Observation of the Talbot effect for ultrasonic waves

The diffraction of ultrasonic radiation on an amplitude diffraction grating in the near-field area (Fresnel diffraction) has been studied. The effect of self-imaging of the grating (Talbot effect) has been detected for ultrasonic radiation at distances from the grating in the range from z = 0 to z = 2L _T, where L _T is the Talbot length. The fractional Talbot effect, i.e., the ultrasonic image of the grating with the period d/2, has been observed.     

Holographic recording on the basis of forbidden singlet-triplet electronic transitions

The possibility of recording holograms in thick layers of a photopolymeric material on the basis of a forbidden singlet-triplet transition of a sensitizing dye, erythrosine, is theoretically substantiated and experimentally confirmed. A single hologram and 16 superimposed holograms are recorded with a low-power He-Ne laser (632 nm) at high concentrations of the sensitizing dye and high optical densities in the range of its main absorption. The diffraction efficiency of the single hologram is ～50%. The dependence of the increase in the diffraction efficiency of a transmission grating in samples of photopolymeric material on the intensity of incident radiation of a Kr⁺ laser (647 nm) is studied. The observed linear dependence of the maximal rate of increase in the diffraction efficiency in the photopolymer on the incident light intensity is explained by the manifestation of a two-step excitation of the dye (T ₁←S ₀, T ₂←T ₁) in the samples studied.     

The Vacuum Electromagnetic Fields and the Schrödinger Equation

We consider the simple case of a nonrelativistic charged harmonic oscillator in one dimension, to investigate how to take into account the radiation reaction and vacuum fluctuation forces within the Schrödinger equation. The effects of both zero-point and thermal classical electromagnetic vacuum fields, characteristic of stochastic electrodynamics, are separately considered. Our study confirms that the zero-point electromagnetic fluctuations are dynamically related to the momentum operator p=?i ? ?/? x used in the Schrödinger equation.     

Steady-state light-induced forces in atomic nanolithography

An analysis of general characteristics of light-induced forces is presented for arbitrary monochromatic masks in which optical pumping of atoms and spontaneous emission play an important role. Dependence of regions of localization on detuning and ellipticity is determined for cyclic transitions of two types: J å J with half-integer J and J å J + 1 with arbitrary J. Numerical simulations of atomic beam focusing with one-and two-dimensional light masks show that spatial atom distributions with narrow features and high contrast can be formed in dissipative masks. In particular, spherical aberration is substantially reduced when the pumping field is tuned to a J å J + 1 transition with large J in lin ～ lin configuration as compared to nondissipative masks.     

Diffraction spectra of order–order transition structural states in titanium monoxide

A new class of M_(n?i)X_(n?i) superstructures (n is an integer constant and i is a rational variable) that are formed after incomplete equilibrium second-order order–order phase transitions in solid solutions and in compounds with atom–vacancy ordering is proposed. New superstructures are superpositions of partially disordered M _n ?X _n superstructures of various symmetries in the matrix of the basic crystal structure. The model parameters affecting the positions and intensities of superstructure reflections on diffraction patterns have been studied by example of the high-temperature ordered phase β-TiO of titanium monoxide. It has been shown that the diffraction spectra of the low-symmetric M_(5-i)X_(5-i) superstructure (space group P1m1) and the high-symmetric M₅X₅ superstructure (space group Pm3?m) at certain parameters are identical in the positions of superstructure reflections.     

Diffraction enhancement effect and new possibilities of measuring the electric charge of the neutron and its inertial-to-gravitational mass ratio

Diffraction enhancement of small effects affecting a neutron undergoing Laue diffraction at Bragg angles θ _B close to 90° is predicted and experimentally observed. The enhancement is due to the delay of the neutron inside the crystal during diffraction and is proportional to tan² θ _B. As a result, the diffraction enhancement factor may be as large as ～10⁸–10⁹. On this basis, a new method is proposed for searching for the electric charge of the neutron and for measuring the ratio of its inertial mass m _i to the gravitational mass m _G . It is shown that the accuracy of the neutron charge measurement can be improved by more than two orders of magnitude in relation to the present-day accuracy and that the ratio m _i /m _G can be measured to an precision of σ(m _i /m _G ) ～ 10^?6.     

Forced snaking: Localized structures in the real Ginzburg-Landau equation with spatially periodic parametric forcing

We study spatial localization in the real subcritical Ginzburg-Landau equation u _t = m ₀ u + Q(x)u + u _xx + d|u|² u ?|u|⁴ u with spatially periodic forcing Q(x). When d>0 and Q ≡ 0 this equation exhibits bistability between the trivial state u = 0 and a homogeneous nontrivial state u = u ₀ with stationary localized structures which accumulate at the Maxwell point m ₀ = ?3d ²/16. When spatial forcing is included its wavelength is imprinted on u ₀ creating conditions favorable to front pinning and hence spatial localization. We use numerical continuation to show that under appropriate conditions such forcing generates a sequence of localized states organized within a snakes-and-ladders structure centered on the Maxwell point, and refer to this phenomenon as forced snaking. We determine the stability properties of these states and show that longer lengthscale forcing leads to stationary trains consisting of a finite number of strongly localized, weakly interacting pulses exhibiting foliated snaking.     

Fundamental Entangling Operators in Quantum Mechanics and Their Properties

For the first time, we introduce so-called fundamental entangling operators \(e^{iQ_{1} P_{2}}\) and \(e^{iP_{1} Q_{2} }\) for composing bipartite entangled states of continuum variables, where Q_i and P_i (i = 1, 2) are coordinate and momentum operator, respectively. We then analyze how these entangling operators naturally appear in the quantum image of classical quadratic coordinate transformation (q₁, q₂) → (Aq₁ + Bq₂, Cq₁ + Dq₂), where AD?BC = 1, which means even the basic coordinate transformation (Q₁, Q₂) → (AQ₁ + BQ₂, CQ₁ + DQ₂) involves entangling mechanism. We also analyse their Lie algebraic properties and use the integration technique within an ordered product of operators to show they are also one- and two- mode combinatorial squeezing operators.     

Coulomb Rydberg electron <Emphasis Type="Italic">L</Emphasis>-mixing in collisions with atomic ions

The cross sections of the Rydberg electron L-mixing in a hydrogen atom and a hydrogen-like ion are calculated for slow collisions with atomic ions H*(n, L) + A⁺ = H*(n, L′) + A⁺ without variation of the principal quantum number n. The probability of the L-mixing L → L′ is associated with the quantum interference of the wave functions of adiabatic states, i.e., with the mixing of the time phases of these functions exp(?i∫E _k (t)dt). The effective cross section of such L-mixing for the states with n = 28 are 4–5 orders of magnitude greater than the cross sections determined in previous investigations. The expansion coefficients of spherical Coulomb wave functions in terms of parabolic ones and vice versa, which are necessary for determining cross sections, are calculated on the basis of a comprehensive analysis of the spatial properties of these functions.     

The Hammond postulate: A quantitative interpretation

The Hammond postulate is considered in terms of the model of intersecting parabolas. It is shown that, in radical detachment reactions of the type X _f ^· + HX _i → X _f H + X _i ^· with a symmetrical reaction center X _i …H…X _f , the H atom in the transition state is equidistant from the X _i and X _f atoms if the enthalpy of the reaction ΔH = 0. The X _i …H distance increases and the X _f …H distance decreases linearly as ΔH grows. The dependence remains linear over the range ΔH _min ≤ ΔH ≤ H _max. The same result was obtained in quantum-chemical calculations for reactions of the type R _f ^· + R _i H. In reactions of the type X^· + HY → XH + Y^· with an asymmetric reaction center X…H…Y, the X…H and Y…H interatomic distances in the transition state at ΔH = 0 depend on the force constants and lengths of the X-H and Y-H bonds. The Y…H distance increases and the X…H distance decreases linearly as ΔH grows. A similar picture is observed in the model of intersecting Morse curves, where the dependence of interatomic distances on ΔH in the transition state is nonlinear. Equations describing interatomic distances in the transition state as functions of the enthalpy of the reaction are presented.     

Phase-space treatment of the driven quantum harmonic oscillator

A recent phase-space formulation of quantum mechanics in terms of the Glauber coherent states is applied to study the interaction of a one-dimensional harmonic oscillator with an arbitrary time-dependent force. Wave functions of the simultaneous values of position q and momentum p are deduced, which in turn give the standard position and momentum wave functions, together with expressions for the ηth derivatives with respect to q and p, respectively. Afterwards, general formulae for momentum, position and energy expectation values are obtained, and the Ehrenfest theorem is verified. Subsequently, general expressions for the cross-Wigner functions are deduced. Finally, a specific example is considered to numerically and graphically illustrate some results.     

Observation of the High-Order Fractional Talbot Effect in the Optical Range

The Talbot effect in the diffraction of light on the amplitude diffraction grating has been investigated experimentally. A high-order fractional Talbot effect up to d/102, where d is the grating period, has been discovered and studied. Possible applications of this phenomenon have been mentioned.     

Cross sections of electron capture by Boron ions in gaseous media

We study the cross sections σ_{i, i?1}, σ_{i, i?2}, and σ _{i, i?3} of capture of one, two, and three electrons by boron ions with charges i=1?5 and velocities V=(1.83?5.50)V₀ in gaseous media with atomic numbers Z_t varying from 1 to 54. The oscillatory form of the Z_t dependence of electron capture cross section by boron ions, which has been established for lighter ions, is confirmed.     

Competing contact processes in the Watts-Strogatz network

We investigate two competing contact processes on a set of Watts–Strogatz networks withthe clustering coefficient tuned by rewiring. The base for network construction isone-dimensional chain of N sites, where each site i is directly linked tonodes labelled as i ±1 and i ±2. So initially, each node has the same degree k_i =4. The periodic boundary conditions are assumed as well. For each nodei the linksto sites i +1 and i +2 are rewired to two randomly selected nodes so far not-connected tonode i. Anincrease of the rewiring probability q influences the nodes degree distribution and thenetwork clusterization coefficient ??. For given values of rewiring probabilityq the set ??(q)={??₁,??₂,...,??_M} of M networks is generated. The network’s nodes aredecorated with spin-like variables s_i ∈ { S,D}. During simulation each S node having a D-site in its neighbourhoodconverts this neighbour from D to S state. Conversely, a node in D state having at least oneneighbour also in state D-state converts all nearest-neighbours of this pairinto D-state. The latter is realized with probabilityp. We plotthe dependence of the nodes S final density n_S^T on initial nodes S fraction n_S⁰. Then, we construct the surface of the unstable fixedpoints in (??, p, n_S⁰) space. The system evolves more often toward n_S^T for (??, p, n_S⁰) points situated above this surface while startingsimulation with (??, p, n_S⁰) parameters situated below this surface leads system to n_S^T=0. The points on this surface correspond to such value ofinitial fraction n_S^* of S nodes (for fixed values ?? and p) for which their final density is n_S^T=1/2.     

Superposition of M<Subscript>5</Subscript>X<Subscript>5</Subscript> superstructures and X-ray diffraction in TiO<Subscript>1.0</Subscript> titanium monoxide

The interpretation of diffraction spectra of ordered high-temperature phases of solid solutions and strongly nonstoichiometric compounds is discussed. It has been shown that variations of the intensities of superstructure reflections, which cannot be explained within simple ordering models, can be due to the superposition of superstructures with different symmetries in the matrix of the basis crystal structure. Using an example of atom–vacancy ordering in TiO_1.0 titanium monoxide, a model of the order–order transition state formed by the superposition of low-temperature monoclinic (space group A2/m (C2/m)) and high-temperature cubic (space group Pm3?m) M₅X₅ superstructures has been proposed. It has been shown that the transition state is thermodynamically equilibrium and should be implemented instead of the M₅X₅ cubic superstructure. The transition state model can be considered as an M_(5–i)X_(5–i) superstructure (i = 1, 14/18, 11/18) with the monoclinic symmetry (space group P1m1).     

Role of initial correlation in coarsening of a ferromagnet

We study the dynamics of ordering in ferromagnets via Monte Carlo simulations of theIsing model, employing the Glauber spin-flip mechanism, in space dimensionsd = 2 and3, on square and simplecubic lattices. Results for the persistence probability and the domain growth arediscussed for quenches to various temperatures (T _f ) below the criticalone (T _c ), from differentinitial temperatures T _i ≥T _c . In long timelimit, for T _i >T _c ,the persistence probability exhibits power-law decay with exponents θ ? 0.22 and? 0.18 in d = 2 and 3, respectively. For finite T _i , the early timebehavior is a different power-law whose life-time diverges and exponent decreases asT _i →T _c . The two steps areconnected via power-law as a function of domain length and the crossover to the secondstep occurs when this characteristic length exceeds the equilibrium correlation length atT =T _i . T _i =T _c is expected toprovide a new universality class for which we obtain θ ≡θ _c ? 0.035 ind = 2 and?0.105 in d = 3. The time dependenceof the average domain size ?, however, is observed to be rather insensitive tothe choice of T _i .     

Prebreakdown excitation of crystals at double multiphoton resonance: I. Probabilities of interband transitions

Expressions for the probabilities of l-photon transitions (for arbitrary l) between the upper valence band v and lower conduction band c at two-photon resonance on the adjacent transition between the band c and the upper conduction band c ₁ are obtained by means of the S transformation of the electron-photon Hamiltonian. The effects of electron band spectrum transformation and photon reemission are taken into account.     

High-resolution X-ray emission <Emphasis Type="Italic">M</Emphasis>α and <Emphasis Type="Italic">M</Emphasis>β spectra of Bi atoms

The structure and relative intensity of x-ray fluorescence Mα and Mβ spectra of Bi atoms have been studied experimentally under excitation by Cr and Cu Kα_1,2 radiation. It has been found that observed short-wavelength satellites are mostly caused by the radiative transitions M ₅ N-N _6,7 N (M ₅ N satellites) and M ₄ N-N ₆ N (M ₄ N satellites), whereas the transitions M ₅ O-N _6,7 O and M ₄ O-N ₆ O are overlapped with the profiles of x-ray diagram Mα_1,2 and Mβ lines and are not observed as individual structures. The M ₅ N and M ₄ N satellites have been separated from total spectral profiles, and the relative intensities of such groups of lines have been determined. A model has been proposed for calculation of emission cross sections of the M ₄ N and M ₄ N satellites, as well as the Mα_1,2 lines along with the M ₅ O satellites and the Mβ line with the M ₄ O satellites. The model takes into account main channels of generation and migration of vacancies in M subshells connected with the Coster-Kronig transitions M _i -M _j N and M _i -M _j O, radiative transitions M _i -M _j and M _i -N _j , and shaking processes upon production of the M _i vacancy, as well as with cascades of such processes. Comparison of experimental values of the relative intensity of the separated satellites with calculated results indicates the correctness of the model used.     

Cross sections of the photoneutron reaction for <Superscript>141</Superscript>Pr and <Superscript>186</Superscript>W nuclei,estimated from physical criteria of data reliability

Using objective physical criteria for data reliability, cross sections of partial photoneutron reactions (γ, 1n), (γ, 2n) and (γ, 3n) that are free of the shortcomings of neutron multiplicity sorting methods used on beams of quasimonoenergetic annihilation photons are obtained for ¹⁴¹Pr and ¹⁸⁶W nuclei. Evaluation is performed using the experimental–theoretical method (ETM), based on the experimental cross section of neutron yield reaction σ^exp(γ, xn) = σ^exp(γ, 1n) + 2 σ^exp(γ, 2ⁿ) + 3 σexp(γ, 3n) + … and ratios F _i ^theor= σ^theor(γ, in)/σ^theor(γ, xn) calculated within the combined model (CM) of photonuclear reactions, which stipulates that σ^eval(γ, in) = F _i ^theor σ^exp(γ, xn). It is found that for ¹⁴¹Pr and ¹⁸⁶W, ratios F ^exp _i do not contradict the data reliability criteria only at energies up to ~21 and ~22 MeV, respectively. At the same time, there are notable discrepancies between F _i ^theor and F ^exp _i, and thus between the evaluated and experimental cross sections of reactions. It is shown that the discrepancies between the evaluated and experimental cross sections are due to the assumed unreliable experimental distribution of neutrons in the channels with multiplicities 1, 2, and 3.     

The vibrational spectrum of the OCS molecule based on the data on spectra of liquid and cryosolutions

The IR absorption spectra of liquid OCS (T = 135(1) K) and of the following solutions—OCS + Ar (T = 90 K), OCS + N₂ (T = 90 K), OCS + Kr (T = 130 K), and OCS + Xe (T = 163 K)—are measured in the range 800–7000 cm^?1. From 16 to 40 bands corresponding to transitions to vibrational states up to the third order inclusive are interpreted for basic isotope modification and for the isotopically substituted molecules ¹⁸O¹²C³²S, ¹⁶O¹³C³²S, and ¹⁶O¹²C³⁴S. In the spectra of the liquids, the spectral moments M(1) and M(2) of all the observed bands are determined. The harmonic frequencies ω _i and the anharmonicity constants x _ik are calculated for all the systems, including the liquid. The anharmonicity is found to be constant within the experimental error. A large shift Δω₃ is primarily determined by the dipole-induced dipole interaction.