Non-Markovian Effects on the Brownian Motion of a Free Particle

Non-Markovian effects upon the Brownian movement of a free particle in the presence as well as in the absence of inertial force are investigated within the framework of Fokker-Planck equations (Rayleigh and Smoluchowski equations). More specifically, it is predicted that non-Markovian features can enhance the values of the mean square displacement and momentum, thereby assuring the mathematical property of differentiability of the these physically observable quantities

Anti-Social Realism

Work included in a group exhibition at Charlie Smith Gallery, London curated by Juan Bolivar and John Stark. Exhibting artists include: Juan Bolivar, Dan Coombs, Graham Crowley, Karen David, Nathan Eastwood, Geraint Evans, John Greenwood, Sigrid Holmwood, Kate Lyddon, Maharishi x Rebecca & Mike, John Salt, John Stark. The term 'Anti-Social Realism', which acts as this exhibitions title, is not one that is commonly understood. It is intended to pose questions such as: is 'revolutionary' art a viable possibility today? What does it mean to be (anti) social in an increasingly interconnected but physically separated society? Can we, through archaic practices such as painting and sculpture, engage with notions of 'social realism’ now presented on a daily basis through the new silver-screen veneer of the digital age? In response, this exhibition attempts to pose pictorial possibilities and create tensions through the selected artworks, tackling notions of contemporary realism and in turn offering us a distant echo of a political reality. The wry misnomer of the exhibition title slips between many interwoven threads, simultaneously conjuring up images of 'anti-social behaviour orders' (ASBO), anarchist riots, or the solitary artist locked away from the world attempting to connect on a higher level. In this light, the exhibiting artists are presented as 'social mystics' and it could be said that their work operates by a means of turning inwards to create social radiation

Persistent charge and spin currents in the long wavelength regime for graphene rings

We address the problem of persistent charge and spin currents on a Corbino disk built from a graphene sheet. We consistently derive the Hamiltonian including kinetic, intrinsic (ISO) and Rashba spin-orbit interactions in cylindrical coordinates. The Hamiltonian is carefully considered to reflect hermiticity and covariance. We compute the energy spectrum and the corresponding eigenfunctions separately for the intrinsic and Rashba spin-orbit interactions. In order to determine the charge persistent currents we use the spectrum equilibrium linear response definition. We also determine the spin and pseudo spin polarizations associated with such equilibrium currents. For the intrinsic case one can also compute the correct currents by applying the bare velocity operator to the ISO wavefunctions or alternatively the ISO group velocity operator to the free wavefunctions. Charge currents for both SO couplings are maximal in the vicinity of half integer flux quanta. Such maximal currents are protected from thermal effects because contributing levels plunge ($\sim$1K) into the Fermi sea at half integer flux values. Such a mechanism, makes them observable at readily accessible temperatures. Spin currents only arise for the Rashba coupling, due to the spin symmetry of the ISO spectrum. For the Rashba coupling, spin currents are cancelled at half integer fluxes but they remain finite in the vicinity, and the same scenario above protects spin currents

Gauge field theory approach to spin transport in a 2D electron gas

We discuss the Pauli Hamiltonian including the spin-orbit interaction within an U(1) x SU(2) gauge theory interpretation, where the gauge symmetry appears to be broken. This interpretation offers new insight into the problem of spin currents in the condensed matter environment, and can be extended to Rashba and Dresselhaus spin-orbit interactions. We present a few outcomes of the present formulation: i) it automatically leads to zero spin conductivity, in contrast to predictions of Gauge symmetric treatments, ii) a topological quantization condition leading to voltage quantization follows, and iii) spin interferometers can be conceived in which, starting from a arbitrary incoming unpolarized spinor, it is always possible to construct a perfect spin filtering condition.Comment: Invited contribution to Statphys conference, June 2009, Lviv (Ukraine

The Transport of Acoustic Energy at Two-Dimensional Material Interfaces

The control of vibrational energy within solids is a fundamental engineering challenge with numerous technological applications. While the control of electrons and photons has revolutionized computation and communication, the control of phonons, the quantized particle of vibrational energy, has been far less successful. Acoustic energy is a form of vibrational energy that involves coherent excitations of phonons to form larger elastic waves. It is this coherence that allows it to be a valuable engineering tool for applications in imaging, frequency/time control, and structural monitoring. Traditional methods of reflecting acoustic energy involve interfacing different phases of matter to reflect via an impedance mismatch, like air gaps and foams. The problem that this thesis addresses is that these methods are not scalable to extreme or nanoscale environments. The objective of this thesis is to demonstrate methods of reflecting acoustic energy by constructing solids with different types of chemical interactions, not by interfacing solids with different phases of matter. We investigate the transport of acoustic energy at the interface of two-dimensional materials. Two-dimensional materials are crystalline layers of atoms that interface with other materials via a weak van der Waals interaction. Our investigation applies both computational and experimental methods. The computational methods blend super-wavelength continuum models with sub-wavelength molecular dynamics simulations. Treating the interface as a thin plate coupled to a bulk elastic material by springs, we predict that the weak van der Waals interaction should produce a pressure-release boundary condition that reflects broad acoustic energy from infrasound to hypersound. These predictions are verified using pitch-catch experiments at 1 MHz in a water tank. The results of these experiments demonstrate a nearly three-decibel attenuation from one 2D layer. When normalized to the atomic thickness of the layer, this system provides orders of magnitude better isolation than foams, rubbers, or metasurfaces