https://kluedo.ub.uni-kl.de/files/1289/no_series_194.pdf

Wannier–Stark resonances in optical and semiconductor superlattices

A critical survey of the literature on the theory of electronic states in, and electron transmission through, models of one-dimensional disordered solids and liquids is given in the first part. Reference to work on three-dimensional systems is included, especially where exact results have been obtained. The relationship between this subject and the problem of elastic vibrations in disordered solids is pointed out. A complete exposition of the authors' work on one-dimensional conductivity is then presented. It provides a rigorous solution of the problem of average resistance, and of the variance (fluctuations) of resistance, for important classes of disorder which are carefully and precisely defined. Conclusions regarding the role of disorder with respect to the transmission properties are presented and discussed. It is also pointed out that, with appropriate modifications, the results apply generally to wave propagation in inhomogeneous media.

Theories of electrons in one-dimensional disordered systems

Spatial and/or temporal propagation of light waves in periodic optical structures offers a unique possibility to realize in a purely classical setting the optical analogues of a wide variety of quantum phenomena rooted in relativistic wave equations. In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based either on spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented. Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair production, the Dirac oscillator, the relativistic Kronig–Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.

https://rd.springer.com/content/pdf/10.1007%2Fs00340-011-4628-7.pdf

Classical simulation of relativistic quantum mechanics in periodic optical structures

A one-dimensional relativistic screened Coulomb potential

Parenting by learning disabled persons is a highly emotive issue, eliciting arguments from both extremes. Many of the arguments against such parenting have their basis in eugenic theory, whereas those in favour, often cite human rights declarations, and philosophies such as 'normalization'. This review of the literature describes the chronological development of theory on the subject, spanning 1900 to the present day. It has become clear that, whereas parents with learning difficulties may be more predisposed to having problems, they can indeed perform as adequate parents, given appropriate training and support. This paper traces the development of current theory, through an in-depth discussion of the available literature.

Parents with learning disabilities: a review of the literature

A computational model based on non-relativistic approach is proposed for the determination of transmission coefficient, resonant tunneling energies, group velocity, resonant tunneling lifetime and traversal time in multibarrier systems (GaAs/AlyGa1−yAs) for the entire energy range e V0, V0, being the potential barrier height. The resonant energy states were found to group into allowed tunneling bands separated by forbidden gaps. The tunneling lifetime and the traversal time are found to have minimum values at the middle of each allowed band. Further, It is observed that the electrons with energies in the higher tunneling band could tunnel out faster than those with energies in the lower band. Moreover, an additional resonant peak in resonant energy spectrum indicated the presence of a surface state where resonant tunneling occurs.

/pdf/transmission-coefficient-resonant-tunneling-lifetime-and-3ttz0k3ln6.pdf

Transmission coefficient, resonant tunneling lifetime and traversal time in multibarrier semiconductor heterostructure

Bloch electrons in finite crystals in the presence of a uniform electric field

Landauer resistance of Thue-Morse and Fibonacci lattices and some related issues

We have reported a relativistic treatment of electrical conduction in a one-dimensional disordered system consisting of a finite number of potential barriers. Our treatment is based on (i) a relativistic generalization of a nonrelativistic approach of Landauer [R. Landauer, Philos. Mag. 21, 863 (1990)] for electrical resistance of a one-dimensional disordered system and (ii) an averaging procedure due to Erd\"os and Herndon [P. Erd\"os and R. C. Herndon, Adv. Phys. 31, 65 (1983)]. We have carried out exhaustive quantitative analyses of our analytical results and indicated, thereby, the circumstances under which the relativistic effects on electrical resistance in disordered systems may be quite significant.

Relativistic study of electrical conduction in disordered systems.

We have studied relativistic effects on the tunnelling of electrons through a multi-barrier system (MBS) consisting of rectangular barrier potentials, by deriving, for the purpose, relativistic formulae for the transmission coefficient and associated relativistic conditions for resonant tunnelling. Among other things, we have discussed critically the quantitative extents of relativistic impacts on tunnelling through MBSS, especially in the context of their measurability.

http://iopscience.iop.org/article/10.1088/0953-8984/5/41/017/pdf

C.L. Roy

Papers

Transmission coefficient, resonant tunneling lifetime and traversal time in multibarrier semiconductor heterostructure

Bloch electrons in finite crystals in the presence of a uniform electric field

Landauer resistance of Thue-Morse and Fibonacci lattices and some related issues

Relativistic study of electrical conduction in disordered systems.

Relativistic impacts on tunnelling through multi-barrier systems