arXiv subjects

Sebastian D. Pinski

Publications and source records attributed to Sebastian D. Pinski.

4 recordsLinked to original sources

arXiv2012

Localization-delocalization transition for disordered cubic harmonic lattices

We study numerically the disorder-induced localization-delocalization phase transitions that occur for mass and spring constant disorder in a three-dimensional cubic lattice with harmonic couplings. We show that, while the phase diagrams exhibit regions of stable and unstable waves, the universality of the transitions is the same for mass and spring constant disorder throughout all the phase boundaries. The combined value for the critical exponent of the localization lengths of $ν= 1.550^{+0.020}_{-0.017}$ confirms the agreement with the universality class of the standard electronic Anderson model of localization. We further support our investigation with studies of the density of states, the participation numbers and wave function statistics.

cond-mat.dis-nn↗

arXiv2011

Anderson universality in a model of disordered phonons

We consider the localization properties of a lattice of coupled masses and springs with random mass and spring constant values. We establish the full phase diagrams of the system for pure mass and pure spring disorder. The phase diagrams exhibit regions of stable as well as unstable wave modes. The latter are of interest for the instantaneous-normal-mode spectra of liquids and the nascent field of acoustic metamaterials. We show the existence of delocalization-localization transitions throughout the phase diagram and establish, by high-precision numerical studies, that the universality of these transitions is of the Anderson type.

cond-mat.dis-nn↗

arXiv2011

Adiabatic Quantum Computing

Adiabatic Quantum Computing (AQC) is a relatively new subject in the world of quantum computing, let alone Physics. Inspiration for this project has come from recent controversy around D-Wave Systems in British Columbia, Canada, who claim to have built a working AQC which is now commercially available and hope to be distributing a 1024 qubit chip by the end of 2008. Their 16 qubit chip was demonstrated online for the Supercomputing 2007 conference within which a few small problems were solved; although the explanations that journalists and critics received were minimal and very little was divulged in the question and answer session. This 'unconvincing' demonstration has caused physicists and computer scientists to hit back at D-Wave. The aim of this project is to give an introduction to the historic advances in classical and quantum computing and to explore the methods of AQC. Through numerical simulations an algorithm for the Max Independent Set problem is empirically obtained.

physics.pop-ph↗

arXiv2011

Study of the localization-delocalization transition for phonons via transfer matrix method techniques

We use a transfer-matrix method to study the localization properties of vibrations in a `mass and spring' model with simple cubic lattice structure. Disorder is applied as a box-distribution to the force-constants $k$ of the springs. We obtain the reduced localization lengths $Λ_M$ from calculated Lyapunov exponents for different system widths to roughly locate the squared critical transition frequency $ω_{\text{c}}^2$. The data is finite-size scaled to acquire the squared critical transition frequency of $ω_{\text{c}}^2 = 12.54 \pm 0.03$ and a critical exponent of $ν= 1.55 \pm 0.002$.

cond-mat.dis-nn↗