Electron wavepacket phases in ionization and rescattering processes by intense laser pulses

Exact numerical solutions of the time-dependent Schrödinger equation, TDSE, are presented for the H atom and H^2/+ molecular ion ionized by short (10 optical cycles), intense I ₀ ≥ 10¹⁴ W/cm², 800 nm laser pulses. Calculations of the time dependent expectation values of the dipole moment d(t), velocity $ \dot d Exact numerical solutions of the time-dependent Schr?dinger equation, TDSE, are presented for the H atom and H^2/+ molecular ion ionized by short (10 optical cycles), intense I ₀ ≥ 10¹⁴ W/cm², 800 nm laser pulses. Calculations of the time dependent expectation values of the dipole moment d(t), velocity (t), and acceleration (t) are used to identify the phase of these physical parameters with respect to the laser field during the harmonic generation process. It is found in general that electron wavepackets in an inner region near the parent ion are out of phase with the response expected from the classical laser induced recollision model, whereas wavepackets in an outer region, far from the parent ion, are in phase with the field force. It is found furthermore that it is the inner electron wavepacket which contributes mainly to the high order harmonic generation, HHG, process, even though its acceleration is out of phase with the field force. This suggests strong Coulomb refocussing effects in the HHG process, especially in the case of H^2/+. Original Russian Text ? Astro, Ltd., 2009. In honor of Prof. N.B. Delone. The article is published in the original.     

Effect of frustration on the magnetization in nickel ferrite-chromites

A study is reported on the behavior of the isotherms of the magnetization σ(H) and of the longitudinal λ_‖(H), transverse λ_⊥(H), volume ω(H), and anisotropic λ_t(H) magnetostrictions measured at T=80 K in the Cu_0.4Fe_0.6[Ni_0.6Cr_1.4]O₄ and Zn_0.4Fe_0.6[Ni_0.6Cr_1.4]O₄ ferrite-chromites having a frustrated magnetic structure. It has been established that these ferrite-chromites do not undergo technical magnetization and that the growth of the magnetization with the field is accounted for by two paraprocesses of different natures.     

Anomalous X-ray scattering studies on superionic glassy (As2Se3)-(AgX) systems (X = halides)

Anomalous X-ray scattering experiments for glassy room-temperature superionic conductors (As₂Se₃)_0.4 (AgI)_0.6 and (As₂Se₃)_0.4(AgBr)_0.6 were performed close to the As, Se, Ag, and Br K edges using a third-generation synchrotron radiation facility, ESRF. The differential structure factors, Δ_iS(Q), were obtained from detailed analyses, indicating that Δ_AsS(Q) and Δ_SeS(Q) of both the glassy superionic semiconductors are similar to those of glassy As₂ Se₃ except the prepeak in Δ_SeS(Q). The Δ_AgS(Q) spectrum of (As₂Se₃)_0.4 (AgI)_0.6 looks molten salt-like. However, the Δ_Ag S(Q) of (As₂Se₃)_0.4(AgBr)_0.6 glass have quite different features from that of (As₂Se₃)_0.4 (AgI)_0.6 glass in the low Q range, and the Δ_BrS(Q) has even a pre-shoulder around 13 nm^? 1 unlike molten salts. In the differential pair distribution functions Δ_ig(r) obtained from the Fourier transforms of Δ_iS(Q), the first peaks of Δ_Asg(r) and Δ_Seg(r) show no correlation with those of Δ_Agg(r) and Δ_Brg(r), and vice versa. From these results, it can be concluded that a pseudo-binary mixture of the As₂Se₃ network matrix and AgX-related ionic conduction pathways is a good structural model for these superionic glasses. Differences between the AgBr- and AgI mixtures were found in the second-neighbor structures around the Ag atoms, which may reflect those in the crystal structures of the AgX salts.     

Anisotropy effects in cesium flouroxide tungsten bronze

The upper critical field H_c2(T) and the specific heat jump ΔC(T_c) are calculated for Cs_0.1WO_2.9F_0.1 using a two-band model. The model parameters are obtained by adjusting the theoretical H_c2(T) values to experimental results. The model calculation predicts an anomalous specific heat jump ΔC as a function of the inverse relation T_c(H).     

The heat capacity of the layer compounds (CH3CH2CH2NH3)2MnCl4 and (CH3CH2CH2NH3)2CdCl4 from 10 K TO 300 K

The heat capacity of the layer compounds tetrachlorobis (n-propylammonium) manganese II and tetrachlorobis (n-propylammonium) cadmium II, (CH₃CH₂CH₂NH₃)₂MnCl₄ and (CH₃CH₂CH₂NH₃)₂CdCl₄ respectively, has been measured over the temperature range 10 K ?T ? 300 K.Two known structural phase transitions were observed for the Mn compound in this temperature region: at T = 112.8 ± 0.1 K (ΔH_t= 586 ± 2 J mol^?1; ΔS_t = 5.47 ± 0.02 J K^?1mol^?1) and at T =164.3 ± (ΔH_t = 496 ± 7 J mol^?1; ΔS_t =3.29 ± 0.05 J K^?1mol^?1). The lower transition is known to be from a monoclinic structure to a tetragonal structure, while the upper is from the tetragonal phase to an orthorhombic one. From comparison with the results for the corresponding methyl Mn compound it is deduced that the lower transition primarily involves changes in H-bonding while the upper transition involves motion in the propyl chain.A new structural phase transition was observed in the Cd compound at T= 105.5 ± 0.1 K (ΔH_t= 1472.3 ± 0.1 J mol^?1; ΔS_t = 13.956 ± 0.001 J K^?1mol^?1), in addition to two transitions that have been observed previously by other techniques. The higher of these transitions(T = 178.7 ± 0.3 K; ΔH_t = 982 ± 4 J mol^?1 ΔS_t = 6.16 ± 0.02 J K^? mol^?1) is known to be between two orthorhombic structures, while the structural changes at the lower transition (T= 156.8 ± 0.2 K; ΔH_t = 598 ± 5 J mol^?1, ΔS_t = 3.85 ± 0.03 J K^?1 mol^?1) and at the new transition are not known. It is proposed that these two transitions correspond respectively to the tetragonal to orthorhombic and monoclinic to tetragonal transitions in the propyl Mn compounds.In addition to the structural phase transitions (CH₃CH₂CH₂NH₃)₂MnCl₄ magnetically orders at t? 130 K. The magnetic contribution to the heat capacity is deduced from the heat capacity of the corresponding diamagnetic Cd compound and is of the form expected for a quasi 2-dimensional Heisenberg antiferromagnet.     

High temperature thermodynamics of H2 and D2 in titanium,and in dilute titanium oxygen solid solutions

The Tian Calvet microcalorimetric method has been improved in order to determine Δ$\text{H}$_H(D), the partial molar enthalpy of mixing of hydrogen (deuterium) in the Ti-H₂(D₂) solid systems for compositions 0 < (H/Ti) < 1.85, at 713 K and in the α TiO_y + H₂ solid solutions (y = (O/Ti)) at 745 K. The combined calorimetric and equilibrium method allows a precise evaluation of the partial molar entropies. The results of this study differ substantially from earlier published data.     

The correlation function for a quantum oscillator in a low-temperature heat bath

The momentum autocorrelation function c(t) for a quantum oscillator coupled with harmonic forces to a heat bath of oscillators is calculated at low temperatures. It is found that c(t) contains two distinct terms: one, the zero-point contribution c₀(t), is temperature independent, and the other, c₁(t), does depend on temperature. We concentrate our attention on the low-temperature case. An expression for c₁(t) is obtained, which is valid for arbitrary strenghts of the coupling and for arbitrary times. It is shown that c₁(t) is governed by the low-frequency behaviour of F(λ) = A²(λ)ϱ(λ), where ϱ(λ) is the density of normal modes and A(λ) is the central-oscillator component of the λth normal mode; other details of the problem are irrelevant. It is found that c₁(t) decays in time as an inverse-power law, with a relaxation time t_q ≈ ħ/kT.     

The resonance decay function method in the determination of the pre-factor of the Néel relaxation time of single-domain nanoparticles

In its simple form, the relaxation time of the Néel relaxation process of the magnetic moment of single-domain particles is given by τ_N=τ_0Nexp(σ), σ being the ratio of anisotropy energy to thermal energy. The pre-factor, τ_0N, is normally given a value of 10⁻⁹ s, but values ranging from 10⁻⁸ to 10⁻¹² s have been reported in literature. Here, by means of the field and frequency dependence of the complex magnetic susceptibility, χ(ω,H)=χ′(ω,H)−iχ″(ω,H), of a magnetic fluid sample, in the MHz-GHz range, in conjunction with the determination of the sample decay function, b(t), the pre-factor τ_0N is determined. b(t) is readily obtained through the inverse Fourier transformation relationship, which exists between b(t) and χ″(ω).     

On the separation of initial and final state effects in photoelectron spectroscopy using an extension of the auger-parameter concept

First, we show that the quantity Δβ(i) = ΔE_A(kii) + 2ΔE_B(i) — ΔE_B(k) is directly related to the final state relaxation contribution ΔE_R(i) of the binding energy shift ΔE_B(i). ΔE_A(kii) is the kinetic energy shift of the Auger transition which corresponds to the decay of a hole state with a hole in level k into a final state with two holes in level i. The shift parameter Δβ(i), which is based on information on two binding energies, is conceptually similar to Wagner's Auger parameter. To establish the relation between Δβ(i) and ΔR(i) one needs, however, less drastic approximations than in the case of Auger parameter shifts. The only approximation necessary is the assumption that ΔR(i) is determined by coulomb contributions.Secondly, we use Δβ (i) to analyse the experimental data of eighteen gaseous phosphorus-containing compounds obtained by Sodhi and Cavell¹. It is shown that ΔR(P_2p) is strongly related to changes in the polarizability of the ligands. The initial state effects derived from our study deviate from those expected on the basis of simple electronegativity considerations.     

Fourier analysis of spherically averaged momentum densities for some gaseous molecules

The spherically averaged autocorrelation function,B(r), of the position-space wavefunction, ψ($\text{r}$), is calculated by numerical Fourier transformation from spherically averaged momentum densities, ?(p), obtained from either theoretical wavefunctions or (e,2e) electron-impact ionization experiments. Inspection of B(r) for the π molecular orbitals of C₄ H₆ establishes that autocorrelation function differences, ΔB(r), can be qualitatively related to bond lengths and numbers of bonding interactions. Differences between B(r) functions obtained from different approximate wavefunctions for a given orbital can be qualitatively understood in terms of wavefunction difference,Δψ($\text{r}$), maps for these orbitals. Comparison of the B(r) function for the 1a_u orbital of C₄H₆ obtained from (e,2e) momentum densities with that obtained from an ab initio SCF MO wavefunction shows differences consistent with expected correlation effects. Thus, B(r) appears to be a useful quantity for relating spherically averaged momentum distributions to position-space wavefunction differences.     

Integrable string models of WZNW model type with constant SU(2), SO(3), SP(2) and SU(3) torsion and hydrodynamic chains

The integrability of string model of WZNW model type with constant SU(2), SO(3), SP(2) torsion is investigated. The closed boson string model in the background gravity and antisymmetric B-field is considered as integrable system in terms of initial chiral currents. The model is considered under assumption that internal torsion related with metric of Riemann-Cartan space and external torsion related with antisymmetric B-field are (anti)coincide. New equation of motion and exact solution this equation was obtained for string model with constant SU(2), SO(3), SP(2) torsion. New equations of motion and new Poisson brackets (PB) for infinite dimensional hydrodynamic chains was obtained for string model with constant SU(n), SO(n), SP(n) torsion for n → ∞.     

A multi-channel scattering theory for some time dependent Hamiltonians,charge transfer problem

Scattering theory for time dependent HamiltonianH(t)=?(1/2) Δ+ΣV _j (x?q _j (t)) is discussed. The existence, asymptotic orthogonality and the asymptotic completeness of the multi-channel wave operators are obtained under the conditions that the potentials are short range: |V _j (x)|≦C _j (1+|x|)^?2?ε, roughly spoken; and the trajectoriesq _j (t) are straight lines at remote past and far future, and |q _j (t)?q _k (t)| → ∞ ast → ± ∞ (j≠k).     

Excitation of the Classical Electromagnetic Field in a Cavity Containing a Thin Slab with a Time-Dependent Conductivity

We derive an exact infinite set of coupled ordinary differential equations describing the evolution of the modes of the classical electromagnetic field inside an ideal cavity containing a thin slab with the time-dependent conductivity σ(t) and dielectric permittivity ε(t) for the dispersion-less media. We analyze this problem in connection with the attempts to simulate the so-called dynamical Casimir effect in three-dimensional electromagnetic cavities containing a thin semiconductor slab periodically illuminated by strong laser pulses. Therefore, we assume that functions σ(t) and δε(t) = ε(t) ? ε(0) are different from zero during short time intervals (pulses) only. Our main goal here is to find the conditions under which the initial nonzero classical field could be amplified after a single pulse (or a series of pulses). We obtain approximate solutions to the dynamical equations in the cases of “small” and “big” maximal values of the functions σ(t) and δε(t). We show that the single-mode approximation used in the previous studies can be justified in the case of “small” perturbations, but the initially excited field mode cannot be amplified in this case if the laser pulses generate free carriers inside the slab. The amplification could be possible, in principle, for extremely high maximum values of conductivity and the concentration of free carries (the model of an “almost ideal conductor”) created inside the slab under the crucial condition providing the negativity of the function δε(t). This result follows from a simple approximate analytical solution confirmed by exact numerical calculations. However, the evaluation shows that the necessary energy of laser pulses must be, probably, unrealistically high.     

The bonded water molecule3ĪII: 180° Flips and diffusion

The proton spin-lattice relaxation time, T₁, is measured as a function of temperature in α -(COOH)₂·-2H₂O, K₂HgCl₄· H₂O and LiCHO·H₂O. The relaxation is caused by 180° flips of the water molecules about their 2-fold axes and good agreement is obtained between calculated and observed values of T₁. Empiricly the flip rate follows a classical Arrhenius equation: P· exp $\text{(? ΔH}\text{(RT))}$. A literature survey of values of P and ΔH obtained from similar investigations on other hydrates is given. The survey shows that the preexponential factor, P, is a function of the activation enthalpy, ΔH. P increases from 10¹² to 10¹⁷ Hz when ΔH changes from 2 to 17 $\text{kcal}\text{mole}$. Using a dynamical rate theory as formulated by Feit, we find the flip rate is given by: K₂· √(ΔH)· exp (K₁ΔH)· exp $\text{(?ΔH}\text{(RT>))}$. This expression can be fitted to the observed data using K₁ = 0.69 $\text{mole}\text{kcal}$ and K₂ = 2 × 10¹¹ Hz · $\text{(kcal}\text{mole)}$$\text{?1}\text{2}$. Thus both the frequency factor, K₂√ (ΔH), and the entropic factor, exp (K₁ΔH), have been obtained for flipping water molecules in hydrates. The values of K₁ and K₂ are shown to be physically reasonable.     

Effect of the amplitude of excitation pulses on the shape of photon-echo signals in two-level systems

It is theoretically established that multiple photon-echo signals reflect the oscillatory structure of the primary echo signal, which arises under the conditions of collinear excitation of two-level active centers by laser pulses having the same width but different amplitudes. It is shown that the oscillatory structure of the primary photon echo exists within the intervals (?t ₁, t ₁) and (?2t ₁, 2t ₁), where t ₁ is the pulse width. It is found that, when the pulse width is of the same order of magnitude as the delay between the pulses and the amplitudes of the excitation pulses obey certain relations, the oscillatory structure of the primary photon-echo signal becomes asymmetric. In the mode of quadratic detection of the primary photon-echo signal, the asymmetric oscillatory structure of the primary echo manifests itself as a manifold of isolated signals (multiple photon echoes), with the time intervals between these signals being equal to the pulse width.     

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.     

An approach to radially symmetrical solutions of the sine-Gordon equation

The solution φ(r, t) of the radially symmetric sine-Gordon equation is considered in three and two spatial dimensions for initial curves, analogous to a 2π-kink, in the expanding and in the shrinking phase, for R(t)j? R(0). It is shown that the parameterization φ(r, t) = 4 arcian exp[γ(r?R(0)] + x(r, t), where R(t) describes the exact propagation of the maximum of φ,(r, t), is suitable. Using an appoximate differential equation, recently given for the propagation of the solitary ring wave, a rough analytic approximation for the correction function x(r = R(t), t) is found and tested numerically. A relationship between the fluctuations in x(r = R(t), t) and those in $\text{R}\text{?}\text{(t), t)}\text{and}\text{R(t)}$ explains why the solitary wave is almost stable. From x(r = R(t), t) and the supposition x(1, t) ≈ x(∞, t) ≈ 0 an assymetry in φ_r(r, t) with respect to r = R(t) is predicted. It also exhibits fluctuations corresponding to those in x(r = R(t), t). The condition for validity of this approximation apparently is also a limit for the stability of the solitary ring wave.     

Electrical transport properties of thermally evaporated phthalocyanine (H2Pc) thin films

Thin films of H₂Pc of various thicknesses have been deposited onto glass substrates using thermal evaporation technique at room temperature. The dark electrical resistivity measurements were carried out at different temperatures in the range 298-473 K. An estimation of mean free path (l_o) of charge carriers in H₂Pc thin films was attempted. Measurements of thermoelectric power confirm that H₂Pc thin films behave as a p-type semiconductor. The current density-voltage characteristics of Au/H₂Pc/Au at room temperature showed ohmic conduction mechanism at low voltages. At higher voltages the space-charge-limited conduction (SCLC) accompanied by an exponential trap distribution was dominant. The temperature dependence of current density allows the determination of some essential parameters such as the hole mobility (μ_h), the total trap concentration (N_t), the characteristic temperature (T_t) and the trap density P(E).     

On the role of the higgs mechanism in present electroweak precision tests

Based on the observablesM _W, Γ _l ,s _W ^?2 (M _Z ² ), we evaluate the parameters Δx, Δy and ε at one-loop level within an electroweak massive vector-boson theory, which does not employ the Higgs mechanism. The theoretical results are consistent with the experimental ones on Δx, Δy, ε. The theoretical prediction for Δy coincides with the standard-model one (apart from numerically irrelevant terms which vanish forM _H→∞). Nonrenormalizability only affects Δx and ε, which differ from the standard-model results by the replacement logM _H→log Λ for a heavy Higgs mass,M _H (where Λ denotes an effective UV cut-off).     

The derivative nonlinear Schrödinger equation on the half-line

We analyze the derivative nonlinear Schrödinger equation on the half-line using the Fokas method. Assuming that the solution q(x,t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter ζ. The jump matrix has explicit x,t dependence and is given in terms of the spectral functions a(ζ), b(ζ) (obtained from the initial data q₀(x)=q(x,0)) as well as A(ζ), B(ζ) (obtained from the boundary values g₀(t)=q(0,t) and g₁(t)=q_x(0,t)). The spectral functions are not independent, but related by a compatibility condition, the so-called global relation. Given initial and boundary values {q₀(x),g₀(t),g₁(t)} such that there exist spectral functions satisfying the global relation, we show that the function q(x,t) defined by the above Riemann-Hilbert problem exists globally and solves the derivative nonlinear Schrödinger equation with the prescribed initial and boundary values.