Resonance Approximation Research Articles

Control of electron current by double-barrier structures using pulsed laser fields

Tunneling current through a double-barrier structure is considered in a strong pulsed ac electric field. By absorbing and emitting photons, an electron is able to penetrate through the barriers. An analytical expression for the current is found in the resonance approximation for electric fields with slowly varying amplitudes. The time-dependent evolution of the current exhibits positive and negative amplitudes, depending on the intensity of the field. With an increase of temperature, the current increases substantially. At particular field intensities, a sequence of input laser pulses can be mapped to no pulses, a single pulse, or two pulses in the output electric current. Thus, the decoding of information is essentially impossible.

Resonant Raman scattering by charge-density and single-particle excitations in semiconductor nanostructures: A generalized interband-resonant random-phase-approximation theory

We develop a generic theory for the resonant inelastic light (Raman) scattering by a conduction band quantum plasma taking into account the presence of the filled valence band in doped semiconductor nanostructures within a generalized resonant random phase approximation (RPA). Our generalized RPA theory explicitly incorporates the two-step resonance process where an electron from the filled valence band is first excited by the incident photon into the conduction band before an electron from the conduction band falls back into the valence band emitting the scattered photon. We show that when the incident photon energy is close to a resonance energy, i.e. the valence-to-conduction band gap of the semiconductor structure, the Raman scattering spectral weight at single particle excitation energies may be substantially enhanced even for long wavelength excitations, and may become comparable to the spectral weight of collective charge density excitations (plasmon). Away from resonance, i.e. when the incident photon energy is different from the band gap energy, plasmons dominate the Raman scattering spectrum. We find no qualitative difference in the resonance effects on the Raman scattering spectra among systems of different dimensionalities (one, two and three) within RPA. This is explained by the decoherence effect of the resonant interband transition on the collective motion of conduction band electrons. Our theoretical calculations agree well (qualitatively and semi-quantitatively) with the available experimental results, in contrast to the standard nonresonant RPA theory which predicts vanishing long wavelength Raman spectral weight for single particle excitations.

High-frequency magnetoconductivity of electrons in non-uniform heterostructures

The high-frequency response of electrons in δ-doped heterostructures with long-scale disorder due to non-uniform donor distribution is studied theoretically. The non-local regime of response is considered when the scale of the variation of the energy level is shorter than the mean free path. The linearized kinetic equation for the elastic scattering case together with the electric neutrality condition are solved in the resonant approximation. The obtained modifications of the lineshape of the cyclotron absorption peak and of the Faraday effect appear to be significant under the condition ω c l c/ v F∼1, where ω c is the cyclotron frequency, l c is the correlation length of disorder, and v F is the Fermi energy. Numerical estimations are performed for the high-mobility AlGaAs/ GaAs heterojunction.

First-principles theory of the temperature and compositional dependence of atomic short-range order in disordered Cu-Pd alloys

We combine the first-principles, Korringa-Kohn-Rostoker coherent potential approximation based calculations of compositional fluctuations with a statistical mechanical ring approximation to study the temperature (T) and composition (c) dependence of the atomic short-range order (SRO) in disordered, face-centred cubic, Cu-Pd alloys. The fourfold splitting of SRO peaks around the equivalent $X(0,1,0)$ points in reciprocal space is obtained in a wide $T\ensuremath{-}c$ region. Such splitting is shown to be an ``energy'' effect caused by the absolute minima of the Fourier transform of the effective atomic interactions and related previously to the existence of nested sheets of the disordered alloy's Fermi surface. However, we find that the T dependence of the SRO peak position is mostly an ``entropy'' effect. Both the calculated T and c dependences of the SRO peaks position are in good correspondence with the experimental data. The real-space effective atomic interactions and SRO parameters indicate the tendency for longer-period structures with increasing Pd concentration, as observed.

Coherent x-ray source due to the quantum reflection of an electron beam from a laser-field phase lattice.

Within the scope of relativistic quantum theory for electron-laser interaction in a medium and using the resonant approximation for the two degenerated states of an electron in a monochromatic radiation field, a nonperturbative solution of the Dirac equation is obtained. The multiphoton cross sections of the electrons' coherent scattering on the plane monochromatic wave at the Cherenkov resonance are obtained, taking into account the specificity of an induced Cherenkov process and spin-laser interaction as well. As a result of coherent reflection from the "phase lattice" of a slowed plane wave in a medium, electron beam quantum modulation at high frequencies occurs. So, a coherent x-ray source in an induced Cherenkov process is expected, since such a beam is a potential source of coherent radiation itself.

Spectral density, memory function, and mean relaxation time for resonant subsystem-reservoir interactions

We show that the projection operators P usually employed to derive the Nakajima–Zwanzig master equation are non-Hermitian. As a consequence the operator QLQ which governs the dynamics of subsystem-reservoir interactions (here Q=1−P and L is the Liouville operator) is also non-Hermitian and possesses a complex temperature-dependent spectrum of resonances. We use the self-consistent Born approximation to derive a formula for the spectral density of QLQ. From this spectral density we calculate the memory function and mean relaxation time of subsystem-reservoir correlations. These formulas are compared with numerical results obtained from the spin–spin-bath model to test their accuracy. The memory function and mean relaxation time are essential ingredients for the SRA (statistical resonance approximation) theory of microscopic dissipation and decoherence. We show that the SRA master equation preserves positivity when the memory function derived in this paper is employed.

Use of the two channels method to determine the guided waves damping coefficients of an asymmetrically fluid-loaded plate: Theory and experiment

Exact and approximate formalisms describing the interactions of acoustic plane waves with an elastic isotropic plate immersed between two different fluids are presented. This is an extention of the Fiorito, Madigosky, and Berall (FMU) theory. Resonant approximations are given for the reflection and transmission coefficients, which assume light fluids loading. These approximations show that the resonance widths are the sum of two independent partial widths, each of them being related to one fluid and to the plate physical properties. In addition, experimental results are presented for a steel plate; the damping coefficients of the propagating leaky Lamb waves along the loaded plate are measured in two different loading situations. In the first situation the plate is embedded in water (water loading on both sides), while in the second situation it is loaded with water on one side and acetone on the other side. The experimental damping coefficient of the acetone-steel-acetone structure is deduced therefrom. The damping coefficient obtained in each case is then compared to the theoretical half resonance width, and the experimental results are found to be in good agreement with the theoretical predictions.

Dynamical stability of an ion in a linear trap as a solid-state problem of electron localization

When an ion confined in a linear ion trap interacts with a coherent laser field, the internal degrees of freedom, related to the electron transitions, couple to the vibrational degree of freedom of the ion. As a result of this interaction, the quantum dynamics of the vibrational degree of freedom becomes complicated, and in some ranges of parameters even chaotic. We analyze the vibrational ion dynamics using a formal analogy with the solid-state problem of electron localization. In particular, we show how the resonant approximation used in analysis of the ion dynamics, leads to a transition from a two-dimensional (2D) to a one-dimensional problem (1D) of electron localization. The localization length in the solid-state problem is estimated in cases of weak and strong interaction between the sites of the 2D cell by using the methods of resonance perturbation theory, common in analysis of 1D time-dependent dynamical systems. We show that the localization length can be used as an indicator of the effective temperature of the trapped ion, which can be experimentally measured.

RPA quasi-elastic responses in infinite and finite nuclear systems

Quasi-elastic responses in nuclear matter and in 12C and 40Canuclei are calculated with the ring approximation to investigate the finite-sizeeffects on the electromagnetic quasi-elastic responses. A method tosimulate these effects in infinite-systems calculations is proposed. Thesensitivity of the results to the various terms of the residual interactionis studied. The results of nuclear matter random-phase approximation calculations arecompared with those obtained in the ring approximation to demonstrate the importanceof the exchange terms.

𝕊-matrix theory applied to acoustic scattering by asymmetrically fluid-loaded elastic isotropic plates

Exact and approximate formalisms describing the interactions of acoustic plane waves with an elastic isotropic plate immersed between two different fluids (asymmetrically fluid-loaded plate) are presented. This constitutes an extension of the Fiorito, Madigosky, and Überall (FMU) [R. Fiorito et al., J. Acoust. Soc. Am. 66, 181 (1979)] theory, refined later by Freedman [A. Freedman, J. Sound Vib. 82, 181 (1982); ibid. 82, 197 (1982)]. The method, based upon the multichannel resonant scattering theory derived from quantum physics [A. Bohm, Quantum Mechanics, Foundations, and Applications (Springer, New York, 1993)], consists of two parts. First, a 2×2 scattering 𝕊-matrix in which the diagonal elements are the two reflection coefficients and the off-diagonal elements are the two transmission coefficients, is built. Second, in order to compare our results with the FMU theory, resonant approximations are given for these coefficients, assuming light fluids when compared to the plate. The approximated coefficients show that the resonance widths are the sum of two independent partial widths, each of them being related to one fluid and to the plate physical properties. Of importance in this extension is the fact that the eigenvalues of the matrix, which reveal all the resonant features of the immersed plate, allow the separation between antisymmetrical and symmetrical modes, contrary to the reflection and transmission coefficients. The eigenvalues also allow the analysis of resonances despite the overlapping phenomenon. For the computations, the exact coefficients and eigenvalues, rather than their approximate forms, are used. This allows us to check the validity of the exact part of the theory under any fluid loading and not especially for light fluid loading.

Dissipation in media with memory: A master equation in the statistical resonance approximation

A non-Markovian master equation is derived for the reduced probability density matrix of a subsystem interacting with a general reservoir of coupled anharmonic modes. Relaxation of the subsystem is mediated through resonant interactions with the reservoir. These interactions correspond to local vibrational motions with finite lifetimes due to diffusion/dephasing. The derivation assumes that the density of these interaction modes is very large so that they can be treated using statistical methods. The resulting master equation is shown to preserve probability, Hermiticity, and translational invariance, and conditions are stated which guarantee the positivity of the reduced density. At long time the master equation reduces to a Markovian equation of dynamical semigroup type. In the high temperature limit the theory is parameter free, and shows good agreement with the exact master equation of a spin-boson system.

Relativistic Calculation of Dielectronic Recombination on the C4+ Ground State

The relativistic multichannel theory has been applied and a nonperturbativeformula adopted to calculate the dielectronic recombination cross sectiondue to ΔN = 1 resonances for the ground state C4+. Thefirst-order approximation is adopted for the radiative process and acorrection based on the isolated resonance approximation is used for thevery narrow resonances to include the radiation width. The convoluted crosssection is in agreement within 5% with that of observation for resonanceswith n⩽5. For n = 6 and 7, the integral cross section isoverestimated by a factor of 6 and 4, respectively. According to ourcalculation, the Rydberg cut-off due to field ionization should be at aprincipal quantum number higher than that given by Mannervik et al. Asmall relativistic effect is noticed at intrashell resonance.

Effect of static displacements of the host atoms on short-range order in the hydrogen subsystem of Ni-H solution

Abstract The temperature and concentration dependences of the short-range order (SRO) parameters and their Fourier transform in H subsystem distributed on the octahedral interstices of fcc Ni are analysed, taking into account both direct (electrochemical) and indirect (strain-induced) contributions into the H-H interaction. The parameters of the electrochemical H-H interaction are estimated within the framework of the semiempirical approximation for atom-atom potentials. In order to calculate the energy parameters of the H-H strain-induced intraction, the Matsubara-Kanzaki-Krivoglaz lattice-statics method is applied. We demonstrate that, in the framework of the considered model, the strain-induced part mainly contributes to the total H-H interatomic mixing potential. For a description of the H-H SRO, the high-accuracy analytical (so-called ring) approximation is used. It is revealed that, for all considered values of the H concentration c = 0.10. 0.25 and 0.50. the H-H SRO Fourier transform is characteriz...

Density fluctuations and entropy

A functional for the entropy that is asymptotically correct both in the high- and low-density limits is proposed. The new form is S=S((id))+S((ln))+S((r))+S((c)), where the term S((c)) depends on the p-body density fluctuations alpha(p) and has the form S((c))/k=<N>ln 2-1+ summation operator(infinity)(p=2) (ln 2)(p)/p! alpha(p)-[exp(alpha(2)-1)-alpha(2)]+Sinsertion mark. Sinsertion mark renormalizes the ring approximation S((r)). This result is obtained by analyzing the functional dependence of the most general expression of the entropy. Two main results for S((c)) are proved: (i) In the thermodynamic limit it is only a functional of the one-body distribution function and (ii) by summing to infinite order the leading contributions in the density a numerical expression for the entropy [Eq. (33)] with a renormalized ring approximation is obtained. The relation of these results to the incompressible approximation for the entropy is discussed and preliminary numerical results on hard spheres are presented.

Interaction of a vortex ring with the free surface of an ideal fluid

The interaction of a small vortex ring with the free surface of a perfect fluid is considered. In the frame of the point ring approximation, the asymptotic expression for the Fourier components of radiated surface waves is obtained in the case when the vortex ring comes from infinity and has both horizontal and vertical components of the velocity. The nonconservative corrections to the equations of motion of the ring, due to Cherenkov radiation, are derived.

Surface- and volume-plasmon excitations in electron inelastic scattering on metal clusters

In this work we treat inelastic scattering of fast electrons on metal clusters in the range of transferred energies above the ionization threshold. We demonstrate that in this energy range many-electron collective excitations, namely, the volume plasmons, provide dominating contribution to the differential cross section resulting in its resonance behavior. The volume-plasmon resonances excited in the cluster during the collision decay via the ionization process. We determine the resonance frequency and the autoionization width of the volume plasmon excitations. In order to elucidate the role of plasmon excitations, we calculate the differential cross section of the process using two different approaches. We calculate the cross section in the random-phase approximation using the Hartree-Fock wave functions as a basis and accounting simultaneously for all single-particle and collective excitations in the cluster. We compare the results of this approach with those obtained in the plasmon resonance approximation.

Symmetry of quantum phase space in a degenerate Hamiltonian system

The structure of the global “quantum phase space” is analyzed for the harmonic oscillator perturbed by a monochromatic wave in the limit when the perturbation amplitude is small. Usually, the phenomenon of quantum resonance was studied in nondegenerate [G. M. Zaslavsky, Chaos in Dynamic Systems (Harwood Academic, Chur, 1985)] and degenerate [Demikhovskii, Kamenev, and Luna-Acosta, Phys. Rev. E 52, 3351 (1995)] classically chaotic systems only in the particular regions of the classical phase space, such as the center of the resonance or near the separatrix. The system under consideration is degenerate, and even an infinitely small perturbation generates in the classical phase space an infinite number of the resonant cells which are arranged in the pattern with the axial symmetry of the order 2μ (where μ is the resonance number). We show analytically that the Husimi functions of all Floquet states (the quantum phase space) have the same symmetry as the classical phase space. This correspondence is demonstrated numerically for the Husimi functions of the Floquet states corresponding to the motion near the elliptic stable points (centers of the classical resonance cells). The derived results are valid in the resonance approximation when the perturbation amplitude is small enough, and the stochastic layers in the classical phase space are exponentially thin. The developed approach can be used for studying a global symmetry of more complicated quantum systems with chaotic behavior.

Effect of Normal Strains in Buckling of Thick Orthotropic Shells

An improved elasticity solution to the problem of buckling of orthotropic cylindrical shells sub- jected to external pressure is presented. The 2D axisymmetric cylindrical shell is studied (ring approximation). Specifically, in the development of the governing equations and boundary conditions for the buckling state, the solution includes the terms with the prebuckling normal strains and stresses as coefficients (i.e., the terms and , which were neglected in the earlier work as being too small compared to the terms and 00 e s9 s e9 s9 kk ij kk ij ij , respectively). The formulation results in a two-point boundary eigenvalue problem for ordinary differential 0 sv 9 kk j equations in r, with the external pressure p as the parameter. The results show that the effect of including the normal strains and stresses is to further decrease the critical load. This decrease (versus the earlier elasticity solution without these terms) depends on the shell thickness and is generally moderate, and in no event com- parable with the (quite large) decrease of the elasticity versus the shell theory prediction. This decrease depends also on the degree of orthotropy, and it is smaller for the isotropic case. Finally, a formula is derived for the critical pressure based on a first-order shear deformation formulation, and the comparison shows an improvement versus the classical shell for thick shells, but still the elasticity solution is noticeably lower than the first-order shear deformation prediction.

Inhomogeneous broadening of intersubband transitions due to nonscreening roughness of heterointerfaces

The shape of the terahertz absorption peak in quantum wells with rough heterointerfaces is studied. Although the long-range variations of the ground level are screened in heavily doped structures, the intersubband in-plane energy remains nonuniform due to the second-level variations. The equation for intersubband polarization is considered in the resonant approximation, taking into account the depolarization shift. The line shape of the intersubband absorption peak is described for the case with long-range variations of heterointerfaces.

Energies, widths and spectral features of the 3Pe resonances of H-

The resolution of the spectrum of 3P H- up to the n = 5 threshold has been achieved to very high accuracy via the state-specific solution of the complex eigenvalue Schrödinger equation, using as a cut-off limit resonance states of widths of about 10-9 au. In this energy region and for this cut-off value, we identified one discrete state, the 2p2 3P and 31 resonance states. We show how an appropriate analysis of the energies, widths and wavefunction characteristics leads to the classification of series of states into unperturbed and perturbed, using the Gailitis-Damburg dipole resonance approximation as the zero-order model. Two loner states are present: the discrete state below the n = 2 threshold and a resonance state below the n = 4 threshold, which overlaps the third member of the dipole resonance series.