Change in the shape of a symmetric light pulse passing through a quantum well

A theory for the response of a 2D two-level system to irradiation by a symmetric light pulse is developed. Under certain conditions, such an electron system approximates an ideal solitary quantum well in a zero field or a strong magnetic field H perpendicular to the plane of the well. One of the energy levels is the ground state of the system, while the other is a discrete excited state with energy ?ω₀, which may be an exciton level for H=0 or any level in a strong magnetic field. It is assumed that the effect of other energy levels and the interaction of light with the lattice can be ignored. General formulas are derived for the time dependence of the dimensionless “coefficients” of the reflection ?(t), absorption A(t), and transmission ?(t) for a symmetric light pulse. It is shown that the ?(t), A(t), and ?(t) time dependences have singular points of three types. At points t ₀ of the first type, A(t ₀)=T(t ₀)=0 and total reflection takes place. It is shown that for γ_r?γ, where γ_r and γ are the radiative and nonradiative reciprocal lifetimes, respectively, for the upper energy level of the two-level system, the amplitude and shape of the transmitted pulse can change significantly under the resonance ω_l=ω₀. In the case of a long pulse, when γ_l<γ_r, the pulse is reflected almost completely. (The quantity γ_l characterizes the duration of the exciting pulse.) In the case of an intermediate pulse duration γ_l?γ_r, the reflection, absorption, and transmission are comparable in value and the shape of the transmitted pulse differs considerably from the shape of the exciting pulse: the transmitted pulse has two peaks due to the existence of the point t ₀ of total reflection, at which the transmission is zero. If the carrier frequency ω_l of light differs from the resonance frequency ω₀, the oscillating ?(t), A(t), and ?(t) time dependences are observed at the frequency Δω=ωl?ω₀. Oscillations can be observed most conveniently for Δω?γ_l. The position of the singular points of total absorption, reflection, and transparency is studied for the case when ω_l differs from the resonance frequency.     

A bound on the number of bound states in the Schrödinger equation

A boundS _l is given for the number of bound statesn _i in thelth partial wave corresponding to a spherically symmetric potential in non-relativistic quantum mechanics. This bound is given by whereV _a(l, r) is the attractive part of the effective potentialV(r)+l(l+1)/r ². Extensive comparative study ofS _i and the Bargmann inequality is made.     

Theoretical study of stereodynamics for the O（3P） ＋ H2 → OH ＋ H reaction

This paper employs the quasi-classical trajectory calculations to study the influence of collision energy on the title reaction on the potential energy surface of the ground ³A' triplet state developed by Rogers et al. (J. Phys. Chem. A 2000 104 2308). It calculates the product angular distribution of P(θ_r), P(φ_r) and P(θ_r, φ_r) which reflects vector correlation. The distribution P(θ_r) shows that product rotational angular momentum vectors j' of the products are strongly aligned along the relative velocity direction k. The distribution of P(φ_r) implies a preference for left-handed product rotation in planes parallel to the scattering plane. Four different polarisation-dependent cross-sections are also presented in the centre-of-mass frame. Results indicate that OH is sensitively affected by collision energies of H₂.     

A rigorous replica trick approach to Anderson localization in one dimension

LetH=?Δ+V onl ²(?), whereV(x),x∈?, are i.i.d.r.v.'s, and letG _L (x,y;E+iη)= 〈x|(H _L?(E+iη))^?1|y〉, whereH _L denotes the operatorH restricted to {?L, ?L+1,...,L} with Dirichlet boundary conditions. We use a supersymmetric replica trick to prove that $$E(|G_L (0,x; E + i\eta )|^2 ) \leqq K\eta ^{ - 2} \exp \{ - m|\log \eta |^{ - \sigma } |x|\} $$ for somem>0, σ>0,K<∞, uniformly inL andE. This estimate, together with the usual necessary estimate on the density of states, implies zero conductivity and gives exponential localization by the Fröhlich, Martinelli, Scoppola, and Spencer method.     

Intrinsic coercivities of molecular beam epitaxy grown single-crystal Ni films on Ag buffer layer

Single-crystal Ni films were made by the molecular beam epitaxy (MBE) method on Si(1 0 0) and Si(1 1 0) substrates, respectively, with an 100 Å thick Ag buffer layer. The growth temperature T_S was 270 °C, and the film thickness t was 500 Å. From reflection high-energy electron diffraction (RHEED) patterns, the crystalline symmetries of the two films are clear and as expected. Intrinsic coercivities, H_C(1 0 0) and H_C(1 1 0), are plotted as a function of the angle of rotation ? around the crystal axes [1 0 0] and [1 1 0], respectively. The results show that both H_C(1 0 0) and H_C(1 1 0) exhibit mixed features of the crystalline (K_C) and the induced uniaxial magnetic (K_u) anisotropies. K_u is the magneto-elastic energy, due to lattice mismatch at the Ni/Ag interface. Moreover, the crystalline anisotropy fields, H_K(1 0 0) and H_K(1 1 0), and the induced anisotropy filed, H_u, can be calculated as a function of ?, respectively. Then, each H_C curve is fitted by the equation: H_C = H_o + H_K + H_u, where H_o is the isotropic pinning field. Meanwhile, domain structures were examined by the Bitter method, using Ferrofluid 707. On the Ni(1 0 0) film, we observed the charged cross-tie walls, and on the Ni(1 1 0) film, the un-charged Bloch walls.     

On size corrections to the diamagnetic susceptibility of a free electron gas

The magnetic behavior of spinless electrons confined in a cylinder of radiusR by a harmonic oscillator potential is calculated over the entire range of sizesR/r _H, wherer _H is the radius of the classical electron orbit due to a constant magnetic fieldH. The magnetic moment is shown to be large and positive in the small size limitR/r _H?1 in agreement with recent experimental work, while in the usual large size limitR/r _H?1 the Landau susceptibility is obtained. The model is compared with a similar calculation in which a periodic boundary condition is applied in order to show explicitly how qualitative differences arise in the small size limit, and the relevance of the results to calculations for rectangular and spherical geometries with hard wall boundary conditions is examined.     

Magnetic properties and peculiarity of magnetic states in dilute antiferromagnets Mn1−x Zn x F2

The dependence of magnetic moment and susceptibility on temperature, magnetic field and frequency of some single crystals Mn_1?x Zn _x F₂ (x≈x _e=0.75—percolation limit) were experimentally investigated. Our experiments show that (Bazhan and Petrov 1984; Cowleyet al 1984; Villain 1984) in these crystals the nonequilibrium magnetic state of spinglass type with finite correlation length appears as temperature decreasesT<T in weak magnetic fields. This state is determined by fluctuation magnetic moments √nμ (wheren is the number of magnetic ions, corresponding to finite correlation length andμ the magnetic moment Mn⁺¹). In the experiments in low magnetic fields and frequencies there are no peculiarities in the magnetic susceptibility temperature dependence atT≠T _f. At temperaturesT>T _f andT<T _f magnetic susceptibility is determined by 1 $$\chi \left( {T > T_f } \right) = \frac{{N\left\langle \mu \right\rangle ^2 }}{{3k\left( {T + \theta } \right)}} = \frac{N}{n}\frac{{\left\langle {\sqrt n \mu } \right\rangle ^2 }}{{3k\left( {T + \theta } \right)}} = \chi \left( {T< T_f } \right)$$ . In strong magnetic fields and large frequencies there are peculiarities in thex(T) dependence atT=T _f. AtT<T _f and strong magnetic fieldsX(T)=x ₀ andT<T _f and at large frequenciesx(T)=x ₀+α/T. The dependences of magnetic susceptibility on the frequency are determined by the magnetic system relaxation. Calculations and comparison with experiments show that the relaxation of the investigated magnetic systems atT<T _f follows the relaxation lawM(t)=M(0) exp[?(t/τ) ^r ], suggested in Palmeret al (1984) for spin-glasses relaxation taking into account the time relaxation distributionτ ₀....τ _max in the system and its ‘hierarchically’ dynamics.     

Solubility and diffusion of H in ordered (L12) and disordered Pd3Mn

Hydrogen isotherms have been measured from 423 to 573 K for the disordered and L1₂ ordered forms of Pd₃Mn and, from these equilibrium isotherms, Δ_HH$\mathrm{\Delta }{H}_{\mathrm{H}}$ and Δ_SH$\mathrm{\Delta }{S}_{\mathrm{H}}$ have been determined over a range of r values where r  =H-to-metal, atom ratio. Δ_HH$\mathrm{\Delta }{H}_{\mathrm{H}}$ values are significantly more negative for the L1₂ ordered form than for the disordered form. H diffusion constants have been determined for the L1₂ and disordered forms of Pd₃Mn from gas phase H permeation measurements through Pd₃Mn membranes (423–573 K). The activation energy for diffusion of H in the L1₂ form is 35.2 kJ/mol H which is more reasonable than the value of 76.3 kJ/mol H previously reported. The diffusion constant is greater for the disordered than for the L1₂ form.     

Quantization and confinement effects in superconducting nanostructures

The confinement of the flux lines by a lattice of submicron holes (‘antidots’) has been studied in nanostructured superconducting Pb/Ge multilayers. By introducing regular arrays of sufficiently large antidots, multi-quanta vortex lattices have been stabilized. Sharp cusp-like magnetization (M) anomalies, appearing at matching fieldsH_m=mφ₀/Sin superconducting films with the antidot lattices having a unit cell areaS, are successfully explained. These anomalies are, analogues of the well-knownM(H) cusp atH_c1, but for the onset of multi-quanta (m+1)φ₀-vortices penetration at each subsequent matching fieldH_m. It is shown that theM(H) curve between the matching fieldsH_m<H<H_m+1follows a simpleM∝ln(H−H_m) dependence. These experimental observations have revealed an unusual expansion of validity of the London limit in superconductors with lattices of relatively large antidots. The successful high quality fit of theM(H,T) curves convincingly demonstrates that a new type of the critical stateB=const (‘single-terrace critical state’) can be realized in superconductors with the antidot lattices.     

Spin waves in paramagnetic Boltzmann gases

As the temperature is lowered we get an interesting temperature region? _d?T?? ²/mr ₀ ² (where? _d is the quantum degeneracy temperature,m the mass of a gas molecule,r ₀ the radius of interparticle interaction) in which the thermal de Broglie wavelength Λ of a particle is considerably greater than its sizer ₀ though Λ turns out to be less than the mean interparticle distanceN ^?1/3?Λ?r ₀. Although the gas molecules obey the classical Boltzmann-Maxwell statistics the system as a whole begins to exhibit a larger number of essentially quantum macroscopic collective features. One of the most interesting and dramatic features is the possibility of propagation of weakly damped spin oscillations in spin-polarized gases (external magnetic field, optical pumping). Such oscillations can propagate both in the low-frequencyθτ?1 regime and the high frequencyθτ?1. The last case is highly non-trivial for a Boltzmann gas with a short range interaction between particles. The weakness of relaxation damping of spin modes implies that the degree of polarization is high enough 1>/|α|?|a|/Λ, whereα=(N ₊?N _?)N,a is the two-particles-wave scattering length. Under these conditions the spectrum of magnons has the form (Bashkin 1981, 1984; Lhuillier and Laloe 1982) 1 $$\omega = \Omega _H + \left( {{{K^2 \nu _{\rm T}^2 } \mathord{\left/ {\vphantom {{K^2 \nu _{\rm T}^2 } {\Omega _{int} }}} \right. \kern-\nulldelimiterspace} {\Omega _{int} }}} \right)\left( {{{1 - i} \mathord{\left/ {\vphantom {{1 - i} {\Omega _{int} }}} \right. \kern-\nulldelimiterspace} {\Omega _{int} }}\tau } \right), \Omega _{int} = {{ - 4\pi ahN\alpha } \mathord{\left/ {\vphantom {{ - 4\pi ahN\alpha } m}} \right. \kern-\nulldelimiterspace} m}, \nu _{\rm T}^2 = {T \mathord{\left/ {\vphantom {T m}} \right. \kern-\nulldelimiterspace} m}$$ where Ω _H is the Larmor precession frequency for spins in the magnetic fieldH. Collisionless Landau damping restricts the region of applicability of (1) with not too large wave vectorsKv _T?|Ω_int|. The existence of collective spin waves has been experimentally confirmed in NMR-experiments with gaseous atomic hydrogen H↑ (Johnsonet al 1984). The presence of undamped spin oscillations means automatically the existence of long range correlations for transverse magnetization. Such correlations decrease with the distance according to the power law 2 $$\delta _{ik} \left( r \right) = 2\left| a \right|\frac{{\left( {\beta N\alpha } \right)^2 }}{\gamma }\delta _{ik} $$ . Hereβ is the molecule magnetic moment. Spin waves being even damped can nevertheless reveal themselves atT?? ²/mr ₀ ² or when |α|?r ₀/Λ. The first experimental discovery or damped spin waves in gaseous³He↑ has been done in Nacheret al 1984. Oscillations of magnetization can also propagate in some condensed media such as liquid³He-⁴He solutions, semimagnetic semiconductors etc.     

Spin-wave resonance in [Co x Ni1 − x ]N and [Co x P1 − x ]N gradient films

Gradient films of ferromagnetic 3d metals with prescribed magnetic potential profile along the film thickness are obtained. It is found that the spin-wave resonance spectrum in these films is characterized by anomalous dependences of resonance fields of spin-wave modes H _r on the mode number: H _r(n) ～ n, H _r(n) ～ n ^2/3.     

Microwave l-type resonance transitions of the v4 = 1 state in PF3: Detailed interactions and molecular structure

Observation of the direct l-type resonance transitions in the microwave spectrum of the v₄ = 1 state of PF₃ has been extended to J = 36. The w-type interaction, (Δl = 0, ΔK = 6), has been found from measurements on the “forbidden” Stark trasitions in the $\text{K}\text{= 3}$ series. Also in this series a close accidental degeneracy was found between J = 30, $\text{K}\text{= 3}$ and 0, leading to new zero-field “forbidden” transitions through the r-type interaction (Δl = 2, ΔK = ?1) and to the determination of the C rotational constant. Nine spectroscopic parameters were determined using 140 observed frequencies including two “forbidden” trasitions. After suitable correction the B and C constants were used to determine the r₀, r_z, and r_e structures for PF₃. The equilibrium structure is estimated to be P-F = 1.561 ± 0.001 Å and ∠FPF = 97.7 ± 0.2°.     

Quantum beats in the 3γ annihilation decay of Positronium observed by perturbed angular distribution

We have applied conventional Time Differential Perturbed Angular Correlation (TDPAC) method to observe the anisotropy oscillations in the 3γ annihilation decay of polarized Positronium in a weak magnetic field. The effect, as predicted theoretically and experimentally demonstrated by Barishevsky et al. [V.G. Barishevsky, O.N. Metelitsa, V.V. Tikhomirov, Oscillations of the positronium decay γ-quantum angular distribution in a magnetic field, J. Phys. B: At. Mol. Opt. Phys.22 (1989) 2835], is induced by the coherent admixture of the m = 0 states of ortho-Positronium (o-Ps) and para-Positronium (p-Ps) in interaction with the magnetic field.The following experimental characteristics are to be considered:

(i)

the oscillation frequency corresponds to the difference in energy of the Ps atom levels in magnetic field and is proportional with H²;

(ii)

in a fixed geometry the modulation depth (oscillations amplitude) depends on the mean positron polarization;

(iii)

privileged angles of the polarization vector, magnetic field and detectors are required for optimizing the observed oscillations amplitude.

The normalized difference spectrum function (R(t)) obtained from time spectra measured in vacuum and in different gaseous atmospheres (Ar, H₂, N₂) have the oscillations amplitude constant and we conclude that the Ps atoms are not fully thermalized over a time interval of about 400 ns.The R(t) functions obtained for o-Ps annihilation decays, in dry air or Ar-O mixture, have the oscillations amplitude time dependent due, probably, to the paramagnetism of the Oxygen molecules.     

Axial-field-dependent circular susceptibility in Fe-rich amorphous wires

The longitudinal magnetic field dependence of low-frequency circular susceptibility, χ(H), is measured for (Fe_1−xCr_x)_77.5Si_7.5B₁₅ (x=0,0.05,0.1, and 0.15) amorphous wires of radius r₀=0.07 mm. In order to explain the experimental results, on the basis of the widely accepted core–shell model, we consider that there are a constant axial anisotropy K_c in the core and a radius-dependent radial anisotropy K_s∝r⁸/r₀⁸ in the shell, both K_c and K_s being functions of stress-energy constant λ_sσ₀. A formula for χ(H) is derived from this model. The experimental data fits indicate that the magnetic structure can be well described by the improved core–shell model with reasonable values of λ_s.     

Evidence for the Bφ decay mode of the ω(1670)

Backward production of ω(1670) is observed in the reactions K^?p→φ⁺φ^?ω⁰Λ⁰ and K^?p→φ⁺φ^?φ⁰φ⁰ for |U'_Λ|<1.0 GeV². The cross section for the ω(1670) →φ⁺φ^?ω⁰ decay mode is 1.90±0.35 μb for 8.25 GeV/c incident K^?. Evidence is presented for the importance of the sequential decay, ω(1670) → Bφ → ωφφ with a branching ratio ω(1670) → Bφ/all ω(1670) → ωφφ=1.0±_0.25^0.00.     

Binding of rare earth metal complexes with an ofloxacin derivative to bovine serum albumin and its effect on the conformation of protein

The water-soluble Pr (Ⅲ) and Nd (Ⅲ) complexes with an ofloxacin derivative have been prepared and characterized. The single-crystal X-ray diffraction showed that the Pr (III) and Nd (III) complexes have the similar molecular structure. Under physiological pH condition, the effects of [PrL(NO₃)₂(CH₃OH)](NO₃) and [NdL(NO₃)₂(CH₃OH)](NO₃) on bovine serum albumin (BSA) were examined using fluorescence spectroscopy in combination with UV-vis absorbance and circular dichroism (CD) spectra. The result reveals that the quenching mechanism of fluorescence of BSA by two complexes is a static quenching process and the number of binding sites is about 1 for both. The thermodynamic parameters (ΔH=−14.52 kJ mol⁻¹, ΔS=56.54 J mol⁻¹ K⁻¹ for [PrL(NO₃)₂(CH₃OH)](NO₃) and ΔH=−24.63 kJ mol⁻¹, ΔS=22.07 J mol⁻¹ K⁻¹ for [NdL(NO₃)₂(CH₃OH)](NO₃)) indicate that hydrophobic and electrostatic interactions are the main binding force in the complexes-BSA system. The binding average distance between complexes and BSA was obtained on the basis of Förster's theory. In addition, it was proved by the CD spectra that the BSA secondary structure was changed in the presence of complexes in an aqueous solution.     

Synthesis and structure of the monolayer hydrate K0.3CoO2·0.4H2O

The monolayer hydrate (MLH) K_0.3CoO₂·0.4H₂O was synthesized from K_0.6CoO₂ by extracting K⁺ cations using K₂S₂O₈ as an oxidant and the subsequent intercalation of water between the layers of edge-sharing CoO₆ octahedra. A hexagonal structure (space group P6₃/mmc) with lattice parameters a=2.8262(1) Å, c=13.8269(6) Å similar to the MLH Na_0.36CoO₂·0.7H₂O was established using high-resolution synchrotron X-ray powder diffraction data. The K/H₂O layer in the K-MLH is disordered, which is in contrast to the Na-MLH. At low temperatures metallic and paramagnetic behavior was found.     

A simple relationship between chandrasekha's S and T functions

Chandrasekhar's equations for the functions S and T which represent the diffuse scattering and the diffuse transmission, respectively, of a beam of radiation by a planar atmosphere are invariant under the transformations S(τ₁; μ, φ - μ₀), φ₀) exp (-τ₁/μ₀) = T(τ₁; μ, φ; μ₀, φ₀) and T(τ₁; μ, φ; -μ₀, φ₀) exp(-τ_t/μ₀) = S(τ₁; μ, φ; μ₀, φ₀). This relationship reflects the physical symmetry of radiative transfer in a planar atmosphere. It offers a simple method for obtaining the expression for S (T) when an analytical expression for T (S) exists. However, it does not appear to ofter any simplification of numerical solutions.     

Lyapunov functional approach to raiative metrics

Lyapunov's second method is applied to the spherical radiative Robinson-Trautman vacuum space-times to prove that they asymptotically settle down to Schwarzschild space-time. This class of Robinson-Trautman metrics is characterized by the surfaceS being topologically a two-sphere, whereS is invariantly defined by the intersection of the hypersurfacesu=const andr=const. It is shown that _S K ² d is a Lyapunov functional, whereK is the Gaussian curvature andd is the invariant measure onS. The critical point occurs atK=0 or, equivalently, at ð² K=0, which condition is shown to characterize Schwarzschild space-time.A product of a collaboration supported by the NSF and the Hungarian Academy of Sciences.