The Emergence of Superconducting Systems in Anti-de Sitter Space

In this article, we investigate the mathematical relationship between a (3+1) dimensional gravity model inside Anti-de Sitter space $\rm AdS_4$, and a (2+1) dimensional superconducting system on the asymptotically flat boundary of $\rm AdS_4$ (in the absence of gravity). We consider a simple case of the Type II superconducting model (in terms of Ginzburg-Landau theory) with an external perpendicular magnetic field ${\bf H}$. An interaction potential $V(r,\psi) = \alpha(T)|\psi|^2/r^2+\chi|\psi|^2/L^2+\beta|\psi|^4/(2 r^k )$ is introduced within the Lagrangian system. This provides more flexibility within the model, when the superconducting system is close to the transition temperature $T_c$. Overall, our result demonstrates that the two Ginzburg-Landau differential equations can be directly deduced from Einstein's theory of general relativity.Comment: 10 pages, 2 figure

Vector Potential and Berry phase-induced Force

We present a general theoretical framework for the exact treatment of a hybrid system that is composed of a quantum subsystem and a classical subsystem. When the quantum subsystem is dynamically fast and the classical subsystem is slow, a vector potential is generated with a simple canonical transformation. This vector potential, on one hand, gives rise to the familiar Berry phase in the fast quantum dynamics; on the other hand, it yields a Lorentz-like force in the slow classical dynamics. In this way, the pure phase (Berry phase) of a wavefunction is linked to a physical force.Comment: 4 pages, 1 figur

Introduction to Graphene Electronics -- A New Era of Digital Transistors and Devices

The speed of silicon-based transistors has reached an impasse in the recent decade, primarily due to scaling techniques and the short-channel effect. Conversely, graphene (a revolutionary new material possessing an atomic thickness) has been shown to exhibit a promising value for electrical conductivity. Graphene would thus appear to alleviate some of the drawbacks associated with silicon-based transistors. It is for this reason why such a material is considered one of the most prominent candidates to replace silicon within nano-scale transistors. The major crux here, is that graphene is intrinsically gapless, and yet, transistors require a band-gap pertaining to a well-defined ON/OFF logical state. Therefore, exactly as to how one would create this band-gap in graphene allotropes is an intensive area of growing research. Existing methods include nano-ribbons, bilayer and multi-layer structures, carbon nanotubes, as well as the usage of the graphene substrates. Graphene transistors can generally be classified according to two working principles. The first is that a single graphene layer, nanoribbon or carbon nanotube can act as a transistor channel, with current being transported along the horizontal axis. The second mechanism is regarded as tunneling, whether this be band-to-band on a single graphene layer, or vertically between adjacent graphene layers. The high-frequency graphene amplifier is another talking point in recent research, since it does not require a clear ON/OFF state, as with logical electronics. This paper reviews both the physical properties and manufacturing methodologies of graphene, as well as graphene-based electronic devices, transistors, and high-frequency amplifiers from past to present studies. Finally, we provide possible perspectives with regards to future developments.Comment: This is an updated version of our review article, due to be published in Contemporary Physics (Sept 2013). Included are updated references, along with a few minor corrections. (45 pages, 19 figures

Adiabatic Geometric Phase for a General Quantum States

A geometric phase is found for a general quantum state that undergoes adiabatic evolution. For the case of eigenstates, it reduces to the original Berry's phase. Such a phase is applicable in both linear and nonlinear quantum systems. Furthermore, this new phase is related to Hannay's angles as we find that these angles, a classical concept, can arise naturally in quantum systems. The results are demonstrated with a two-level model.Comment: 4 pages, 2 figure

Facilitated diffusion of DNA-binding proteins: Simulation of large systems

The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be calibrated in numerical simulations inside a test system of moderate size. Once this is done, reaction times of systems of arbitrary dimensions are derived by extrapolation, with an accuracy of 10 to 15 percent. The achieved speed up, when compared to explicit simulations of the reaction process, is increasing proportional to the extrapolated volume of the cell.Comment: 8 pages, 4 figures, submitted to J. Chem. Phy

Oscillation of spin polarization in a two-dimensional hole gas under a perpendicular magnetic field

Spin-charge coupling is studied for a strongly confined two-dimensional hole gas subject to a perpendicular magnetic field. The study is based on spin-charge coupled drift-diffusion equations derived from quantum-kinetic equations in an exact manner. The spin-orbit interaction induces an extra out-of-plane spin polarization. This contribution exhibits a persistent oscillatory pattern in the strong-coupling regime.Comment: 11 pages and 1 figur

Lattice Statistics in Three Dimensions: Exact Solution of Layered Dimer and Layered Domain Wall Models

Exact analyses are given for two three-dimensional lattice systems: A system of close-packed dimers placed in layers of honeycomb lattices and a layered triangular-lattice interacting domain wall model, both with nontrivial interlayer interactions. We show that both models are equivalent to a 5-vertex model on the square lattice with interlayer vertex-vertex interactions. Using the method of Bethe ansatz, a closed-form expression for the free energy is obtained and analyzed. We deduce the exact phase diagram and determine the nature of the phase transitions as a function of the strength of the interlayer interaction.Comment: 22 pages in Revtex, 6 PS files, submitted to PR

Feedback effects on the current correlations in Y-shaped conductors

We study current fluctuations in a Y-shaped conductor connected to external leads with finite impedances. We show that, due to voltage fluctuations in the circuit, the moments of the transferred charges cannot be obtained from simple rescaling of the bare values already in the second moments. The cross-correlation between the output terminals can change from negative to positive under certain parameter regimes.Comment: 4 pages, figures attached separatel