A double quantum well in a driving laser field

The dynamic effect of electrons in a double quantum well under the influence of a monochromatic driving laser field is investigated. Closed-form solutions for the quasienergy and Floquet states are obtained with the help ofSU (2) symmetry. For the case of weak interlevel coupling, explicit expressions of the quasienergy are presented by the use of perturbation theory, from which it is found that as long as the photon energy is not close to the tunnel splitting, the electron will be confined in an initially occupied eigenstate of the undriven system during the whole evolution process. Otherwise, it will transit between the lowest two levels in an oscillatory behavior.     

The generalized WKB method in the three-dimensional case. IV

A method of successive approximations is developed for obtaining solutions of the basic equations of the WKB method in the three-dimensional case. Explicit expressions are found for the first approximations to the energy levels and wave functions of the bound states of a particle in a three-dimensional potential well which were obtained in zeroth approximation in [1, 2].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 53–60, November, 1976.     

Two-level system in the field of two intense waves

The problem of a two-level system in the field of two intense monochromatic waves is reduced to the problem of a two-level system in the field of a nonmonochromatic but periodic (in time) wave, which makes it possible to introduce quasienergy states. An investigation is made by the method proposed in [1, 2]. For the quasienergy an analytic expression is obtained that is valid in the complete range of variation of the frequencies at all values of one of the intensity parameters and moderate values of the other. The quasienergy is also calculated in the case of asymptotically large values of the parameters of both intensities when one of the frequencies of the external field is equal to the resonance frequency. The Fourier components of the density matrix at the frequencies of the external field are also calculated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 23–25, August, 1980.We thank M. L. Ter-Mikaelyan for interest in the work.     

Quasiclassical coherent trajectory states of a spinless relativistic particle in an arbitrary electromagnetic field

Approximate (quasiclassical) solutions of the Klein-Gordon equation for a charge in an arbitrary electromagnetic field are constructed. One of the decisive properties of these solutions is that the average quantum-mechanical values of the coordinates and momenta in these states are the exact solutions of the classical relativistic Hamiltonian equations.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 48–50, April, 1982.     

The Fokker–Planck–Kolmogorov Equation with Nonlocal Nonlinearity in the Semiclassical Approximation

A scheme for constructing quasi-classical concentrated solutions of the Fokker–Planck–Kolmogorov equation with local nonlinearity is presented on the basis of the complex WKB-Maslov method. Formal, asymptotic in a series expansion parameter D, D 0 solutions of the Cauchy problem for this equation are constructed with a power accuracy O(D ^3/2). A set of the Hamilton–Ehrenfest equations (a set of equations for average and centered moments) derived in this work is of considerable importance in construction of these solutions. An approximate Green's function is constructed and a nonlinear principle of superposition is formulated in the class of semiclassical concentrated solutions of the Fokker–Planck–Kolmogorov equations.     

Metastable states of a nonlinear vector field with values on a sphere

In the nonlinear theory of a vector field which takes values on a sphere, solutions are found to the equations of motion that realize a minimum of the action; these are metastable states. The geometrical meaning of the solutions is elucidated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 45–48, April, 1980.I thank A. A. Belavin, D. E. Burlankov, and V. N. Dutyshev for helpful discussions.     

A semiclassical approach to the ground state and density oscillations of quantum dots

A semiclassical Thomas–Fermi method, including a Weizsäcker gradient term, is implemented to describe ground states of two-dimensional nanostructures of arbitrary shape. Time-dependent density oscillations are addressed in the same spirit using the corresponding semiclassical time-dependent equations. The validity of the approximations is tested, both for ground state and density oscillations, compared with the available microscopic Kohn–Sham solutions.     

Quasienergy pseudopotential method in the theory of interaction of a coherent electromagnetic field with matter

We formulate the quasienergy pseudopotential methods, allowing us to study the behavior of the electronic structure of a material in a coherent electromagnetic field. We show that after canonical transformation, we can look for the solution to the nonsteady-state Schrödinger equation in a basis of wave functions from extended Hubert space, substituting the quasienergy pseudopotential for the true nonsteady-state electronic potential. We prove that the familiar compensation theorem remains valid even in this case.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 33–37, February, 1992.     

Dynamic stiffness matrix of thin-walled composite I-beam with symmetric and arbitrary laminations

For the spatially coupled free vibration analysis of thin-walled composite I-beam with symmetric and arbitrary laminations, the exact dynamic stiffness matrix based on the solution of the simultaneous ordinary differential equations is presented. For this, a general theory for the vibration analysis of composite beam with arbitrary lamination including the restrained warping torsion is developed by introducing Vlasov's assumption. Next, the equations of motion and force–displacement relationships are derived from the energy principle and the first order of transformed simultaneous differential equations are constructed by using the displacement state vector consisting of 14 displacement parameters. Then explicit expressions for displacement parameters are derived and the exact dynamic stiffness matrix is determined using force–displacement relationships. In addition, the finite-element (FE) procedure based on Hermitian interpolation polynomials is developed. To verify the validity and the accuracy of this study, the numerical solutions are presented and compared with analytical solutions, the results from available references and the FE analysis using the thin-walled Hermitian beam elements. Particular emphasis is given in showing the phenomenon of vibrational mode change, the effects of increase of the modulus and the bending–twisting coupling stiffness for beams with various boundary conditions.     

The quasienergy spectrum of semiconductors with direct band gaps in the laser field

Explicit analytical expressions are derived for Floquet states and the quasienergy spectrum of semiconductors with zinc-blende structure and direct band gaps, taking into account the real symmetry properties of the degenerate valence bands.The author would like to thank Academician professor Nguyen Van Hieu for suggesting the problem and for valuable discussions.     

Mean-field dynamics of a quantum dot-microcavity system

Mean-field evolution equations for the exciton and photon populations and polarizations (Bloch–Lamb equations) are written and numerically solved in order to describe the dynamics of electronic states in a quantum dot coupled to the photon field of a microcavity. The equations account for phase space filling effects and Coulomb interactions among carriers, and include also (in a phenomenological way) incoherent pumping of the quantum dot, photon losses through the microcavity mirrors, and electron–hole population decay due to spontaneous emission of the dot. When the dot may support more than one electron–hole pair, asymptotic oscillatory states, with periods between 0.5 and 1.5 ps, are found almost for any values of the system parameters.     

Newton's equation as a consequence of a semiclassical method of solving the Schrödinger equation

Using the one-dimensional Schrbdinger equation as an example, it is shown that the classical equations of motion necessarily arise during the construction of semiclassical solutions of quantum mechanical equations with the aid of V. P. Maslov's complex-germ method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 77–80, July, 1991.     

Probing a subcritical instability with an amplitude expansion: An exploration of how far one can get

We explore methods to locate subcritical branches of spatially periodic solutions in pattern forming systems with a nonlinear finite-wavelength instability. We do so by means of a direct expansion in the amplitude of the linearly least stable mode about the appropriate reference state which one considers. This is motivated by the observation that for some equations fully nonlinear chaotic dynamics has been found to be organized around periodic solutions that do not simply bifurcate from the basic (laminar) state. We apply the method to two model equations, a subcritical generalization of the Swift–Hohenberg equation and a novel extension of the Kuramoto–Sivashinsky equation that we introduce to illustrate the abovementioned scenario in which weakly chaotic subcritical dynamics is organized around periodic states that bifurcate “from infinity” and that can nevertheless be probed perturbatively. We explore the reliability and robustness of such an expansion, with a particular focus on the use of these methods for determining the existence and approximate properties of finite-amplitude stationary solutions. Such methods obviously are to be used with caution: the expansions are often only asymptotic approximations, and if they converge their radius of convergence may be small. Nevertheless, expansions to higher order in the amplitude can be a useful tool to obtain qualitatively reliable results.     

Quantum cyclotron resonance in a degenerate system. Quasienergetic states

We study the quantum dynamics of a charged particle rotating in a constant magnetic field and in the field of a monochromatic wave propagating perpendicular to the magnetic field under the condition of cyclotron resonance. Quasienergies and quasienergy functions are numerically calculated in the resonance approximation. The passage to the limit from the quantum model to the classical one is discussed.Lobachevskii State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 38, No. 3-4, pp. 232–240, March–April, 1995.     

Exciton-Boson Formalism in the Theory of Laser-Excited Semiconductors and Its Application in Coherent Four-Wave-Mixing Spectroscopy

By the use of a bosonization transformation and group-theoretical arguments, the Hamiltonian of an electron–hole–photon system in a laser-excited direct two-band semiconductor is transcribed into that of an exciton–photon system with the particle spins rigorously taken into consideration. It is shown that the third-order optical nonlinearities in the spectral region below the band edge have their microscopic origin in two-exciton correlations, which are expressed in terms of the effective exciton–exciton and anharmonic exciton–photon interactions. The dependence of the interparticle interactions on the spin states of quasiparticles is behind the polarization dependence of the semiconductor nonlinear optical response. On the example of the system of heavy hole excitons in quantum wells, grown from compounds with the zinc blende type of symmetry, it is demonstrated that the effective exciton–exciton interaction in two-exciton states with nonzero total spin is repulsive, while in zero-spin states it is attractive, which may result in the biexciton formation. The derived Heisenberg equations of motion for the exciton and biexciton operators form the basis for a theoretical study of the coherent four-wave-mixing in GaAs and ZnSe quantum wells. It is readily apparent from the equations that in different polarization configurations the coherent four-wave-mixing is generated by different ingredients of two-exciton Coulomb correlations: in the co-circular configuration, it is the interexciton repulsion, in the cross-linear configuration, the formation of the biexciton and its coupling to excitons, and in the collinear configuration, both of them jointly. The obtained expressions for the time-resolved and frequency-resolved four-wave-mixing signals adequately describe the main characteristics and various details of wave mixing phenomena, including a biexciton signature in the appropriate polarization configurations. Results of the work clarify the microscopic mechanism of the polarization dependence in coherent four-wave-mixing spectroscopy in semiconductor quantum wells.     

An algebraic approach to soliton solutions

Within the scope of a new algebraic method for the construction of soliton solutions of nonlinear equations [10–13], concrete examples of the system are considered which are connected with the algebra sl(2, R).     

Using Numerical Solutions in the Fourier Method for the Fokker–Planck–Kolmogorov Equation in the Analysis of First-Order Stochastic Nonlinear Systems for Nonlinear Detectors

We present a method for analyzing the characteristics of nonlinear detectors using the algorithms of first-order nonlinear differential equations. This method is based on numerical solutions of the Fokker–Planck–Kolmogorov (FPK) equations in the form of series of functions over Hermite–Chebyshev polynomials for both nonlinear systems and their linear counterparts. The results of the solutions for the linear case are extended to nonlinear systems in a recurrent way.     

Energy Eigenstates of a Quantum Gate System

We report exact solutions of the Poyatos–Cirac–Zoller quantum gate system withtwo trapped ions [Phys. Rev. Lett. 81, 1322 (1998)]. It is the superposition ofentangled states among the pure states of two harmonic oscillators and describesa mixed mode involving the center-of-mass and relative motions withcommensurable frequencies. Theoretical analysis of the exact solutions showsthat for a given trapping frequency the relative motion cannot be laser-cooled.     

Determination of the Constants of Binding of Acridine Dyes with Micelles of Sodium Dodecyl Sulfate Using the Quenching of Delayed Fluorescence by Heavy Atoms

The constants of binding dye molecules with the micelles of sodium dodecyl sulfate are determined using quenching of delayed fluorescence of acridine dyes by sodium iodide in aqueous–micellar solutions. Kinetic equations have been composed that describe the processes of deactivation of the excited states of dyes. By solving these equations at the concentration of the quencher sodium iodide corresponding to the minimum lifetime of triplet states and at the concentration of micelles corresponding to the least value of the delayed fluorescence quenching rate constants, we obtained the constants of binding dyes with micelles equal to 1.3·10⁷, 2.9·10⁷, and 3.1·10⁷ M^–1 for trypaflavine, acridine orange, and acridine yellow, respectively. We calculated the rate constants of quenching of the triplet states of the molecules of dyes by iodide ions (I ^–) that decreased in transition from trypaflavine to acridine orange and acridine yellow.