(1+1)-Dirac bound states in one dimension, with position-dependent Fermi velocity and mass

We extend Panella and Roy’s [17] work for massless Dirac particles with position-dependent (PD) velocity. We consider Dirac particles where the mass and velocity are both position-dependent. Bound states in the continuum (BIC)-like and discrete bound state solutions are reported. It is observed that BIC-like solutions are not only feasible for the ultra-relativistic (massless) Dirac particles but also for Dirac particles with PDmass and PD-velocity that satisfy the condition m(x) v _F ² (x) = A, where A ≥ 0 is constant. Dirac Pöschl-Teller and harmonic oscillator models are also reported.     

Critical assessment of the Schrödinger picture of quantum mechanics

We provide an example in which the Heisenberg and the Schrödinger pictures of quantum mechanics give different results, thus confirming the statement of P.A.M. Dirac that the two pictures may lead to inequivalent results. We consider a one-dimensional nonrelativistic charged harmonic oscillator (frequency ω₀ and mass m), and take into account the action of the radiation reaction and the vacuum electromagnetic forces on the charged oscillator. We show that the Heisenberg picture gives the correct value, ℏω₀/2, for the ground state energy of the harmonic oscillator in both cases of classical and quantized vacuum fields. In the case of the Schrödinger picture, considering classical vacuum fields, and using a simple calculation for the classical radiation reaction force that is valid in the limit of large mass (mc²⪢ℏω₀), we obtain the value ℏω₀ for the ground state energy of the harmonic oscillator. We show that the vacuum electromagnetic forces play a very important role in the understanding of this discrepancy.     

Dynamical symmetries of two-dimensional systems in relativistic quantum mechanics

The two-dimensional Dirac Hamiltonian with equal scalar and vector potentials has been proved commuting with the deformed orbital angular momentum L. When the potential takes the Coulomb form, the system has an SO(3) symmetry, and similarly the harmonic oscillator potential possesses an SU(2) symmetry. The generators of the symmetric groups are derived for these two systems separately. The corresponding energy spectra are yielded naturally from the Casimir operators. Their non-relativistic limits are also discussed.     

A novel method for extracting oscillator strength of select rare-earth ion optical transitions in nanostructured dielectric materials

A new technique to obtain the oscillator strength of select rare-earth optical transitions in nanostructured dielectric materials (nanophosphors) is presented. It is based on the experimentally observed nanophosphor lifetime dependence on the embedding medium. A constant oscillator strength and parity-allowed electric dipole transitions of the RE ion emission are assumed. The oscillator strength is obtained from the slope of the 1/τ_ij vs. n(n²+2)² plot, where τ_ij is the radiative lifetime of transition between states i and j, and n is the index of refraction of the embedding medium. The use of the technique is illustrated for the Y ₂SiO₅:Ce nanophosphor.     

Effect of incorporating nonlanthanoidal indium on optical properties of ferroelectric Bi4Ti3O12 thin films

Bi₄Ti₃O₁₂ (BTO) and Bi_3.25In_0.75Ti₃O₁₂ (BTO:In) thin films were prepared on fused quartz and LaNiO₃/Si (LNO) substrates by chemical solution deposition (CSD). Their microstructures, ferroelectric and optical properties were investigated by X-ray diffraction, scanning electron microscope, ferroelectric tester and UV-visible-NIR spectrophotometer, respectively. The optical band-gaps of the films were found to be 3.64 and 3.45 eV for the BTO and BTO:In films, respectively. Optical constants (refractive indexes and extinction coefficients) were determined from the optical transmittance spectra using the envelope method. Following the single electronic oscillator model, the single oscillator energy E₀, the dispersion energy E_d, the average interband oscillator wavelength λ₀, the average oscillator strength S₀, the refractive index dispersion parameter (E₀/S₀), the chemical bonding quantity β, and the long wavelength refractive index n_∞ were obtained and analyzed. Both the refractive index and extinction coefficient of the BTO:In films are smaller than those of the BTO films. Furthermore, the refractive index dispersion parameter (E₀/S₀) increases and the chemical bonding quantity β decreases in the BTO and BTO:In films compared with those of bulk.     

An xp model on AdS2 spacetime

In this paper we formulate the xp model on the AdS₂ spacetime. We find that the spectrum of the Hamiltonian has positive and negative eigenvalues, whose absolute values are given by a harmonic oscillator spectrum, which in turn coincides with that of a massive Dirac fermion in AdS₂. We extend this result to generic xp models which are shown to be equivalent to a massive Dirac fermion on spacetimes whose metric depend of the xp   Hamiltonian. Finally, we construct the generators of the isometry group SO(2,1)$\mathit{SO}(2,1)$ of the AdS₂ spacetime, and discuss the relation with conformal quantum mechanics.     

Use of harmonic oscillator potential in the analysis of muonic transition energies

Energy levels: 1s _1/2, 2p _1/2, 2p _3/2, 3d _3/2, and 3d _5/2 of the muon in the spherical nuclei:¹²⁰Sn,¹⁹⁷Au and²⁰⁸Pb have been calculated under the assumption of harmonic oscillator potential. The levels are corrected for vacuum polarisation. The agreement with experimental values is better than 0·5%. An accurate method of solving the Dirac equation to obtain the energy eigenvalues is outlined. The importance of choosing the ‘classical turning point’ as the radius for matching the interior and exterior solutions is discussed.     

Realistic neutrinogenesis with radiative vertex correction

We propose a new model for naturally realizing light Dirac neutrinos and explaining the baryon asymmetry of the universe through neutrinogenesis. To achieve these, we present a minimal construction which extends the Standard Model with a real singlet scalar, a heavy singlet Dirac fermion and a heavy doublet scalar besides three right-handed neutrinos, respecting lepton number conservation and a Z₂$Z_2$ symmetry. The neutrinos acquire small Dirac masses due to the suppression of weak scale over a heavy mass scale. As a key feature of our construction, once the heavy Dirac fermion and doublet scalar go out of equilibrium, their decays induce the CP asymmetry from the interference of tree-level processes with the radiative vertex corrections (rather than the self-energy corrections). Although there is no lepton number violation, an equal and opposite amount of CP asymmetry is generated in the left-handed and the right-handed neutrinos. The left-handed lepton asymmetry would then be converted to the baryon asymmetry in the presence of the sphalerons, while the right-handed lepton asymmetry remains unaffected.     

Yangian Realization for Dirac Oscillator

We investigate the realizations of Yangian algebra for a Dirac oscillator. Applying the representation theory of Y(sl(2)) to Dirac oscillator, shift operaors for different energy levelsfor this system are obtained.     

Yangian Realization for Dirac Oscillator

We investigate the realizations of Yangian algebra for a Dirac oscillator. Applying the representation theory of Y(sl(2)) to Dirac oscillator, shift operators for different energy levels for this system are obtained.     

Properties of optical phonons in Zn1−x−yMgyBexSe quaternary mixed crystal

Long wavelength optical lattice vibration and dielectric constants of the quaternary mixed crystal Zn_1−x−yMg_yBe_xSe are investigated based on the pseudo-unit-cell mode and Born-Huang procedure. It is found that this material shows a three-mode behavior and the oscillator strength of each mode is mainly controlled by only one component. The theoretical results also show that the linear interpretation method for dielectric constants is reliable. The vibrational frequencies and the oscillator strengths of the ternary mixed crystals Be_xZn_1−xSe, Be_xMg_1−xSe and Mg_xZn_1−xSe are also calculated as special cases of the quaternary mixed crystal for comparing with experiments. The calculation shows agreement with the experimental results.     

Polarizabilities of shallow donors in finite-barrier nanodots

Polarizabilities of shallow donors in finite-barrier GaAs/Ga_1−xAl_xAs of harmonic oscillator nanodots are calculated, within the effective-mass approximation, using the Hasse variational method. The magnetic field dependence of polarizabilities and the diamagnetic susceptibilities are computed.     

类Quesne环状球谐振子势场中的赝自旋对称性

提出了一种新的类Quesne环状球谐振子势,应用二分量方法求解1/2-自旋粒子满足的Dirac方程, Dirac哈密顿量由标量和矢量类Quesne环状球谐振子势构成.在Σ=S(r)+V(r)=0的条件下,得到了Dirac旋量波函数下分量的束缚态解和能谱方程, 显示出类Quesne环状球谐振子势场中的赝自旋对称性.讨论了束缚态波函数和能谱方程的有关性质. 关键词： 类Quesne环状球谐振子势 Dirac方程 赝自旋对称性 束缚态     

On the Chirality Quantum Phase Transition of the Dirac Oscillator

Dirac oscillator subjects to an external magnetic field is re-examined. We show that this model can be mapped onto different quantum optics models if one insists to introduce two kinds of phonons which associate with the excitations of Dirac oscillator and magnetic field respectively. The conclusion about chirality quantum phase transition in the paper “Chirality quantum phase transition in the Dirac oscillator” (Bermudez et al. Phys. Rev. A, 77, 063815 2008) is only valid for a specific mapped quantum optics models rather than the Dirac oscillator itself. Thus, the conclusions about chirality quantum phase transitions in this paper are not universal.     

Dynamics of Dirac quasi-particles in lattice vibration and anomalous phonon frequency shift of graphene

By exact solution of time-dependent Schrödinger equation of electron in graphene under interaction with E_2g phonons, we investigate the dynamical behavior of Dirac quasi-particle in the process of lattice vibration. Due to the global geometric phases acquired by electron during lattice vibration, an anomalous shift of the vibration frequency is obtained. We calculate the Fermi energy dependence of frequency shift which is in consistence with experiment in case of small doping density.     

Relativistic versus nonrelativistic solution of the N-fermion problem in a hyperradius-confining potential

We investigate the quantum system of N identical fermions in the relativistic limit. In this article the considered potential is a combination of Coulombic, linear confining and harmonic oscillator terms. By using Jacobi coordinates and introducing the hyperradius quantity we obtain the wave functions of the system as well as the corresponding energy eigenvalues. Assuming that all particles are confined within a hypersphere we calculate the corresponding x _bag . In particular we consider the case N = 3 which corresponds to baryonic systems. By using the experimental values of the charge radius of each baryon we calculate the potential coefficients. Within our treatment the results of the MIT bag model are recovered for N = 1. Finally we compare the results obtained by the Dirac equation with the corresponding results of the Schrödinger equation and we find that the energy spectra obtained by the former are much closer to experimental values.     

Abnormal electronic transport in disordered graphene nanoribbon

We investigate the conductivity σ of graphene nanoribbons with zigzag edges as a function of Fermi energy E_F in the presence of the impurities with different potential range. The dependence of σ(E_F) displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of σ(E_F) and a wide dip near the Dirac point, due to the special properties of long range potential and edge states. These behaviors agree well with the results from a recent experiment by Miao et al. [Science 317 (2007) 1530 (SOM)].     

Influence of porous morphology on optical dispersion properties of template free mesoporous titanium dioxide (TiO2) films

This paper focuses the influence of porous morphology on the microstructure and optical properties of TiO₂ films prepared by different sol concentration and calcination temperatures. Mesoporous TiO₂ thin films were prepared on the glass substrates by sol-gel dip coating technique using titanium (IV) isopropoxide. Porous morphology of the films can be regulated by chemical kinetics and is studied by scanning electron microscopy. The optical dispersion parameters such as refractive index (n), oscillator energy (E_d), and particle co-ordination number (N_c) of the mesoporous TiO₂ films were studied using Swanepoel and Wemple-DiDomenico single oscillator models. The higher precursor concentration (0.06 M), films exhibit high porosity and refractive index, which are modified under calcination treatment. Calcinated films of low metal precursor concentration (0.03 M) possess higher particle co-ordination number (N_c = 5.05) than that of 0.06 M films (N_c = 4.90) due to calcination at 400 °C. The lattice dielectric constant (E_∞) of mesoporous TiO₂ films was determined by using Spintzer model. Urbach energy of the mesoporous films has been estimated for both concentration and the analysis revealed the strong dependence of Urbach energy on porous morphology. The influence of porous morphology on the optical dispersion properties also has been explained briefly in this paper.     

Reflection and vibrational spectra of SbSCl0.1I0.9 crystals in the ferroelectric phase-transition region

SbSCl_0.1I_0.9 crystals were grown from the vapor phase and reflection spectra were recorded using a Fourier-transform IR spectrometer. The optical parameters and optical functions along the c axis were calculated using an improved Kramers–Kronig technique with two confining spectral limits. The reflection spectra were analyzed using the oscillator parameter fitting technique for comparison of results. The vibrational frequencies ω_L and ω_T were evaluated. The ferroelectric phase-transition temperature was estimated as 330 K for SbSCl_0.1I_0.9 from experimental reflection measurements and theoretical investigation of the potential energy of Sb atoms for B_1u soft normal modes of SbSI and SbSCl_0.1I_0.9 crystals.