The Casimir Force in a Lorentz Violating Theory

We study the effects of the minimal extension of the standard model including Lorentz violation on the Casimir force between two parallel conducting plates in vacuum. We provide explicit solutions for the electromagnetic field using scalar field analogy, for both the cases in which the Lorentz violating terms come from the CPT-even or CPT-odd terms. We also calculate the effects of the Lorentz violating terms for a fermion field between two parallel conducting plates and analyze the modifications of the Casimir force due to the modifications of the Dirac equation. In all cases under consideration, the standard formulas for the Casimir force are modified by either multiplicative or additive correction factors, the latter case exhibiting different dependence on the distance between the plates.Comment: 20 pages, no figures, references added, accepted for publication in Phys. Rev.

Evanescence in Coined Quantum Walks

In this paper we complete the analysis begun by two of the authors in a previous work on the discrete quantum walk on the line [J. Phys. A 36:8775-8795 (2003) quant-ph/0303105 ]. We obtain uniformly convergent asymptotics for the "exponential decay'' regions at the leading edges of the main peaks in the Schr{\"o}dinger (or wave-mechanics) picture. This calculation required us to generalise the method of stationary phase and we describe this extension in some detail, including self-contained proofs of all the technical lemmas required. We also rigorously establish the exact Feynman equivalence between the path-integral and wave-mechanics representations for this system using some techniques from the theory of special functions. Taken together with the previous work, we can now prove every theorem by both routes.Comment: 32 pages AMS LaTeX, 5 figures in .eps format. Rewritten in response to referee comments, including some additional references. v3: typos fixed in equations (131), (133) and (134). v5: published versio

On factorization of q-difference equation for continuous q-Hermite polynomials

We argue that a customary q-difference equation for the continuous q-Hermite polynomials H_n(x|q) can be written in the factorized form as (D_q^2 - 1)H_n(x|q)=(q^{-n}-1)H_n(x|q), where D_q is some explicitly known q-difference operator. This means that the polynomials H_n(x|q) are in fact governed by the q-difference equation D_qH_n(x|q)=q^{-n/2}H_n(x|q), which is simpler than the conventional one.Comment: 7 page

The Bivariate Rogers-Szeg\"{o} Polynomials

We present an operator approach to deriving Mehler's formula and the Rogers formula for the bivariate Rogers-Szeg\"{o} polynomials $h_n(x,y|q)$. The proof of Mehler's formula can be considered as a new approach to the nonsymmetric Poisson kernel formula for the continuous big $q$-Hermite polynomials $H_n(x;a|q)$ due to Askey, Rahman and Suslov. Mehler's formula for $h_n(x,y|q)$ involves a ${}_3\phi_2$ sum and the Rogers formula involves a ${}_2\phi_1$ sum. The proofs of these results are based on parameter augmentation with respect to the $q$-exponential operator and the homogeneous $q$-shift operator in two variables. By extending recent results on the Rogers-Szeg\"{o} polynomials $h_n(x|q)$ due to Hou, Lascoux and Mu, we obtain another Rogers-type formula for $h_n(x,y|q)$. Finally, we give a change of base formula for $H_n(x;a|q)$ which can be used to evaluate some integrals by using the Askey-Wilson integral.Comment: 16 pages, revised version, to appear in J. Phys. A: Math. Theo

Residents\u27 Social Interactions in Market Square and Its Impact on Community Well-Being

This study aims at ameliorating the associated challenges emanated from the ineffective planning, management and design of market square as well as appraisal of the interactions among people of diverse ethnicity. Hence, the study explores users\u27 interactions and activities within three markets square in rural neighborhoods of South-west, Nigeria. The significant relationship between resident\u27s interactions and the community well-being was explored. Consequently, this study highlights the influence of the market square as a typical neighborhood open space on residents\u27 well-being. The study\u27s quantitative approach encircled the purposive structured survey questionnaire data obtained from Yorubas, Hausas, and Ibos respondents (n=382); and analyzed by SPSS statistical package (version 22). Meanwhile, the qualitative data included observation of various activity pattern among the three ethnic groups. The study\u27s findings revealed that an improvement in the market square quality becomes necessary in order to increase residents\u27 interactions and well-being. Also, the study elucidates the appropriate link between the built environment, residents\u27 interactions, and well-being. It is concluded that residents\u27 well-being is a reflection of an experience manifested within the interplay of individuals and groups\u27 social interactions. This study of people and place relationships could better equip the professionals in the built environment on the importance of creating a sustainable open space towards improving residents\u27 well-being and rural community revitalization efforts

Numerical study of multilayer adsorption on fractal surfaces

We report a numerical study of van der Waals adsoprtion and capillary condensation effects on self-similar fractal surfaces. An assembly of uncoupled spherical pores with a power-law distributin of radii is used to model fractal surfaces with adjustable dimensions. We find that the commonly used fractal Frankel-Halsey-Hill equation systematically fails to give the correct dimension due to crossover effects, consistent with the findings of recent experiments. The effects of pore coupling and curvature dependent surface tension were also studied.Comment: 11 pages, 3 figure

Electron focusing, mode spectroscopy and mass enhancement in small GaAs/AlGaAs rings

A new electron focusing effect has been discovered in small single and coupled GaAs/AlGaAs rings. The focusing in the single ring is attributed solely to internal orbits. The focusing effect allows the ring to be used as a small mass spectrometer. The focusing causes peaks in the magnetoresistance at low fields, and the peak positions were used to study the dispersion relation of the one-dimensional magnetoelectric subbands. The electron effective mass increases with the applied magnetic field by a factor of $50$, at a magnetic field of $0.5T$. This is the first time this increase has been measured directly. General agreement obtains between the experiment and the subband calculations for straight channels.Comment: 13 pages figures are available by reques

Effect of Layer-Stacking on the Electronic Structure of Graphene Nanoribbons

The evolution of electronic structure of graphene nanoribbons (GNRs) as a function of the number of layers stacked together is investigated using \textit{ab initio} density functional theory (DFT) including interlayer van der Waals interactions. Multilayer armchair GNRs (AGNRs), similar to single-layer AGNRs, exhibit three classes of band gaps depending on their width. In zigzag GNRs (ZGNRs), the geometry relaxation resulting from interlayer interactions plays a crucial role in determining the magnetic polarization and the band structure. The antiferromagnetic (AF) interlayer coupling is more stable compared to the ferromagnetic (FM) interlayer coupling. ZGNRs with the AF in-layer and AF interlayer coupling have a finite band gap while ZGNRs with the FM in-layer and AF interlayer coupling do not have a band gap. The ground state of the bi-layer ZGNR is non-magnetic with a small but finite band gap. The magnetic ordering is less stable in multilayer ZGNRs compared to single-layer ZGNRs. The quasipartcle GW corrections are smaller for bilayer GNRs compared to single-layer GNRs because of the reduced Coulomb effects in bilayer GNRs compared to single-layer GNRs.Comment: 10 pages, 5 figure

Chiral Disorder in QCD

Using the Gell-Mann-Oakes-Renner (GOR) relation and semi-classical arguments, we show that the bulk quark spectrum in QCD exhibits a variety of regimes including the ergodic one described by random matrix theory. We analyze the quark spectral form-factor in the diffusive and ballistic regime. We suggest that a class of chiral transitions in QCD is possibly of the metal-insulator type, with a universal spectral statistics at the mobility edge