Localization or tunneling in asymmetric double-well potentials

An asymmetric double-well potential is considered, assuming that the wells are parabolic around the minima. The WKB wave function of a given energy is constructed inside the barrier between the wells. By matching the WKB function to the exact wave functions of the parabolic wells on both sides of the barrier, for two almost degenerate states, we find a quantization condition for the energy levels which reproduces the known energy splitting formula between the two states. For the other low-lying non-degenerate states, we show that the eigenfunction should be primarily localized in one of the wells with negligible magnitude in the other. Using Dekker’s method (Dekker, 1987), the present analysis generalizes earlier results for weakly biased double-well potentials to systems with arbitrary asymmetry.     

Effects of barrier penetration on energy spectrum and wave functions in the path integral formalism

We present a systematic approximation scheme for the non-relativistic Green function in the path integral representation which takes into account barrier penetration effects on the energy spectrum and wave functions for potentials having several minima. The method is applied to the cases of a symmetric potential with two minima and to a periodic potential. The energy spectrum is shown to agree with the usual WKB results. For the first mentioned case we also determine the wave functions in the classically allowed and forbidden regions from the residues of the Green function. They agree with those obtained in the standard WKB approximation.     

Nonlocal potentials and their exact and approximate local and velocity-dependent equivalents

We show that good approximations to the exact equivalent local potential (ELP) and damping factor of a nonlocal Perey-Buck potential can be calculated in the partial wave WKB approximation of Horiuchi. The exact ELP and damping factor are obtained by means of a method previously given by one of us. We also confirm that an approximate ELP proposed by Bauhoff et al. is of comparable accuracy as the Horiuchi approximation. Thesel-dependent ELP's exhibit reduced attraction in the interior and provide a test for higher order WKB approximations. We subsequently obtain an equivalent velocity dependent potential (EVDP) which is even exactly wave function equivalent to the original nonlocal potential. This almost local potential, unlike the trivial equivalent local potential, is smooth and well-behaved and is therefore particularly useful in nuclear reactions where the off-shell behaviour of the potential is important.     

Improved calculation of band gap of Sr2Bi2O5 crystal using modified Becke–Johnson exchange potential

The electronic structure of Sr₂Bi₂O₅ is calculated by the scalar-relativistic full potential linearized augmented plane wave (FLAPW+lo) method using the modified Becke–Johnson potential combined with the local density approximation correlation (MBJ–LDA). Both the valence band maximum (VBM) and conduction band minimum (CBM) exist at the Γ-point, indicating that Sr₂Bi₂O₅ is a direct-band-gap material. The band gap is calculated to be 3.17 eV, which is very close to the experimental value. This result is in great contrast to the underestimation based on the GGA calculation. On the other hand, there is only a small difference in the effective masses of holes and electrons photogenerated near the VBM and CBM for the MBJ–LDA and GGA approaches. The optical properties of Sr₂Bi₂O₅ are calculated from the complex dielectric function ε(ω)=ε₁(ω)+iε₂(ω). A highly polarized peak is observed at 3.5 eV in the ε₂(ω) function. Furthermore, the absorption coefficient estimated from the MBJ–LDA is very similar to that from the experimental result.     

Origin of the triple decay-time in the low-energy emission of KI:TI

Non radiative transitions occuring between different minima on the ³T_1u potential surface of Tl⁺-like impurities in alkali-halides, have been studied by the WKB method to explain the presence of three different decay-times in the low-energy emission of KI:Tl.     

Stimulated Raman scattering of sub-millimeter waves in bismuth

A high-power sub-millimeter wave propagating through bismuth, a semimetal with non-spherical energy surfaces, parametrically excites a space-charge mode and a back-scattered electromagnetic wave. The free carrier density perturbation associated with the space-charge wave couples with the oscillatory velocity due to the pump to derive the scattered wave. The scattered and pump waves exert a pondermotive force on electrons and holes, driving the space-charge wave. The collisional damping of the decay waves determines the threshold for the parametric instability. The threshold intensity for 20 μm wavelength pump turns out to be ∼2×10¹² W/cm². Above the threshold, the growth rate scales increase with ω_o, attain a maximum around ω_o=6.5ω_p, and, after this, falls off.     

Structural, electronic, elastic and optical properties of fluoro-perovskite KZnF3

We determine the structural, electronic, elastic and optical properties of fluoro-perovskite KZnF₃ using the full potential linear augmented plane wave approach (FP-LAPW) based on the density functional theory (DFT). The exchange-correlation potential is treated by the local density approximation (LDA) and the generalized gradient approximation (GGA). The calculated structural parameters are in good agreement with the available data. We have obtained an indirect band gap. The effect of the pressure on the band gaps is investigated. We evaluate the elastic constants (C_ij), elastic moduli and the Debye temperature. The imaginary and the real parts of the dielectric function ε(ω) and some optical constants are also calculated.     

Oscillating two-stream instability of beat waves in a hot magnetized plasma

It is shown that an electrostatic electron plasma beat wave is efficiently unstable for a low-frequency and short-wave-length purely growing perturbation (ω, k), i.e. an oscillating two-stream instability in a transversely magnetized hot plasma. The nonlinear response of electrons and ions with strong finite Larmor radius effects has been obtained by solving the Vlasov equation expressed in the guiding-center coordinates. The effect of ion dynamics has been found to play a vital role around ω ∼ ω_ci, where ω_ci is the ion-cyclotron frequency. For typical plasma parameters, it is found that the maximum growth rate of the instability is about two orders higher when ion motion is taken into account in addition to the electron dynamics.     

Semiclassical scattering theory with complex trajectories. I. Elastic waves

The WKB approximation to the one-particle Schrödinger equation is used to obtain the wave function at a given point as a sum of semiclassical terms, each of them corresponding to a different classical trajectory ending up at the same point. Besides the usual, real trajectories, also possible complex solutions of the classical equations of motion are considered. The simplicity of the method makes its use easy in practical cases and allows realistic calculations. The general solution of the one-dimensional WKB equations for an arbitrary number of complex turning points is given, and the solution is applied to calculate the position of the Regge poles of the scattering amplitude. The solution of the WKB equations in three dimensions for a central analytical potential is also obtained in a way that can be easily generalized to N-dimensions, provided the problem is separable. A multiple reflection series is derived, leading to a separation of the scattering amplitude into a smooth “background” term (single reflection approximation) that can be treated using classical but complex trajectories and a second resonating term that can be treated using the Sommerfeld-Watson transformation. The physical interpretation of the complex solutions of the classical equations of motion is given: they describe diffractive effects such as Fresnel, Fraunhofer diffraction, or the penetration of the quantal wave into shadow regions of caustics. They arise also in the scattering by a complex potential in an absorptive medium. The comparison with exact quantal calculations shows an astonishingly good agreement, and establishes the complex semiclassical approximation as a quantitative tool even in cases where the potential varies rapidly within a fraction of a wavelength. An approximate property of classical paths is discussed. The general pattern of the trajectories depends only on the product ? = EΘ, and not on energy and angle separately. This property is confirmed by experiments and besides the signature it gives for the semiclassical behavior, it simplifies considerably the search for all trajectories scattering through the same angle. Finally, a general classification of the different types of elastic heavy ion cross sections is given.     

Correlation between the anisotropy of hopconduction magnetoresistance and reciprocal band masses in Ge

Near 70 kG the d.c. magnetoresistance of phonon-assisted hopping of charge carriers between shallow impurities is found to have an anistropy depending on the reciprocal effective mass calculated from the L₁ conduction band minima in the case of n-type Ge and from the heavy hole component of the Γ′₂₅ valence band maximum in case of p-type Ge. These correlations are discussed and it is suggested that they are connected with the symmetry of the impurity wave functions and that the magnetic field tends to remove the light hole component of an acceptor wave function.     

Influence of the sum frequency on optically pumped parametric amplifiers

Parametric traveling-wave interactions are calculated with the aid of a plane wave approximation, considering the 4 frequencies ω _s , ω _p , ω _I =ω _p ?ω _s and ω _Σ =ω _p +ω _s . Special attention is paid to the case where ω _p ?ω _s . Competition between parametric amplification and upconversion is studied as a function of phase matching and the results are illustrated by means of numerical examples. It is shown that parametric gain disappears if the linear combination of wave vectors, 2k _p-k_I-k_Σ, vanishes. In this situation upconversion with power gain up to about (ω _Σ /ω _s )² is possible. It is concluded that fork _p?k_s the sum frequency ω _Σ can significantly influence parametric forward amplification but does not affect backward wave amplification.     

Mixed alkali effects in Na/Ag β-alumina

Mixed Na/Ag β-aluminas show the characteristic mixed alkali effect. Pronounced minima in conductivity isotherms are accompanied by a corresponding maximum in the activation energy. An entirely new effect is a change in ac response at high frequencies. In the region of the so-called Jonscher dispersion, where σ_ac = Aωⁿ, n falls from about 0.6 in pure Ag and Na β-aluminas to about 0.2 near the conductivity minimum. It is suggested that this reflects the disappearance of collective many-body interactions among the mobile cations.     

Optical properties of the alkaline-earth fluorohalides matlockite-type structure SrFX (X=Cl, Br, I) compounds

The optical properties of the SrFX (X=Cl, Br, I) compound have been reported using the full potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code. We employed the generalized gradient approximation (GGA), which is based on exchange-correlation energy optimization to calculate the total energy. Also we have used the Engel-Vosko GGA formalism, which optimizes the corresponding potential for band structure calculations. Our calculations show that the valence band maximum (VBM) and conduction band minimum (CBM) are located at Γ resulting in a direct energy gap. We present calculations of the frequency-dependent complex dielectric function ε(ω) and its zero-frequency limit ε₁(0). We find that the value of ε₁(0) increases on decreasing the energy gap. The reflectivity spectra and absorption coefficient have been calculated and compared with the available experimental data.     

Commensurate photon-irradiated Fano-Kondo tunneling through a quantum dot embedded Aharonov-Bohm interferometer

The commensurate photon-irradiated mesoscopic transport in a strongly correlated quantum dot (QD) embedded Aharonov-Bohm (AB) interferometer has been investigated. We focus our investigation on the dynamic Kondo and Fano cooperated effect affected by the double commensurate MWFs with q=ω₂/ω₁ being an arbitrary integer, where ω₁ and ω₂ are the two frequencies of the fields. The general tunneling current formula is derived by employing the nonequilibrium Green's function technique, and the different photon absorption and emission processes induced nonlinear properties have been studied to compare with the single-field system where q=0. Our numerical calculations are performed for the special cases with two commensurate fields possessing q=1,2. The Kondo peak can be suppressed to be a Kondo valley for the case where the commensurate number q=1, and the Fano asymmetric structure exhibits in the differential conductance quite evidently. Different commensurate number q contributes different photon absorption and emission effects. However, the conductance for the case of q=2 possesses more peaks and heavier asymmetric structure than the situations of q=0,1. The enhancement of satellite peaks behaves quite differently for the two cases with q=1, and q=2. The asymmetric peak-valley structure is adjusted by the gate voltage, commensurate MWFs, AB flux, source-drain bias, and non-resonant tunneling strength to form novel Fano and Kondo resonant tunneling.     

Inverse problem in atom-atom scattering in WKB approach

The WKB phase of a scattering problem including high angular momenta can be written as a Jeffreys-Born integral, $${}^{\delta WKB}(\beta ,K) = - \frac{A}{{2K}}\int\limits_\beta ^\infty {\frac{{Q(t,K)tdt}}{{\sqrt {t^2 - \beta ^2 } }}} $$ where β=(l+1/2)/A is the reduced collision parameter. The quasipotential Q(t, K) defined by this formula is connected with the potential in an easily understandable way. Its introduction allows the solution of the inversion problem (in WKB approximation) by treating this formula as an integral equation forQ. It further permits to investigate the relation between potential and phase function. The evaluation of experimental atom-atom-scattering data, using a phase function with seven parameters is given as an example how potential parameters can be used. Potentials leading to observed differential cross sections thus can easily be computed. Computation times are about a factor 50 smaller than in conventional methods.     

Theory of the local field correction in an electron gas

The wave-vector- and frequency-dependent dielectric function ?(k,ω) of an electron gas can be expressed in terms of Lindhard's function and a complex local field correctionG(k,ω) which incorporates all the effects of dynamic exchange and correlation in the system. The general properties ofG(k,ω) are discussed, in particular the static and high-frequency limits. It is shown that for smallk, bothG(k, 0) andG(k, ∞) vary ask ², with different coefficients, but both determined by the average kinetic and potential energies per particle. For largek,G(k, ∞) varies again ask ² and it is argued that the same holds true forG(k, 0), with both coefficients (though different) determined by the average kinetic energy per particle. General formulas for the plasma dispersion relation and damping, involving, respectively, the real and imaginary parts ofG(k,ω), are given. The term in the plasma frequency which is proportional tok ² is given directly in terms of the average kinetic and potential energies per particle, a result true at all temperatures. A calculation of the frequency dependence ofG(k,ω), starting from the exact equation of motion for the particle-hole operator and employing a decoupling approximation introduced previously by Toigo and Woodruff, is presented. Explicit results forG(k,ω) are obtained for smallk and allω. The complete expressions forG(k, 0) andG(k, ∞) in this approximation have been obtained and are plotted.     

Second-order optical nonlinearities from χ gratings induced by holographic all-optical poling

The paper presents the second-order optical nonlinearities from χ⁽²⁾ gratings induced by holographic all-optical poling for azobenzene polymer. Second harmonic (SH) signal along the directions with two different vectors was measured. One is strong SH signal diffracted in the same direction as 2ω writing beam with wave vector k_2ω and the other is weak SH signal diffracted in the direction of wave vector of 4k_ω - k_2ω + Δk where k_ω is wave vector of ω beam and Δk is the wave vector mismatch whose vector is parallel to k_ω. The latter signal was used as a tool to monitor the formation of holographic χ⁽²⁾ gratings in real-time because it has off-axis wave vector different from both k_ω and k_2ω. The increase of 2ω intensity on poling process led to the large increase of second-order optical nonlinearity. The real-time monitoring showed that it also gave the large relaxation of second-order optical nonlinearity on poling process. The increase of 2ω (532 nm) energy enhanced the increase of local heating, which led to easier alignment of azobenzene chromophore and also larger relaxation of aligned chromophore.