω_g) we find a simplified expression for χ⁽³⁾ that is compared with other theories. A fit using parameters relevant for InSb leads to good agreement with experimental results.     

On the optical absorption due to particle-hole excitations in thin metal films

We present here a qualitative discussion on the optical absorption due to particle-hole excitations in thin metal films. We show that in sufficiently thin films, such excitations yield resonant absorption, when P-polarized light is obliquely incident on the metal surface. For instance, for frequency ω #62; ε_F where ε_F is the Fermi-energy, such resonances occur whenever ω satisfies the condition ω/ε_F = (1 + nπ/dq_F)² - 1, where n = 1,3,5,…,q_F is the Fermi wave-vector and d is the thickness of the film. The experimental observability of this effect is also discussed.     

On the asymptotic behaviour of the mass operator near the Fermi energy

By taking due account of momentum conservation, it is shown that, when ω is near the Fermi energy ω_F, the imaginary part of the mass operator $\text{M(}\text{k}\text{, ω)}$ for an infinite Fermi system behaves like (ω ? ω_F)^p(k) where the exponent p(k) ? 2 depends on the interval in which $\text{|}\text{k}\text{|}$ is lying. In particular, the commonly asserted quadratic behaviour (ω ? ω_F² is shown to be true only for $\text{|}\text{k}\text{| ? 3k}{}_{\mathrm{<mtext>F</mtext>}}$. It is explicity assumed that the Fermi system admits a perturbative type treatment.     

Study of the OZI selection rule in hadronic processes

In the experiments with LEPTON-F and SPHINX spectrometers the pion-induced charged exchange reactions π- + p → ? + n and π- + p → ω + n at Pπ-=32.5 GeV, as well as proton-induced diffractive reactions p + N → [p?] + N and p + N → [pω] + N at E _p =70 GeV were studied. The comparison of the cross-sections for ? and ω-production in these reactions is used for testing the OZI selection rule in hadronic processes. It has been demonstrated that in pion reactions the ratio of the yields of ? and ω-mesons R(?/ω) = (3 ± 1) · 10^?3 is in a good agreement with naive quark model prediction based on the mixing in vector meson nonet and on the OZI rule (R(?/ω)ozi = tg ²Δθ _V ? 4 · 10^?3). At the same time in proton reactions the effective ratio of ? and ω yields is ～ (4 ÷ 7) · 10^-2, i.e. a strong violation of the OZI rule is observed in proton-nucleon interactions. This violation can be in favor of possible existence of some exotic ss? component in the quark structure of protons.     

Nonlinear Raman scattering of photons by a channeled particle

Channeled particles are characterized by the discrete spectrum of bound transverse motion. The interaction of photons with channeled particles in single crystals can be accompanied by energy transitions between the levels of transverse motion of the channeled particle. The Raman scattering of photons at a quasibound channeled particle leads to the appearance of a combination of frequencies: the incident radiation frequency ω₀ and the frequency Δω_{m, n}, i.e., ω = ω₀ ± Δω_m,n where Δω_m,n = 2Δε_m,nγ²; Δε_{m, n} is the energy of the transition between quantum states (m and n) of the transverse motion of the channeled particle; and γ = E/mc² is the Lorentz factor of the channeled particle. The appearance of a violet satellite (the anti-Stokes component) in the Raman scattering spectrum is analyzed. The three-photon Raman-type transition, which is the process of the simultaneous absorption of two photons with the frequency ω₀ with the emission of a photon with the frequency ωs = 2ω₀ ± 2Δε_m,nγ², is considered. The conditions for resonance observation during the formation of the second harmonic (ω = 2ω₀) are discussed.     

In-medium ω photoproduction with CBELSA/TAPS

Recent experimental results on the in-medium modification of the ω meson are discussed. The experiment described was performed at the ELSA accelerator facility in Bonn using the combined detector system of Crystal Barrel and TAPS. The ω meson was identified via the reaction γ+A → ω+X → π⁰γ+X.     

Imaging properties of electrostatic energy analyzers with toroidal fields

Numerical values of the second-order aberration coefficients are given for two classes of toroidal fields, namely (1) the “quasi-spherical” field with c = 1, c′ ≠ ? 1, and (2) fields with c in the region 1.6–1.8. For the “quasi-spherical” fields, the second-order coefficients are given as functions of the deflection angles ω for 90° ≤ ω ≤ 180°. The third-order coefficients for the spherical field are given in the same region.For the devices in the second class, which have one intermediary axial image, the second-order coefficients are studied as functions of c and ω, subject to the condition that double-focussing should be obtained. The conditions under which the radial and axial image planes coincide are considered. The influence of axially curved entrance and exit surfaces is investigated. One special case (ω = 180°, c = 1.691, c′= ? 1.11), which may be favourable for an electron monochromator is discussed.     

Measurement of elastic ω photoproduction at HERA ZEUS Collaboration

The reaction γp →ωp(ω → π⁺π^?π⁰ and π⁰ → γ γ) has been studied in ep interactions using the ZEUS detector at photon-proton centre-of-mass energies between 70 and 90GeV and ∣t∣ < 0.6GeV², where t is the squared four momentum transferred at the proton vertex. The elastic ω photoproduction cross section has been measured to be σ_{γp → ωp} = 1.21 ±0.12 ±0.23 μb. The differential cross section dσ_γp→ωp/d¦t¦ has an exponential shape e^?b∣t∣ with a slope b =10.0 ± 1.2 ± 1.3 GeV^?2. The angular distributions of the decay pions are consistent with s-channel helicity conservation. When compared to low energy data, the features of ω photoproduction as measured at HERA energies are in agreement with those of a soft diffractive process. Previous measurements of the ρ⁰ and ? photoproduction cross sections at HERA show a similar behaviour.     

Quantum chemical investigation on the structure and first hyperpolarizability for N‐substituted [n]cyclacene

Six N‐substituted [n]cyclacene (n = 5, 6, 7,…,10) molecules were designed to study the relationship between the structure and first hyperpolarizability. Their static first hyperpolarizabilities (β₀) were obtained by MP2/6‐31 + g(d) level. Two interesting relationships between the β₀ value and the structure have been found: (1) The β₀ value increases with the increase of the number n when n is odd: 3155 ([5]cyclacene) < 48,905 ([7]cyclacene) < < 393,444 ([9]cyclacene), and when n is even: 357,620 ([6]cyclacene) < 618,608 ([8]cyclacene) < 3,513,644 a.u. ([10]cyclacene). (2) The β₀ values (in the range of 357,620 ~ 3,513,644 a.u.) of the N‐substituted [n]cyclacene (when n is odd) are much larger (in the range of 3155~393,444 a.u.) than that of the N‐substituted [n]cyclacene (when n is even). Furthermore, their frequency‐dependent β (?2ω; ω, ω) and β (?ω; ω, 0) (ω = 0.005, 0.01, and 0.0239 a.u.) were also estimated by Møller–Plesset perturbation/6‐31 + g(d) level. Among the frequency‐dependent β (ω), [10]cyclacene has the largest β (?ω; ω, 0) and β (?2ω; ω, ω) to be 1.2 × 10⁸ (ω = 0.01) and 2.9 × 10⁷ a.u. (ω = 0.005 a.u.), which are much larger than the static β₀ = 3.5 × 10⁶ a.u. by 34 and 8 times. Our present work may offer a new idea in the design of high‐performance tubiform nonlinear optical materials. Copyright © 2011 John Wiley & Sons, Ltd.     

Induction kinetics in 2D electron systems at the Hall plateaus

Specific features of the induction excitation of 2D electron systems at the Hall plateaus are discussed. The corresponding kinetics is shown to have several frequency regimes. In the region ω ? ω_D, where ω_D is the frequency characteristic of the kinetics at the Hall plateaus, an induction-caused variation of electron density follows the magnetic-field variation with time. For the frequencies ω ≤ ω_D, a noticeable relaxation of the electron disturbance appears, and the induction polarization of 2D samples at the Hall plateaus noticeably decreases as compared to the maximum possible polarization. Finally, in the limit ω ≤ ω_slow, where ω_slow corresponds to another characteristic time of the quantum Hall effect, the so-called adiabatic approximation takes place with the 2D system responding to the derivative of magnetic field dH/dt rather than to the magnetic field itself H(t). The results of calculations are compared with the experimental data reported in the literature.     

希土离子对铁磁共振的影响

本文利用关联函数的方法(久保理论),讨论了强交换耦合系统的亚铁磁共振,给出了系统总磁化率张量的一般表达式,由此可以定出铁磁支与交换支的共振场H₀(或共振频率)和峯宽2△ω。所得结果表明,所谓快弛豫及慢弛豫机理不过是铁磁共振的两个分支(横分支与纵分支)。横分支相应于J及S的横向磁矩之间的耦合运动J,S分别为希土离子及铁离子的磁矩),而纵分支相应于J的纵向分量与S的横向分量之间的耦合运动。由于晶场及各向异性交换场的作用,J的量子化方向与S的量子化方向偏离一个角度φ。此外由于交换作用的各向异性,在交换作用哈密顿J·λ·S中,张量λ的非对角元可以相当大。结果表明,纵分支对峯宽的贡献近似地正比于φ²及λ_i3(i=1,2)。根据2△ω的一般表达式,在极低温下(4.2°K以下),峯宽主要是由横分支决定的。沿某些晶轴方向?_a,当希土离子最低两个能级接近“交叉”时,共振场及峯宽应该出现反常峯值,这在实验上已经得到了证实。当温度升高时,纵分支将逐渐“压过”横分支。当纵向弛豫频率达到高频场的频率ω时,峯宽将出现极大值,一般实验中观察到的就是这个极大值。当温度继续升高时,横分支又将起主要作用。当横向弛豫频率接近相应于希土离子最低两个能级之间的间距ω₂₁时(?=1),峯宽将出现第二个极大值。实验上只有沿希土离子最低两个能级接近交叉的方向进行测量时,才有可能观测到第二个峯值。当频率足够高,满足|ω₂₁(?_a)-ω|<<ω的条件时,在极低温下,将出现由横分支决定的尖锐的峯宽极大值。根据所得理论结果,除上述现象外,还可以统一地解释在希土石榴石铁氧体中观测到的下列实验事实:有效旋磁比随温度的显著变化;在抵消点附近峯宽的急剧上升;在镱铁氧体中观测到的在峯宽极大值出现的温度共振场显著上升等。指出了经典磁矩运动方程的局限性,在铁氧体中,晶场的作用与交换场其大小可以相比时,利用经典方程求解所得出的结果只能定性地解释某些与希土离子具体能级结构无关的现象。