Direct measurement of the spatial displacement of Bloch-oscillating electrons in semiconductor superlattices

We present a novel experimental technique which allows to precisely measure the spatial displacement of Bloch-oscillating electrons in semiconductor superlattices as a function of time: The dipole field caused by the motion of the electrons is traced by small shifts of the Wannier–Stark ladder states. The electron wave packet displacement can then be derived from these shifts with the excitation density as the only free parameter. Using this method, we show that the optically generated electron wave packets perform harmonic oscillations, as predicted by Zener for the semiclassical motion of electrons in 1934. The absolute amplitudes of the wave packets depend inversely on the static field and are close to the values expected from semiclassical theory.     

Dust ion-acoustic wave oscillations in single-walled carbon nanotubes

In this paper, a charged single-walled carbon nanotube that surrounded by charged nanoparticles is modeled as a cylindrical shell of electron–ion–dust plasma. By employing the fluid theory for electron–ion–dust plasma, the dispersion relation of the dust ion-acoustic wave oscillations in the composed system is studied. For negatively charged dust particles, with increasing dust charge density, the phase velocity of the dust ion-acoustic wave will increase in comparison to the pure ion-acoustic wave oscillations.     

Quantum Cosmology in CGBD Theory

We apply the theory developed in quantum cosmology to a model of charged generalized Brans–Dicke gravity. This is a quantum model of gravitation interacting with a charged Brans–Dicke type scalar field which is considered in the Pauli frame. The Wheeler–DeWitt equation describing the evolution of the quantum Universe is solved in the semiclassical approximation by applying the WKB approximation. The wave function of the Universe is also obtained by applying both the Vilenkin-like and the Hartle–Hawking-like boundary conditions. We then make predictions from the wave functions and infer that the Vilenkin's boundary condition is more reasonable in the Brans–Dicke gravity models leading a large vacuum energy density at the beginning of the inflation.     

Quantum corrections to the conductivity and periodic orbits: Integrable systems

We extend the recently developed semiclassical theory for the conductivity to periodic semiconductor structures whose classical dynamics is integrable. We find that the conductivity of integrable systems exhibits quantum oscillations as function of magnetic field and Fermi energy which are closely related to both the Shubnikov-de Haas oscillations and the oscillations observed in the conductivity of antidot lattices. A general expression for the quantum oscillations is derived which is analogous to the Berry-Tabor formula for the spectral density of integrable systems.     

The effects of macroscopic inhomogeneities on the magnetotransport properties of the electron gas in two dimensions

In experiments on electron transport, the macroscopic inhomogeneities in the sample play a fundamental role. In this paper and a subsequent one, we introduce and develop a general formalism that captures the principal features of sample inhomogeneities (density gradients, contact misalignments) in the magnetoresistance data taken from low-mobility heterostructures. We present detailed assessments and experimental investigations of the different regimes of physical interest, notably the regime of semiclassical transport at weak magnetic fields, the plateau–plateau transitions as well as the plateau–insulator transition that generally occurs at much stronger values of the external field only.It is shown that the semiclassical regime at weak fields plays an integral role in the general understanding of the experiments on the quantum Hall regime. The results of this paper clearly indicate that the plateau–plateau transitions, unlike the plateau–insulator transition, are fundamentally affected by the presence of sample inhomogeneities. We propose a universal scaling result for the magnetoresistance parameters. This result facilitates, amongst many other things, a detailed understanding of the difficulties associated with the experimental methodology of H.P. Wei et al. in extracting the quantum critical behavior of the electron gas from the transport measurements conducted on the plateau–plateau transitions.     

Escape of photo-detached electron from an annular nanomicrocavity

The escaped probability density of the photo-detached electron in an annular nanomicrocavity shows strong oscillations as a function of the length of the escape orbits. We present a semiclassical theory that describes theses oscillations in terms of bundles of escape orbits. Due to the interference effects of the electron waves travelling along different escaped orbits, oscillatory structures appear in the escaped probability density. In addition, the calculation results suggest that the escaped probability density of the photo-detached electron is not only related to the inner radius of the annular microcavity, but also related to the laser polarization. In order to show the correspondence between the escaped probability density and the detached electron’s escaped orbits clearly, we calculate the Fourier transformed semiclassical wave function and find that the peak positions agree well with the length of the detached electron’s orbits. We hope that our results will be useful in understanding the escape and propagation process of particles through semiconductor microjunctions or ballistic microstructure.     

Spectral Statistics of the Rectangular Billiard with a Flux Line

The density of states of a rectangular billiard with an Aharonov–Bohm flux line in its center was calculated in the semiclassical approximation and was used for the calculation of the form factor in the diagonal approximation. The distribution of nearest level spacings and the form factor were calculated also numerically. For some values of the flux these were found to be close to the ones of the semi-Poisson statistics. The difference between the numerical results and the semiclassical ones were found to be much larger than for chaotic and for integrable systems within similar approximations. Possible reasons for these discrepancies are discussed.     

Analytical results for the electronic shell structure in mesoscopic systems: Balian-Bloch type theory for spheres,discs, rings and anti-dot lattices

The electronic shell structure resulting from the interference of closed orbital paths is determined for mesoscopic systems like spherical clusters, discs and rings by extending the semiclassical theory of Balian and Bloch. Analytical results for the shell structure in the density of states are obtained. Thus, the dependence of the shell structure on dimension, size and geometry and potential of the mesoscopic system and on an external magnetic field can be studied systematically. Comparison of the semiclassical results and those of quantum mechanical calculations permits analysis of typical quantum mechanical effects and shows the validity of the semiclassical theory. Our results should stimulate new experiments, can be used to calculate oscillations in the binding-energy, ionization-potential, and can be applied to analyze oscillations in the electronic density of states of quantum dot systems like anti-dot lattices.     

Semiclassical Correspondence Principle for Charge Motion and Spin Precession in a Homogeneous Magnetic Field

Solutions to the classical equation of charge motion and the Bargmann–Michel–Telegdi spin equation are derived within a semiclassical approximation (for high energy levels) using the associated solutions to the Dirac–Pauli equation.     

Stark Broadening of Ne II and Ne III Spectral Lines

Using a semiclassical approach, the widths and shifts of the spectral lines of three Ne II and six Ne III multiplets caused by collisions with electrons, protons, and helium ions at a density of perturbing particles of 10¹⁷ cm^–3 and different temperatures have been calculated. The results obtained have been compared with the known experimental and theoretical data.     

Spin–orbit coupling and semiclassical electron dynamics in noncentrosymmetric metals

Spin–orbit coupling of electrons with the crystal lattice plays a crucial role in materials without inversion symmetry, lifting spin degeneracy of the Bloch states and endowing the resulting nondegenerate bands with complex spin textures and topologically nontrivial wavefunctions. We present a detailed symmetry-based analysis of the spin–orbit coupling and the band degeneracies in noncentrosymmetric metals. We systematically derive the semiclassical equations of motion for fermionic quasiparticles near the Fermi surface, taking into account both the spin–orbit coupling and the Zeeman interaction with an applied magnetic field. Some of the lowest-order quantum corrections to the equations of motions can be expressed in terms of a fictitious “magnetic field” in the momentum space, which is related to the Berry curvature of the band wavefunctions. The band degeneracy points or lines serve as sources of a topologically nontrivial Berry curvature. We discuss the observable effects of the wavefunction topology, focusing, in particular, on the modifications to the Lifshitz–Onsager semiclassical quantization condition and the de Haas-van Alphen effect in noncentrosymmetric metals.     

Resonant tunneling through Andreev levels

We use a semiclassical approach for analyzing the tunneling transport through a normal conductor in contact with superconducting mirrors. Our analysis of the electron–hole propagation along semiclassical trajectories shows that resonant transmission through Andreev levels is possible resulting in an excess, low-energy quasiparticle contribution to the conductance. The excess conductance oscillates with the phase difference between the superconductors having maxima at odd multiples of π for temperatures much below the Thouless temperature.     

Two-dimensional electron gas in a lattice of antidots with a period of 80 nm

The magnetotransport in a two-dimensional electron gas with a lattice of antidots, which has a record-breaking small (80 nm) period and size (20–40 nm) of antidots comparable with the de Broglie wavelength of electrons, has been experimentally studied. A wide variety of new features of the magnetoresistance behavior has been observed both under semiclassical conditions and in the regime of quantizing magnetic fields. In particular, the anomalous semiclassical magnetoresistance peak induced by the nonmonotonic scattering effects has been revealed. The Shubnikov-de Haas oscillations have been revealed to exhibit an unusual transition from the anomalous period constant in the magnetic field to the normal constant in the inverse magnetic field. The effect of the generation and suppression of the oscillations has also been observed; this effect is induced by the transformation of the short and long-range scattering potentials in the lattice owing to the variation of the density of the two-dimensional electrons.     

The Aharonov–Bohm Phase Shift and Boyer's Critical Considerations: New Experimental Result but Still an Open Subject?

The main experiments concerning the Aharonov–Bohm phase shifts, seen in an electron interference pattern, and their Boyer semiclassical explanations are reviewed. A new experiment is also presented which emphasizes the subtleties involved in the interpretations of the magnetic Aharonov–Bohm phase shift as a result of a non-dispersive or dispersive effect.     

Interaction Dynamics of the External and Internal Degrees of Freedom of an Atom in the Resonant Field of a Standing Light Wave

The theory of the dynamic interaction of the external (translational) and internal (electronic) degrees of freedom of a twolevel atom in the field of a standing light wave in a perfect cavity of the Fabry–Perot type was developed. The theory describes the energy exchange between three subsystems, namely, translational, electronic, and field subsystems, as opposed to the theories of the parametric interaction (in the approximations of Raman–Nath and/or large resonance detuning) and of the atomic motion in free space. In the semiclassical approximation, the corresponding Heisenberg equations of motion were shown to form a closed Hamiltonian dynamic system with two degrees of freedom, namely, translational and collective electron–field degrees of freedom. This system is integrated in terms of the elliptic Jacobian functions in the resonance limit. The solutions obtained describe the effects of trapping of an atom in the periodic potential of the standing light wave, and its cooling and heating, as well as the effect of the dynamic Rabi oscillations. The latter is caused by the interaction of the internal and external atomic degrees of freedom through the radiation field.     

The LIF Excitation Spectrum of Jet-Cooled 2,6-Dicyano-3, 5-Dimethylaniline

The laser-induced fluorescence (LIF) excitation spectrum of jet-cooled 2, 6-dicyano-3,5-dimethylaniline (DCDMA) has been measured in the spectral range of 29,750–32,250cm^–1. The band origin at 29,860.8 cm^–1 and as many as 250 vibrational bands have been identified in the excitation spectrum. The analysis of the excitation spectrum of DCDMA gives more than 28 vibrational modes involving aromatic ring oscillations and oscillations related to the substituent groups. DCDMA is nonplanar in the ground state, with the NH₂ plane at about 9° with respect to the molecular plane (RHF/6-31G*). The singlet excited molecule is planar (CIS/6-31G*). Both CIS/6-31G* and CASPT2 calculations predict that the lowest excited state of DCDMA involves a dominant HOMO-LUMO excited configuration. The characteristic feature of the excitation spectrum of DCDMA is the presence of progressions in the low-frequency mode, 112 cm^–1. The calculations suggest that this mode and some other active modes involve motions of the amino group and strongly interacting adjacent cyano substituents.     

Higher-derivative Quantum Cosmology

The quantum cosmology of a higher-derivative gravity theory arising from the heterotic string effective action is reviewed. A new type of Wheeler–DeWitt equation is obtained when the dilaton is coupled to the quadratic curvature terms. Techniques for solving the Wheeler–DeWitt equation with appropriate boundary conditions shall be described, and implications for semiclassical theories of inflationary cosmology will be outlined.     

Algebraically Self-Consistent Quasiclassical Approximation on Phase Space

The Wigner–Weyl mapping of quantum operators to classical phase space functions preserves the algebra, when operator multiplication is mapped to the binary * operation. However, this isomorphism is destroyed under the quasiclassical substitution of * with conventional multiplication; consequently, an approximate mapping is required if algebraic relations are to be preserved. Such a mapping is uniquely determined by the fundamental relations of quantum mechanics, as is shown in this paper. The resultant quasiclassical approximation leads to an algebraic derivation of Thomas–Fermi theory, and a new quantization rule which—unlike semiclassical quantization—is non-invariant under action transformations of the Hamiltonian, in the same qualitative manner as the true eigenvalues. The quasiclassical eigenvalues are shown to be significantly more accurate than the corresponding semiclassical values, for a variety of 1D and 2D systems. In addition, certain standard refinements of semiclassical theory are shown to be easily incorporated into the quasiclassical formalism.     

Double-quantum nutations in a two-level spin system

We report experimental results of the oscillatory response of a two-level spin system (E'₁ centres in glassy silica) excited by a step-modulated radiation tuned to the double-quantum (DQ) resonance. On the basis of a semiclassical calculation of the transient regime, the observed oscillations are ascribed to the nutations of the DQ transitions.     

Particle Creation in the Oscillatory Phase of Inflaton

A thermal squeezed state representation of inflaton is constructed for a flat Friedmann–Robertson–Walker (FRW) background metric and the phenomenon of particle creation is examined during the oscillatory phase of inflaton, in the semiclassical theory of gravity. An approximate solution to the semiclassical Einstein equation is obtained in thermal squeezed state formalism perturbatively and is found obey the same power-law expansion as that of classical Einstein equation. In addition to that the solution shows oscillatory in nature except on a particular condition. It is also noted that, the coherently oscillating nonclassical inflaton, in thermal squeezed vacuum state, thermal squeezed state, and thermal coherent state, suffers particle production and the created particles exhibit oscillatory behavior. The present study can account for the postinflation particle creation due to thermal and quantum effects of inflation in a flat FRW universe.