Use of Dirac matrices in polarization optics

Several matrix methods have been developed for studying polarization properties of light. Jones was the first to apply the matrix method to the study of polarization optics. In Jones matrix formalism the polarized wave field is represented by 2-element column matrix known as Jones Vector and the polarization device encountered by light is represented by a 2×2 matrix, known as the characteristic Jones matrix of the device. Mueller introduced a new matrix method where the wave field is represented by a 4-dimensional vector. The elements of the vector are the Stokes parameters of the beam. In Mueller matrix formalism the optical device is represented by a 4×4 real matrix known as ‘Mueller Matrix’ of the device. The use of coherency matrix also proves to the useful in the study of partially polarized light. Pauli spin matrices have been used to unify the different matrix treatments of polarization optical phenomena. The present article is an attempt to unify the analysis of polarization phenomena using Dirac matrices used by Dirac in quantum mechanics. We have however redefined the set of Dirac matrices in terms of the Kronecher product of Pauli spin matrices.     

Causal horizons in a bouncing universe

As our understanding of the past in a bouncing universe is limited, it becomes difficult to propose a cosmological model which can give some understanding of the causal structure of the bouncing universe. In this article we address the issue related to the particle horizon problem in the bouncing universe models. It is shown that in many models the particle horizon does not exist, and consequently the horizon problem is trivially solved. In some cases a bouncing universe can have a particle horizon and we specify the conditions for its existence. In the absence of a particle horizon the Hubble surface specifies the causal structure of a bouncing universe. We specify the complex relationship between the Hubble surface and the particle horizon when the particle horizon exists. The article also address the issue related to the event horizon in a bouncing universe. A toy example of a bouncing universe is first presented where we specify the conditions which dictate the presence of a particle horizon. Next we specify the causal structures of three widely used bouncing models. The first case is related to quintom matter bounce model, the second one is loop quantum cosmology based bounce model and lastly f(R) gravity induced bounce model. We present a brief discussion on the horizon problem in bouncing cosmologies. We point out that the causal structure of the various bounce models fit our general theoretical predictions.     

Physico-chemical and electrical properties of rapid thermal oxides on Ge-rich SiGe heterolayers

Rapid thermal oxidation of high-Ge content (Ge-rich) Si_1−xGe_x (x = 0.85) layers in dry O₂ ambient has been investigated. High-resolution X-ray diffraction (HRXRD) and strain-sensitive two-dimensional reciprocal space mapping X-ray diffractometry (2D-RSM) are employed to investigate strain relaxation and composition of as-grown SiGe alloy layers. Characterizations of ultra thin oxides (∼6-8 nm) have been performed using Fourier transform infrared spectroscopy (FTIR) and high-resolution X-ray photoelectron spectroscopy (HRXPS). Formation of mixed oxide i.e., (SiO₂ + GeO₂) and pile-up of Ge at the oxide/Si_1−xGe_x interface have been observed. Enhancement in Ge segregation and reduction of oxide thickness with increasing oxidation temperature are reported. Interface properties and leakage current behavior of the rapid thermal oxides have been studied by capacitance-voltage (C-V) and current-voltage (J-V) techniques using metal-oxide-semiconductor capacitor (MOSCAP) structures and the results are reported.     

Magnetic and electric properties of antimony selenide (Sb2Se3) crystals

The magnetic susceptibility in the three principal crystallographic directions, and the electrical conductivity and thermoelectric power parallel and perpendicular to the basal plane of Sb₂Se₃ single crystals, have been measured over the temperature range 100–550 K. The different results obtained from the magnetic and electric studies have been accounted for on the basis of non-stoichiometry of the compound and localized lone electrons. A hopping mechanism in the higher temperature region simultaneously with impurity excitation is suggested.     

Joint determination of optimal safety stocks and production policy for an imperfect production system

In this article, we develop an imperfect economic manufacturing quantity (EMQ) model for an unreliable production system subject to process deterioration, machine breakdown and repair and buffer stock. The basic model is developed under general process shift, machine breakdown and repair time distributions. We suggest a computational algorithm for determination of the optimal safety stock and production run time which minimize the expected cost per unit time in the steady state. For a numerical example, we illustrate the outcome of the proposed model and perform a sensitivity analysis with respect to the model-parameters which have direct influence on the optimal decisions.     

String Cosmology with Brans–Dicke Theory in Higher Dimensional Space-Time

We develop string cosmology in the presence ofa Brans–Dicke (BD) scalar field coupled toEinstein gravity for higher dimensional space-time.Solutions are obtained for the equation of state for thep-string, and physical situations arediscussed.     

Quantum cascade transitions in nanostructures

In this article we review the physical characteristics of quantum cascade transitions (QCTs) in various nanoscopic systems. The quantum cascade laser which utilizes such transitions in quantum wells is a brilliant outcome of quantum engineering that has already demonstrated its usefulness in various real-world applications. After a brief introduction to the background of this transition process, we discuss the physics behind these transitions in an externally applied magnetic field. This has unravelled many intricate phenomena related to intersubband resonance and electron relaxation modes in these systems. We then discuss QCTs in a situation where the quantum wells in the active regions of a quantum cascade structure are replaced by quantum dots. The physics of quantum dots is a rapidly developing field with its roots in fundamental quantum mechanics, but at the same time, quantum dots have tremendous potential applications. We first present a brief review of those aspects of quantum dots that are likely to be reflected in a quantum-dot cascade structure. We then go on to demonstrate how the calculated emission peaks of a quantum-dot cascade structure with or without an external magnetic field are correlated with the properties of quantum dots, such as the choice of confinement potentials, shape, size and the low-lying energy spectra of the dots. Contents PAGE 1 Introduction 456 2 Intersubband transitions in quantum wells 458 3 Quantum cascade transitions 462 3.1. Basic principles 462 3.1.1. Minibands and minigaps 464 3.1.2. Vertical transitions 464 3.1.3. GaAs/AlGaAs quantum cascade lasers 464 3.1.4. QCLs based on superlattice structures 465 3.1.5. Type-II quantum cascade lasers 466 3.1.6. Recent developments 466 3.2. Applications: sense-ability and other qualities 466 4 Quantum cascade transitions in novel situations 467 4.1. External magnetic field 467 4.1.1. Parallel magnetic field 468 4.1.2. Many-body effects: depolarization shift 470 4.1.3. The role of disorder 471 4.1.4. Tilted magnetic field 475 4.2. Magneto-transport experiments and phonon relaxation 479 4.3. Magneto-optics experiment and phonon relaxation 484 5 A brief review of quantum dots 485 5.1. From three- to zero-dimensional systems 485 5.2. Making the dots 487 5.2.1. Lithographic patterning 487 5.2.2. Self-assembled quantum dots 488 5.3. Shell filling in quantum dots 489 5.4. Electron correlations: spin states 490 5.5. Anisotropic dots 491 5.6. Influence of an external magnetic field 491 5.6.1. The Fock diagram 491 5.6.2. The no-correlation theorem 492 5.6.3. Correlation effects and magic numbers 492 5.6.4. Spin transitions 493 5.7. Quantum dots in novel systems 494 5.8. Potential applications of quantum dots 494 5.8.1. Single-electron transistors (SETs) 494 5.8.2. Single-photon detectors 494 5.8.3. Single-photon emitters 495 5.8.4. Quantum-dot lasers 495 6 Quantum cascade transitions in quantum-dot structures 496 6.1. Quantum dots versus quantum wells 496 6.2. QCT with rectangular dots 497 6.2.1. Vertical transitions 500 6.2.2. Diagonal transitions 501 6.3. QCT in a parabolic dot 504 6.4. Magnetic field effects on intersubband transitions 506 6.5. Mid-IR luminescence from a QD cascade device 512 7 Summary and open questions 513 Acknowledgements 515 References 515     

Enhanced vacuum-photoconductivity of chemically synthesized ZnO nanostructures

We report on the enhanced ultraviolet (UV) photoconductivity of zinc oxide (ZnO) nanostructures in vacuum. Nanoparticles and nanorods of ZnO were fabricated using a simple cost-effective solid state grinding method. Morphology of the nanostructures was studied using transmission electron microscopy, while the optical properties were investigated using UV–visible absorption and photoluminescence spectroscopy. The emission spectra of the nanostructures revealed the existence of various native defect states of ZnO and also indicated the presence of surface adsorbed water molecules. In the photoconductivity measurements, although the ZnO nanoparticles exhibited lower photoconductivity in comparison to the nanorods, a similar trend of photoresponse was observed for both the cases. An initial decrease in the photoconductivity followed by a large enhancement was observed in vacuum compared to that in ambient condition. Such unusually increased photoconductivity has been correlated to the desorption of physisorbed water molecules from nanostructure surfaces under vacuum. This desorption is responsible for the rise in dark current and an initial decrease in photoconductivity. Continual UV irradiation in vacuum leads to the desorption of chemisorbed water molecules from the defect sites of the nanostructures, resulting in the occurrence of high photoconductivity.     

On the Fourier coefficients of certain Hilbert modular forms

We prove that given any \(\epsilon >0\), a non-zero adelic Hilbert cusp form \({\mathbf {f}}\) of weight \(k=(k_1,k_2,\ldots ,k_n)\in ({\mathbb {Z}}_+)^n\) and square-free level \(\mathfrak {n}\) with Fourier coefficients \(C_{{\mathbf {f}}}(\mathfrak {m})\), there exists a square-free integral ideal \(\mathfrak {m}\) with \(N(\mathfrak {m})\ll k_0^{3n+\epsilon }N(\mathfrak {n})^{\frac{6n^2+1}{2}+\epsilon }\) such that \(C_{{\mathbf {f}}}(\mathfrak {m})\ne 0\). The implied constant depends on \(\epsilon , F\).

     

Towards a more efficient dynamic mesh adaptation methodology for continuum discretization in complex engineering problems

A novel and efficient method of adaptive mesh generation, for dynamically adaptive unstructured grids, is proposed. A locally refined triangulation is constructed on a coarse background mesh, subdividing each triangle in the refinement region R into four congruent sub-triangles iteratively, by connecting edge midpoints, until triangles of a prescribed lengthscale are obtained. The unavoidable propagation outside the refinement region R is restricted to a single triangle in the coarse background mesh. The triangles, in the immediate vicinity of region R, are broken down using the concept of iterated function systems, widely used in fractal modeling, by recursive generation of sub-triangles with a gradation towards the region R triangles. A quantitative assessment of the present algorithm proves its superiority over other comparable models reported in the literature. The time cost of the algorithm is linear, and the method can be easily extended to three dimensions.