Optimal traps in graphene

We transform the two-dimensional Dirac-Weyl equation, which governs the charge carriers in graphene, into a non-linear first-order differential equation for scattering phase shift, using the so-called variable phase method. This allows us to utilize the Levinson Theorem to find zero-energy bound states created electrostatically in realistic structures. These confined states are formed at critical potential strengths, which leads to us posit the use of `optimal traps' to combat the chiral tunneling found in graphene, which could be explored experimentally with an artificial network of point charges held above the graphene layer. We also discuss scattering on these states and find the zero angular momentum states create a dominant peak in scattering cross-section as energy tends towards the Dirac point energy, suggesting a dominant contribution to resistivity.Comment: 11 pages, 5 figure

Back gating of a two-dimensional hole gas in a SiGe quantum well

A device comprising a low-resistivity, n-type, Si substrate as a back gate to a p-type (boron), remote-doped, SiGe quantum well has been fabricated and characterized. Reverse and forward voltage biasing of the gate with respect to the two-dimensional hole gas in the quantum well allows the density of holes to be varied from 8 × 1011 cm–2 down to a measurement-limited value of 4 × 1011 cm–2. This device is used to demonstrate the evolution with decreasing carrier density of a re-entrant insulator state between the integer quantum Hall effect states with filling factors 1 and 3

Tunneling in Fractional Quantum Mechanics

We study the tunneling through delta and double delta potentials in fractional quantum mechanics. After solving the fractional Schr\"odinger equation for these potentials, we calculate the corresponding reflection and transmission coefficients. These coefficients have a very interesting behaviour. In particular, we can have zero energy tunneling when the order of the Riesz fractional derivative is different from 2. For both potentials, the zero energy limit of the transmission coefficient is given by $\mathcal{T}_0 = \cos^2{\pi/\alpha}$, where $\alpha$ is the order of the derivative ($1 < \alpha \leq 2$).Comment: 21 pages, 3 figures. Revised version; accepted for publication in Journal of Physics A: Mathematical and Theoretica

Adiabatic Approximation for weakly open systems

We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is ``physically reasonable'' as under wide conditions it leads to a completely positive evolution, if the original master equation can be written on a time-dependent Lindblad form. We demonstrate the approximation for a non-Abelian holonomic implementation of the Hadamard gate, disturbed by a decoherence process. We compare the resulting approximate evolution with numerical simulations of the exact equation.Comment: New material added, references added and updated, journal reference adde

Analytic approach to bifurcation cascades in a class of generalized H\'enon-Heiles potentials

We derive stability traces of bifurcating orbits in H\'enon-Heiles potentials near their saddlesComment: LaTeX revtex4, 38 pages, 7 PostScript figures, 2 table

Resoundings of the flesh: Caring for others by way of “second person” perspectivity

In bringing ourselves to the encounter with the experience of others, we bring our bodies with us—and, in doing so, we are able to resonate not only intellectually but also empathically with the other's experiences and expressions (which are given to us both verbally and nonverbally). In remaining faithful to our foundations in phenomenology (Husserl, Heidegger, Merleau-Ponty, and Levinas), we shall talk about taking notice of others from within the relational “exchange” and reflect upon what, precisely, are the experientially given “affairs” to which Husserl invited us to return. Our interest begins with the other's “first person” experience, but since we cannot access this directly, we must rely on the resonance we find within ourselves, within our own lived bodies, when we are addressed by the other, whether in word or in gesture. I am wondering what the other is experiencing and all my powers of perception are driven toward this other, whose first person experience remains just out of reach and accessible only insofar as I have this capacity for a deeper “bodily felt” awareness in which the other's experience takes possession of me. Merleau-Ponty's notion of bearing “witness” to behavior is useful in illuminating this “second person” perspective, which takes its point of departure from Husserl's (1910–1911) intersubjective reduction, by means of which we “participate in the other's positing” (1952/1989, emphasis added) and thereby grasp the meaning of the other's expression. Ultimately, the intuitive talent of the caring professional will be shown to reside in his or her being able to move beyond what the other is able to say to a more deeply felt attunement to what is being revealed to us in the other's presence. Applications to patient care are discussed

Gender-Inclusive HCI Research and Design: A Conceptual Review

Previous research has investigated gender and its implications for HCI. We consider inclusive design of technology whatever the gender of its users of particular importance. This conceptual review provides an overview of the motivations that have driven research in gender and inclusive HCI design. We review the empirical evidence for the impact of gender in thinking and behavior which underlies HCI research and design. We then present how HCI design might inadvertently embed and perpetuate gender stereotypes. We then present current HCI design approaches to tackle gender stereotypes and to produce gender-inclusive designs. We conclude by discussing possible future directions in this area

Heat exchange mediated by a quantum system

We consider heat transfer between two thermal reservoirs mediated by a quantum system using the generalized quantum Langevin equation. The thermal reservoirs are treated as ensembles of oscillators within the framework of the Drude-Ullersma model. General expressions for the heat current and thermal conductance are obtained for arbitrary coupling strength between the reservoirs and the mediator and for different temperature regimes. As an application of these results we discuss the origin of Fourier's law in a chain of large, but finite subsystems coupled to each other by the quantum mediators. We also address a question of anomalously large heat current between the STM tip and substrate found in a recent experiment. The question of minimum thermal conductivity is revisited in the framework of scaling theory as a potential application of the developed approach.Comment: 16 pages, 6 figure

Far-off-resonant wave interaction in one-dimensional photonic crystals with quadratic nonlinearity

We extend a recently developed Hamiltonian formalism for nonlinear wave interaction processes in spatially periodic dielectric structures to the far-off-resonant regime, and investigate numerically the three-wave resonance conditions in a one-dimensional optical medium with $\chi^{(2)}$ nonlinearity. In particular, we demonstrate that the cascading of nonresonant wave interaction processes generates an effective $\chi^{(3)}$ nonlinear response in these systems. We obtain the corresponding coupling coefficients through appropriate normal form transformations that formally lead to the Zakharov equation for spatially periodic optical media.Comment: 14 pages, 4 figure

Occurrence of periodic Lam\'e functions at bifurcations in chaotic Hamiltonian systems

We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lam\'e equation as classified in 1940 by Ince. In Hamiltonians with C_${2v}$ symmetry, they occur alternatingly as Lam\'e functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lam\'e equation. We also show that the two pairs of orbits created at period-doubling bifurcations of touch-and-go type are given by two different linear combinations of algebraic Lam\'e functions with period 8K.Comment: LaTeX2e, 22 pages, 14 figures. Version 3: final form of paper, accepted by J. Phys. A. Changes in Table 2; new reference [25]; name of bifurcations "touch-and-go" replaced by "island-chain