Fictitious-Time Wave-Packet Dynamics in Atomic Systems

Effects of external electric and magnetic fields on the linear and nonlinear optical properties of InAs cylindrical quantum dot with modified Pöschl-Teller and Morse confinement potentials

In classical mechanics the harmonic oscillator (HO) provides the generic example for the use of angle and action variables and I > 0 which played a prominent role in the “old” Bohr‐Sommerfeld quantum theory. However, already classically there is a problem which has essential implications for the quantum mechanics of the (φ,I)‐model for the HO: the transformation is only locally symplectic and singular for (q,p) = (0,0). Globally the phase space {(q,p)} has the topological structure of the plane ℝ2, whereas the phase space {(φ,I)} corresponds globally to the punctured plane ℝ2 ‐(0,0) or to a simple cone with the tip deleted. From the properties of the symplectic transformations on that phase space one can derive the functions h0 = I, h1 = Icos φ and h2 = ‐Isin φ as the basic coordinates on {(φ,I)}, where their Poisson brackets obey the Lie algebra of the symplectic group of the plane. This implies a qualitative difference as to the quantum theory of the phase space {(φ,I)} compared to the usual one for {(q,p)}: In the quantum mechanics for the (φ,I)‐model of the HO the three hj correspond to the self‐adjoint generators Kj, j = 0,1,2, of certain irreducible unitary representations of the symplectic group or one of its infinitely many covering groups, the representations being parametrized by a (Bargmann) index k > 0. This index k determines the ground state energy of the (φ,I)‐Hamiltonian . For an m‐fold covering the lowest possible value for k is k = 1/m, which can be made arbitrarily small by choosing m accordingly! This is not in contradiction to the usual approach in terms of the operators Q and P which are now expressed as functions of the Kj, but keep their usual properties. The richer structure of the Kj quantum model of the HO is “erased” when passing to the simpler (Q,P)‐model! This more refined approach to the quantum theory of the HO implies many experimental tests: Mulliken‐type experiments for isotopic diatomic molecules, experiments with harmonic traps for atoms, ions and BE‐condensates, with charged HOs in external electric fields and the (Landau) levels of charged particles in external magnetic fields, with the propagation of light in vacuum, passing through strong external electric or magnetic fields. Finally it may lead to a new theoretical estimate for the quantum vacuum energy of fields and its relation to the cosmological constant.

Recent laboratory and epidemiological results have stimulated interest in the hypothesis that human beings may exhibit biological responses to magnetic and/or electric field transients with frequencies in the range between 100 Hz and 100 kHz. Much can be learned about the response of a system to a transient stimulation by understanding its response to sinusoidal disturbances over the entire frequency range of interest. Thus, the main effort of this paper was to compare the strengths of the electric fields induced in homogeneous ellipsoidal models by uniform 100 Hz through 100 kHz electric and magnetic fields. Over this frequency range, external electric fields of about 25-2000 V/m (depending primarily on the orientation of the body relative to the field) are required to induce electric fields inside models of adults and children that are similar in strength to those induced by an external 1 microT magnetic field. Additional analysis indicates that electric fields induced by uniform external electric and magnetic fields and by the nonuniform electric and magnetic fields produced by idealized point sources will not differ by more than a factor of two until the sources are brought close to the body. Published data on electric and magnetic field transients in residential environments indicate that, for most field orientations, the magnetic component will induce stronger electric fields inside adults and children than the electric component. This conclusion is also true for the currents induced in humans by typical levels of 60 Hz electric and magnetic fields in U.S. residences.

In this study, for the first time, the combined effects of external magnetic, electric, and Aharonov-Bohm (AB) flux fields on quantum levels of the hydrogen atom embedded in Debye and quantum plasmas modeled by the more general exponential cosine screened Coulomb (MGECSC) potential are investigated within cylindrical coordinate formalism using the asymptotic iteration method. The MGECSC potential includes four different potential forms when considering different sets of the parameters in the potential. The corresponding Schrödinger equation is solved numerically in order to examine both strong and weak regimes and confinement effects of external fields. The influence of screening parameters of the MGECSC potential on quantum levels of the hydrogen atom is also studied in detail in the presence of external magnetic, electric, and AB flux fields. As it is possible to model both Debye and quantum plasmas by using screening parameters in the MGECSC potential, the effects of each plasma environment on quantum levels of the hydrogen atom are also considered in the external fields. It is observed that there are important results of external fields on the total interaction potential profile, and the most dominant one in these fields is the magnetic field. Furthermore, the effects of confinement on the physical state of the plasma environment is a subject of this study. These details would be important in experimental and theoretical investigations in plasma and atomic physics fields.

Energy dispersion and electron g-factor of quantum wire in external electric and magnetic fields with Rashba spin orbit interaction

It is theoretically proved that the excited wave in two-valley semiconductors is growing. It is indicated that the directions of external fields play an essential role for the appearance of growing waves in the sample. It is shown that oscillations can occur at certain values of the sample dimensions L ,L ,L x y z Analytical formulas for the frequency of the growing waves are obtained. The interval of variation of the external electric field in a strong magnetic field μH>>c has been determined. The paper takes into account that the time of transition from the lower valley to the upper valley differs from the time of transition from the upper valley to the lower valley. It means τ12≠τ21 In the sample, the total concentration is constant, and therefore, n0=na+nb=const. The changes in the corresponding concentrations are equal to each other and have na'=-nb'. It is taken into account that at critical values of the electric and magnetic fields and the corresponding concentrations they change as a monochromatic wave. And the change in these quantities differs little from their equilibrium value. For simplicity of mathematical calculations, the external electric and magnetic fields are directed in the same way, i.e. in x direction. Since the current oscillations in one direction (for example, along x) are studied in the experiment, the following equalities were taken into account jy'=0, jz'=0. In the vicinity of the critical field at the beginning of the current oscillation in the sample, the current oscillation frequency is ϖ=ϖ0+iϖ1, ϖ1<<ϖ0. In addition, the magnitude of the critical electric field, at which the current fluctuation changes depending on the magnetic field as follows .

We derive an analytical solution to the time-dependent Schrödinger equation for the transmission of a Gaussian wave packet through an arbitrary potential of finite range. We consider the situation where the initial Gaussian wave packet is sufficiently broad in momentum space to include the full resonance structure of the system in the dynamical description. We find that the transmitted wave packet may be written as the free evolving Gaussian wave packet solution times a transient term. We demonstrate that both at very large distances and very long times the transient term tends to the transmission amplitude of the system and hence the time-evolving solution reproduces the resonance spectra of the system. We also prove that at a fixed distance and very long times the analytical solution is t−3/2 which extends previous analysis on this issue to arbitrary finite-range potentials. Our results are exemplified for a multibarrier system.

Understanding the profile of a qubit's wave function is key to its quantum applications. Unlike conducting systems, where a scanning tunneling microscope can be used to probe the electron distribution, there is no direct method for solid-state-defect-based qubits in wide-band-gap semiconductors. In this work, we use pressure as a tuning method and a nuclear spin as an atomic scale probe to monitor the hyperfine structure of negatively charged nitrogen-vacancy (N-$V$) centers in diamonds under pressure. We present a detailed study on the nearest-neighbor ${}^{13}\mathrm{C}$ hyperfine splitting in the optically detected magnetic resonance spectrum of N-$V$ centers at different pressures. By examining the ${}^{13}\mathrm{C}$ hyperfine interaction upon pressurizing, we show that the N-$V$ hyperfine parameters have prominent changes, resulting in an increase in the N-$V$ electron spin density and rehybridization from $s{p}^{3}$ to $s{p}^{2}$ bonds. The ab initio calculations of strain dependence of the N-$V$ center's hyperfine levels are done independently. The theoretical results qualitatively agree well with experimental data without introducing any fitting parameters. Furthermore, this method can be adopted to probe the evolution of wave function in other defect systems. This potential capability could play a role in developing magnetometry and quantum information processing using the defect centers.

The recent discovery of borospherene B40 marks the onset of a new class of all-boron fullerenes. External electric field can influence the structure and property of molecule. It is necessary to understand the electrostatic field effect in the borospherene B40. In this work, density functional theory method at the PBE0 level with the 6-31G* basis set is used to investigate the ground state structures, mulliken atomic charges, the highest occupied molecular orbital (HOMO) energy levels, the lowest unoccupied molecular orbital (LUMO) energy levels, energy gaps, electric dipole moments, infrared spectra and Raman spectra of borospherene B40 under the external electric field within the range of values F=0-0.06 a.u.. The electronic spectra (the first 18 excited states contain excited energies, excited wavelengths and oscillator strengths) of borospherene B40 are calculated by the time-dependent density functional theory method (TD-PBE0) with the 6-31G* basis set under the same external electric field. The results show that borospherene B40 can be elongated in the direction of electric field and B40 molecule is polarized under the external electric field. Meanwhile, the addition of external electric field results in lower symmetry (C2v), however, electronic state of borospherene B40 is not changed under the external electric field. Moreover, the calculated results show that the electric dipole moment is proved to be increasing with the increase of the external field intensity, but the total energy and energy gap are proved to decrease with the increase of external field intensity. The addition of external electric field can modify the infrared and Raman spectra, such as the shift of vibrational frequency and the strengthening of infrared and Raman peaks. Furthermore, the calculated results indicate that the external electric field has a significant effect on the electronic spectrum of borospherene B40. The increase of the electric field intensity can lead to the redshift of electronic spectrum. With the change of the electric field intensity, the strongest excited state (with the biggest oscillator strength) can become very weak (with the small oscillator strength) or optically inactive (with the oscillator strength of zero). Meanwhile, the weak excited state can become the strongest excited state by the external field. The ground state properties and spectral properties of borospherene B40 can be modified by the external electric field. Our findings can provide theoretical guidance for the application of borospherene B40 in the future.

Effects of the medium fractionality and oscillating potential profiles on the Superarrivals of the Gaussian wave packets

We study the semiclassical dynamics of interacting electrons in a biased crystal lattice. A complex dynamical scenario emerges from the interplay between the Coulomb and the external electric fields. When the electrons are far apart, the Coulomb potential may be small compared to the external potential and the electrons oscillate with effective Bloch frequencies, determined by the local electric field. In the opposite case, nearby electrons either separate or form a bound pair, depending on the initial energy compared to the band width. The pair due to the Coulomb field is stable even in the absence of the external field.

Based on electro-magneto-rheological (EMR) effect, this paper presents a novel micro machining method to form an instantaneous tiny-grinding wheel to polish the surface of optical glass, ceramic and other rigid-fragile materials under both electric and magnetic field. Experiments were conducted to reveal the synergistic effect of electrorheological and magnethorheological effect, and the effects of process parameters, such as intensity of electric field, intensity of magnetic field, working time, machining gap between the workpiece and the needle-like tool, on material removal rate of glass surface. Experimental results confirm the effectiveness of the micro machining technique with EMR effect-based tiny-grinding wheel and the machining efficiency under the combination of electric and magnetic field is much greater than the one under applied external electric or magnetic field. The material removal rate of workpiece is directly proportional to the intensity of external electric field and will maintain stable when the voltage of external electric field reaches 2000v, while the material removal rate is directly proportional to the intensity of external magnetic field. The material removal rate markedly descends with the increase of the machining gap. In addition, the working time is directly proportional to the amount of material removal of workpiece, but inversely proportional to material removal rate.

Variational and wave packet perturbation theory methods are implemented to study the effects on photodissociation and scattering cross sections due to nonadiabatic coupling between two electronic potential energy surfaces. The simplest variational method we implemented can handle large coupling strengths between surfaces, but its restriction to one Gaussian wave packet per surface is found to be too severe in some instances. In such situations the wave packet perturbation theory, which coherently superimposes multiple Gaussians on each surface, overcomes the difficulties encountered by the variational method and is seen to give quite accurate photodissociation and Landau–Zener cross sections over a wide energy range, so long as the coupling between surfaces is reasonably small. In this paper we give details of the appropriate computational schemes to adopt for calculating photodissociation and scattering cross sections from propagating wave packets. In addition, we discuss the strengths and weaknesses of Gaussian wave packet methods for studying nonadiabatic effects.

The effect of an external static electric field on the grain growth in nanocrystalline Cu films was studied at different annealing temperatures. Transmission electron microscopy and x-ray diffraction indicate that the grain growth in Cu films is accelerated with various rates by an external electric field at different annealing temperatures. It is found that there is a coupling effect from the external electric and temperature fields on grain growth in Cu films during annealing. The growth rate is accelerated proportional to a factor $f(E)\ensuremath{\cdot}{\ensuremath{\mu}}^{T/100\text{ }\ifmmode^\circ\else\textdegree\fi{}\text{C}}$, which is determined from the theoretical derivation. The analysis indicates that the enhanced grain growth is achieved by the effect of the electric field on the vacancies migration and dislocation climb along grain boundaries.

Tuning of the vacuum Rabi exciton-photon coupling in semiconductor quantum microcavity structures by external electric and magnetic fields is presented. Contrasting effects due to the two external perturbations are found, principally due to the decrease of exciton oscillator strength in electric field and increase of oscillator strength in magnetic field. The strong coupling limit is easily achieved in these high quality structures with line widths on resonance as small as 1 meV. In addition to the tuning phenomena, the effects of exciton Zeeman splitting on the spectra and unexpected linewidth narrowing phenomena on resonance are reported.