Scattering and bound states of spinless particles in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Scattering and bound states of spin-0 particles in a nonminimal vector double-step potential

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Scaling dynamics for a particle in a time-dependent potential well

Some dynamical properties for a classical particle confined in an infinitely deep box of potential containing a periodically oscillating square well are studied. The dynamics of the system is described by using a two-dimensional non-linear area-preserving map for the variables energy and time. The phase space is mixed and the chaotic sea is described using scaling arguments. Scaling exponents are obtained as a function of all the control parameters, extending the previous results obtained in the literature. (c) 2012 Elsevier B.V. All rights reserved.

Escape of particles in a time-dependent potential well

We investigate the escape of an ensemble of noninteracting particles inside an infinite potential box that contains a time-dependent potential well. The dynamics of each particle is described by a two-dimensional nonlinear area-preserving mapping for the variables energy and time, leading to a mixed phase space. The chaotic sea in the phase space surrounds periodic islands and is limited by a set of invariant spanning curves. When a hole is introduced in the energy axis, the histogram of frequency for the escape of particles, which we observe to be scaling invariant, grows rapidly until it reaches a maximum and then decreases toward zero at sufficiently long times. A plot of the survival probability of a particle in the dynamics as function of time is observed to be exponential for short times, reaching a crossover time and turning to a slower-decay regime, due to sticky regions observed in the phase space.

Trapping of a particle in a short-range harmonic potential well

Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed. © 2012 Springer Science+Business Media, LLC.

Dynamical properties for an ensemble of classical particles moving in a driven potential well with different time perturbation

We consider dynamical properties for an ensemble of classical particles confined to an infinite box of potential and containing a time-dependent potential well described by different nonlinear functions. For smooth functions, the phase space contains chaotic trajectories, periodic islands and invariant spanning curves preventing the unlimited particle diffusion along the energy axis. Average properties of the chaotic sea are characterised as a function of the control parameters and exponents describing their behaviour show no dependence on the perturbation functions. Given invariant spanning curves are present in the phase space, a sticky region was observed and show to modify locally the diffusion of the particles. © 2013 Elsevier B.V.

Scattering and bound states of fermions in a mixed vector-scalar smooth step potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Evaluation of a potential well field near Church Rock as a water supply for Gallup, New Mexico /

Prepared in cooperation with the U.S. Bureau of Reclamation.

Discrete Models of Time-Fractional Diffusion in a Potential Well

Mathematics Subject Classification: 26A33, 45K05, 60J60, 60G50, 65N06, 80-99.

Non-square-well potential profile and suppression of blinking in compositionally graded Cd1−xZnxSe/CdxZn1−xSe nanocrystals

Random blinking is a major problem on the way to successful applications of semiconducting nanocrystals in optoelectronics and photonics, which until recently had neither a practical solution nor a theoretical interpretation. An experimental breakthrough has recently been made by fabricating non-blinking Cd1-xZnxSe/ZnSe graded nanocrystals [Wang et al., Nature, 2009, 459, 686]. Here, we (1) report an unequivocal and detailed theoretical investigation to understand the properties (e.g., profile) of the potential-well and the distribution of Zn content with respect to the nanocrystal radius and (2) develop a strategy to find the relationship between the photoluminescence (PL) energy peaks and the potential-well due to Zn distribution in nanocrystals. It is demonstrated that the non-square-well potential can be varied in such a way that one can indeed control the PL intensity and the energy-level difference (PL energy peaks) accurately. This implies that one can either suppress the blinking altogether, or alternatively, manipulate the PL energy peaks and intensities systematically to achieve a controlled non-random intermittent luminescence. The approach developed here is based on the ionization energy approximation and as such is generic and can be applied to any non-free-electron nanocrystals.

Spin splitting of conduction subbands in Al0.3Ga0.7As/GaAs/AlxGa1-x As/Al0.3Ga0.7As step quantum wells

By means of the transfer matrix technique, interface-induced Rashba spin splitting of conduction subbands in Al0.3Ga0.7As/GaAs/AlxGa1-xAs/Al0.3Ga0.7As step quantum wells which contain internal structure inversion asymmetry introduced by the insertion of AlxGa1-xAs step potential is investigated theoretically in the absence of electric field and magnetic field. The dependence of spin splitting on the well width, step width and Al concentration is investigated in detail. We find that the sign of the first excited subband spin splitting changes with well width and step width, and is opposite to that of the ground subband under certain conditions. The sign and strength of the spin splitting are shown to be sensitive to the components of the envelope function at three interfaces. Copyright (C) EPLA, 2009

Intersubband absorption energy shifts in 3-level system for asymmetric quantum well terahertz emitters

Intersubband absorption energy shifts in 3-level system stemming from depolarization and excitonlike effects are investigated. Analytically, the expressions we derive present good explanations to the conventional 2-level results and bare potential transition energy results; and numerical results show that they are more exact than the previous studies to describe the 3-level system depolarization and excitonlike shift (DES) character especially for higher carrier density (more than 8 x 10(11) cm(-2)). One interesting detail we find is that the "large blue" DES becomes "slight redshift" in the low doping limit (less than 1.9 x 10(11) cm(-2)), which may be neglected by the previous studies of intersubband transitions. Temperature character of DES in the step well structure is also numerically studied. Finally the above are applied to calculate asymmetric step quantum well structures. The two main functional aspects of terahertz (THz) emitters are discussed and several basic optimizing conditions are considered. By adjusting the well geometry parameters and material composition systematically, some optimized structures which satisfy all of the six conditions are recommended in tables. These optimizations may provide useful references to the design of 3-level-based optically pumping THz emitters.

Scattering of neutral fermions by a pseudoscalar potential step in two-dimensional spacetime

The problem of scattering of neutral fermions in two-dimensional spacetime is approached with a pseudoscalar potential step in the Dirac equation. Some unexpected aspects of the solutions beyond the absence of Klein's paradox are presented. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength. Added plausibility for the existence of bound-state solutions in a pseudoscalar double-step potential found in a recent Letter is given. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Step and flash imprint lithography: Fabrication of patterned media for extremely high density magnetic data storage devices

Currently the data storage industry is facing huge challenges with respect to the conventional method of recording data known as longitudinal magnetic recording. This technology is fast approaching a fundamental physical limit, known as the superparamagnetic limit. A unique way of deferring the superparamagnetic limit incorporates the patterning of magnetic media. This method exploits the use of lithography tools to predetermine the areal density. Various nanofabrication schemes are employed to pattern the magnetic material are Focus Ion Beam (FIB), E-beam Lithography (EBL), UV-Optical Lithography (UVL), Self-assembled Media Synthesis and Nanoimprint Lithography (NIL). Although there are many challenges to manufacturing patterned media, the large potential gains offered in terms of areal density make it one of the most promising new technologies on the horizon for future hard disk drives. Thus, this dissertation contributes to the development of future alternative data storage devices and deferring the superparamagnetic limit by designing and characterizing patterned magnetic media using a novel nanoimprint replication process called "Step and Flash Imprint lithography". As opposed to hot embossing and other high temperature-low pressure processes, SFIL can be performed at low pressure and room temperature. Initial experiments carried out, consisted of process flow design for the patterned structures on sputtered Ni-Fe thin films. The main one being the defectivity analysis for the SFIL process conducted by fabricating and testing devices of varying feature sizes (50 nm to 1 μm) and inspecting them optically as well as testing them electrically. Once the SFIL process was optimized, a number of Ni-Fe coated wafers were imprinted with a template having the patterned topography. A minimum feature size of 40 nm was obtained with varying pitch (1:1, 1:1.5, 1:2, and 1:3). The Characterization steps involved extensive SEM study at each processing step as well as Atomic Force Microscopy (AFM) and Magnetic Force Microscopy (MFM) analysis.

Vibration spectra of ferroelectric alkali trihydrogen selenites and the nature of the hydrogen bond potential in these crystals

Raman spectra of the ferroelectric LiH3 (SeO3)2 and NaH3(SeO3)2 and the anti-ferroelectric KH3 (SeO3)2 have been recorded at room temperature using a He-Ne and also an Ar-ion laser source. The infrared absorption spectra of these crystals and their deuterated analogues have been recorded in the region 400–4000 cm−1 both below and above the Curie temperature. From an analysis of the spectrum in the region 400–900 cm−1 it is concluded that (i) in LiH3 (SeO3)2 the protons are ordered in an asymmetric double minimum potential with a low barrier and the spectrum can be interpreted in terms of HSeO3− and H2SeO3 vibrations, (ii) in NaH3 (SeO3)2 all three protons occupy a single minimum potential at room temperature and below the transition temperature the groups HSeO3− and H2SeO3 are present, (iii) the proton at the inversion centre in KH3(SeO3)2 is in a broad troughed potential well and the low temperature spectrum is more likely to be due to H3SeO3+ and SeO32− species. This deviation of the spectrum from that of the previous two crystals is attributed to the difference in H-bond scheme and hence the absence of any cooperative motion of protons in this crystal.