Slowing down of the wave packets in quantum graphs

Necklace-type devices are studied, which are optical lines with periodically located segments replaced by two arches of different lengths. It is shown that one can choose parameters of the necklace in such a way that the dispersion relation for the whole line will be very flat in the neighbourhood of the prescribed frequency (although the corresponding band is not narrow). It is also shown that a finite piece of such a line creates a slowdown of wave packets without any significant loss of the energy due to the reflection.     

Effect of pulsed excitation of a bounded medium on a plane electromagnetic wave

An analysis is made of the transformation of a plane monochromatic electromagnetic wave in response to a temporal change in the permittivity and conductivity of a semibounded medium. The change in the parameters of the medium takes the form of a rectangular pulse of arbitrary duration and amplitude. The detailed structure of the electric field and its evolutional redistribution are determined. The asymptotic formation of a backward wave is demonstrated, whose amplitude may exceed that of the primary wave for parameters typical of a semiconductor. Zh. Tekh. Fiz. 69, 84–92 (August 1999)     

Global Well-Posedness for the KP-I Equation on the Background of a Non-Localized Solution

We prove that the Cauchy problem for the KP-I equation is globally well-posed for initial data which are localized perturbations (of arbitrary size) of a non-localized (i.e. not decaying in all directions) traveling wave solution (e.g. the KdV line solitary wave or the Zaitsev solitary waves which are localized in x and y periodic or conversely).     

Optical study of parameters of the passage of a shock wave from air to water

A study is made of the penetration of shock waves from air into water. The shock wave in air is generated as a result of dielectric breakdown induced by pulsed CO₂-laser radiation. A combination of the double-exposure shadow method and holographic interferometry is used to measure the shock-wave parameters. Density and pressure profiles behind the wave front are obtained at different times after onset of breakdown. It is shown experimentally that as the wave passes through the interface from the air to the water, there is a fourfold amplification of the pressure in the shock wave front. Estimates of the width of the shock wave front formed in the water are given in the context of studies of large-scale explosion processes. It is shown that simple empirical dependences, established in the course of studies of large-scale explosions, are also valid with certain corrections for microscopic laboratory experiments. Zh. Tekh. Fiz. 68, 39–43 (August 1998)     

Potential surface waves at the boundary of a metal with a magnetoactive plasma at finite pressure

The propagation of surface-type potential waves along the interfacial boundary of a plasma with an ideally conducting metal in an external magnetic field perpendicular to the boundary is examined. It is shown that a necessary condition for the existence of these waves in the system is a finite gas kinetic pressure. Dispersion relations for these waves and expressions for the penetration depth of the wave fields into the plasma are obtained, and they are studied numerically for various plasma parameters. The frequency region for propagation of these waves is found. It is also shown that in a nonzero external magnetic field a system of this kind has a range of frequencies in which the wave is a generalized surface wave. Zh. Tekh. Fiz. 69, 30–33 (November 1999)     

Mechanism of spontaneous radiation relaxation of an impurity atom in a photonic band-gap crystal

On the base of the concept of radiative interaction between atoms of two different species, a novel electric-dipole mechanism of spontaneous radiating relaxation of an impurity atom in a medium with a gap in the photonic density of states about the transition frequency has been suggested. A kinetic equation for an impurity atom has been derived, and polarizations of the photonic band-gap crystal and an induced electromagnetic wave at the spontaneous transition frequency due to the suggested mechanism have been investigated. The parameters of the induced wave are determined by those of the suggested mechanism, and this dependence can be used in experimental investigations of these parameters. Zh. éksp. Teor. Fiz. 116, 469–484 (August 1999)     

Increase of the atomic phase density in a hollow laser waveguide

A study is made of the channeling of atoms in a narrowing hollow waveguide carrying on its inner surface a surface wave with positive detuning for the absorption line of an atom. The inelastic reflection of atoms from the surface light wave and the convergent geometry of the waveguide make it possible to decrease the temperature and increase the phase density of an ensemble of atoms introduced continuously into the hollow convergent waveguide from a magnetooptic trap, by a factor of 10⁵. It is suggested that such a waveguide be used to study collective phenomena in quantum-mechanical systems with a high density (Bose-Einstein condensate) and as a high-luminosity coherent source of cold atoms. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 763–767 (25 May 1996)     

Dynamics of mixed lump-solitary waves of an extended (2 + 1)-dimensional shallow water wave model

To explore the features of lump solutions, which are local in every direction of space, a ($2+1$)-dimensional extended shallow water wave model is studied, based on its bilinear representation. Several ansatzes have been utilized to determine single lump waves, lump-kink waves, single kinks and multi-lumps leading to breathers in terms of function patterns for the model. Through analyzing interactions between solitons, the impact of free parameters involved in the solutions on interaction types is exhibited. We determine a condition on the parameters under which a single kink wave can be converted into a multi-lump wave. To illustrate the interaction of exponential and periodic function waves, we show that multi-lump waves in the form of breather waves especially come into sight as a straight line or an X shape. To realize dynamics, we make various graphical analyses on the presented solutions, which gives an essential improvement in the physical realizing of higher-dimensional lump waves in oceanography and nonlinear optics.     

Localization of a nonlinear switching wave in an active bistable medium with an isolated inhomogeneity

An analysis is made of the one-dimensional propagation of a switching wave in an active medium when one of the parameters of the medium is a function of the coordinate over a certain region and remains constant outside this region. The possibility of localization (stopping) of the wave at this type of inhomogeneity is investigated. An analytical expression is obtained for the wave shift in the case of a small-amplitude inhomogeneity. Constraints on the amplitude and length of the inhomogeneity at which localization takes place are obtained for an inhomogeneity of finite dimensions. Zh. Tekh. Fiz. 67, 14–20 (August 1997)     

Optical activity of incommensurate crystals with plane-wave modulation

A phenomenological approach is used to discuss the propagation of polarized light in the incommensurately modulated phases of crystals of the family A₂BX₄ with spatially averaged inversion symmetry. The Jones-matrix technique for an anisotropic inhomogeneous medium is used to calculate the optical parameters of a crystal with sinusoidally modulated dielectric parameters. It is demonstrated that these crystals can exhibit a weak optical activity, i.e., weaker than that of crystals without inversion symmetry. Also discussed are boundary conditions on the phase of the modulation wave at the surface of a crystal plate. Results are obtained suggesting that the optical properties of an incommensurately modulated crystal need not depend on the shape of the modulation wave. Fiz. Tverd. Tela (St. Petersburg) 39, 1360–1365 (August 1996)     

Electron dynamics in Na and Pt clusters from time-dependent Hartree-Fock theory

We present a method for the numerical investigation of the electron dynamics in small metallic clusters in intense laser fields. We obtain information about collective excitations and relaxation processes in the Na ₉ ⁺ and Pt₃ clusters analyzing the power spectrum of the dipole moment within a mean-field approach. The power spectrum is computed for various laser pulse parameters as well as for the limit of an infinitely short laser pulse. Due to the basis set expansion of the wave function our method is capable to follow the dynamics not only of the whole electron cloud, but of any particular molecular orbital. Received 28 March 2002 / Received in final form 31 May 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: pavlyukh@mpi-halle.de     

Scattering of Rayleigh waves by a statistical inhomogeneity of the mass density

The problem of the scattering of a Rayleigh wave by a surface inhomogeneity of the mass density of an isotropic solid is solved in the Born approximation of perturbation theory. The inhomogeneity is statistical with a Gaussian correlation function in the plane parallel to the surface and is deterministic with an exponentially decaying dependence on the coordinate perpendicular to the surface. Expressions are derived for the displacement fields in the scattered longitudinal (P), transverse (SV and SH), and Rayleigh (R) waves at large distances from the inhomogeneity. The Rayleigh wave energy scattering coefficients are calculated as functions of the wavelength λ, the correlation length a of the inhomogeneity, the depth d of the defective layer, and the Poisson ratio of the medium, σ. The angular distribution of the scattered Rayleigh wave energy is determined. Asymptotic expressions are obtained for the scattering coefficient in various limiting cases with respect to the parameters a/λ and λ/d. The relation between the energies in the scattered P, SV, SH, and R waves is established. The resulting equations are used to calculate the scattering coefficients numerically over a wide range of variation of the parameters a/λ, λ/d, and σ; the results are presented in the form of graphs and a table. A physical pattern of the scattering process is constructed and used as a basis for interpreting the results of the study. Fiz. Tverd. Tela (St. Petersburg) 39, 267–274 (February 1997)     

Gain coefficient of a high harmonic emitted during the above-threshold ionization of atoms

The problem of the amplification of high harmonics generated during the above-threshold ionization of atoms in a high-power laser wave field is examined for the first time. An estimate of the gain coefficient as a function of the parameters of the atom beam and the pump wave is given. Zh. éksp. Teor. Fiz. 115, 1630–1641 (May 1999)     

Problems of interpretation of holographic interferograms near shock wave fronts

A method of avoiding ambiguity in the interpretation of interferograms near a shock wave front is proposed. The method is based on combining the double-exposure schlieren method and holographic interferometry. Relations for calculating, on the basis of data obtained by analyzing double-exposure schlieren photographs, both the density at the shock wave front and the gradient of the density directly behind the front, which is necessary for calculating the shifts of the interference fringes near the shock wave front, are presented. Zh. Tekh. Fiz. 68, 88–91 (September 1998)     

Computational study of cold ions trapped in a double-well potential

We report a rigorous computational treatment of quantum dynamics of cold ions in a double-well trap using the time-dependent Schrödinger equation. Our method employs a numerically accurate approach that avoids approximations, such as assumption of weak coupling between the wells; normal mode nature of vibrations; or harmonic approximation for energy spectrum of the double-well system. Our goal is to reproduce, from first principles, the process of energy swaps between the wells observed in the experiments at NIST [Nature 471, 196 (2011)] and Innsbruck [Nature 471, 200 (2011)]. The model parameters and the initial conditions are carefully chosen to mimic experimental conditions. We obtain accurate energies and wave functions of the system numerically, and study the evolution of motional wave packets to provide new insight. This model reproduces experimental results obtained by NIST and Innsbruck in detail. We explain the energy transfer in terms of wave packet dynamics in the asymmetric potential energy well. We also show that, for a localised initial wave packet, this phenomenon can be interpreted using the terms of classical dynamics, such as trajectory of motion governed by the well-known simple principle: the angle of reflection equals the angle of incidence.     

Motion of an electronic wave packet in an electromagnetic field

An equation is derived for the matrix of the parameters of a small Gaussian wave packet moving in arbitrary fixed electromagnetic fields. The equation can be used to describe the evolution of wave packets in a wide class of vacuum devices. A simple example of the evolution of a packet in a constant magnetic field is studied. Pis’ma Zh. éksp. Teor. Fiz. 64, No. 8, 515–520 (25 October 1996)     

Possibility of the appearance of spin autowaves in a model of a ferromagnet with nonuniform dissipation

A model of a ferromagnet with nonuniform dissipation is introduced for the Landau-Lifshitz equations. It is shown that in this model a ferromagnet can be regarded as an oscillating active medium where the formation of autowave structures — spin autowaves, pacemakers, and spiral waves — is possible. Their wave characteristics, expressed in terms of the parameters of the medium, are found for a special case. Fiz. Tverd. Tela (St. Petersburg) 39, 513–515 (March 1997)     

Electronic wave packets in vacuum photodetectors and the possibility of observing them

The motion of an electronic wave packet in the interelectrode space of a vacuum photodetector is investigated. It is shown that the dimensions of such a packet are of the order of 1 micron and are comparable to the optical wavelength. On interacting with a powerful laser pulse the packet scatters a large number of photons and is deflected from its initial trajectory. Both effects can be used to determine the parameters of an electronic wave packet. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 6, 408–411 (25 March 1996)     

Isotope-selective femtosecond wave packet dynamics: The rare molecule

For the first time, the femtosecond real-time vibrational dynamics of the rare ^41,41K₂ isotope, excited to the electronic state, could be selectively studied by means of time-resolved three photon ionization. A vibrational period of fs is determined. Superimposed, a beat structure with a period of 20 ps is observed. A detailed Fourier analysis reveals a strong band of three lines centered around 65.5 cm^-1. A significant perturbation of the wave packet caused by spin-orbit coupling of the A and the crossing state is found. This perturbation is the reason for the fast dephasing of the initially generated wave packet within about 10 ps. The spectrogram of the real-time data shows total revivals of the wave packet at 20 ps and 40 ps. Fractional revivals are found for times around 10 ps and 30 ps. Due to high intensity effects a remarkable slightly broadened line at 90 cm^-1 appears and can be assigned to the wave packet propagation generated in the dimer's ground state by impulsive stimulated Raman scattering. Revivals of this ground state wave packet are found at 17ps and 34ps. A comparison with other isotopes of K₂ is given. Received: 9 February 1998 / Revised: 15 May 1998 / Accepted: 2 June 1998     

Semiclassical energy levels of electrons in metals with band degeneracy lines

We show that in calculating the semiclassical energy levels of electrons in metals located in a magnetic field, one must determine whether or not the corresponding electron paths in the space of wave vectors k are attached to a band degeneracy line. Calculations in the two possible cases, i.e., with and without such attachment, differ by |e|ℏ/2m*c, where e is the electron charge and m* is the cyclotron mass of the electron. This shift in the energy levels is of a topological nature, and its existence depends neither on the specific form of the electron dispersion relation ε(k) near the electron path nor on the shape or size of this path. The reason for this shift lies in the fact that the electron orbit is attached to the band degeneracy line, which is the line of singular points of the Bloch wave functions. In many respects this effect is similar to the Aharonov-Bohm effect if the band degeneracy line is considered an infinitely thin “solenoid.” This shift in energy levels should become apparent in studies of oscillation phenomena in metals. We give examples of metals in which the conditions for observing the shift is probably the most favorable. Zh. éksp. Teor. Fiz. 114, 1375–1392 (October 1998)