Heterogeneity and Disorder: Contributions of Rolf Landauer

Rolf Landauer made important contributions to many branches of science. Within the broad area of transport in disordered media, he wrote seminal papers on electrical conduction in macroscopically inhomogeneous materials, as well as fundamental analyses of electron transport in quantum mechanical systems with disorder on the atomic scale. We review here some of these contributions. We also briefly describe some main events in his personal and scientific life.Comment: 10 pages, 3 figures; presented on the occasion when Rolf Landauer was awarded, posthumously, the inaugural ETOPIM Medal at the ETOPIM 8 Conference, which took place during 7--12 June, 2009 in Rethymnon, Cret

Universal conductance reduction in a quantum wire

Even a single point defect in a quantum wire causes a conductance reduction. In this paper we prove (without any approximations) that for any point impurity this conductance reduction in all the sub-bands is exactly 2e^2/h. Moreover, it is shown that in the case of a surface defect, not only is the conductance minimum independent of the defect characteristics, but the transmission matrix also converges to universal (defect-independent) values. We also discuss particle confinement between two arbitrarily weak point defects.Comment: 4 pages, 4 figures (Revtex

TV synchronization system features stability and noise immunity

Horizontal jitter in the video presentation in television systems is prevented by using an additional sync level. This circuitry uses simultaneous signals at both sync and porch frequencies, providing a sync identification from which a coincidence circuit can generate pulses having the required stability and noise immunity

Means for generating a sync signal in an FM communication system Patent

Circuitry for generating sync signals in FM communication systems including video informatio

Exploring the operation of a tiny heat engine

We model a tiny heat engine as a Brownian particle that moves in a viscous medium in a sawtooth potential (with or without load) assisted by $\it {alternately}$ placed hot and cold heat baths along its path. We find closed form expression for the steady state current as a function of the model parameters. This enables us to deal with the energetics of the model and evaluate either its efficiency or its coefficient of performance depending upon whether the model functions either as a heat engine or as a refrigerator, respectively. We also study the way current changes with changes in parameters of interest. When we plot the phase diagrams showing the way the model operates, we not only find regions where it functions as a heat engine and as a refrigerator but we also identify a region where the model functions as neither of the two.Comment: 8 pages and 13 figure

Conductance and polarization in quantum junctions

We revisit the expression for the conductance of a general nanostructure -- such as a quantum point contact -- as obtained from the linear response theory. We show that the conductance represents the strength of the Drude singularity in the conductivity $\sigma(k,k';i\omega \to 0)$. Using the equation of continuity for electric charge we obtain a formula for conductance in terms of polarization of the system. This identification can be used for direct calculation of the conductance for systems of interest even at the {\it ab-initio} level. In particular, we show that one can evaluate the conductance from calculations for a finite system without the need for special ``transport'' boundary conditions

Energy-Entanglement Relation for Quantum Energy Teleportation

Protocols of quantum energy teleportation (QET), while retaining causality and local energy conservation, enable the transportation of energy from a subsystem of a many-body quantum system to a distant subsystem by local operations and classical communication through ground-state entanglement. We prove two energy-entanglement inequalities for a minimal QET model. These relations help us to gain a profound understanding of entanglement itself as a physical resource by relating entanglement to energy as an evident physical resource.Comment: 16 pages, 1 figure, to appear in Physics Letter

The Landauer Resistance and Band Spectra for the Counting Quantum Turing Machine

The generalized counting quantum Turing machine (GCQTM) is a machine which, for any N, enumerates the first $2^{N}$ integers in succession as binary strings. The generalization consists of associating a potential with read-1 steps only. The Landauer Resistance (LR) and band spectra were determined for the tight binding Hamiltonians associated with the GCQTM for energies both above and below the potential height. For parameters and potentials in the electron region, the LR fluctuates rapidly between very high and very low values as a function of momentum. The rapidity and extent of the fluctuations increases rapidly with increasing N. For N=18, the largest value considered, the LR shows good transmission probability as a function of momentum with numerous holes of very high LR values present. This is true for energies above and below the potential height. It is suggested that the main features of the LR can be explained by coherent superposition of the component waves reflected from or transmitted through the $2^{N-1}$ potentials in the distribution. If this explanation is correct, it provides a dramatic illustration of the effects of quantum nonlocality.Comment: 19 pages Latex, elsart.sty file included, 12 postscript figures, Submitted to PhysComp96 for publication in Physica-

Escaping the Trap of too Precise Topic Queries

At the very center of digital mathematics libraries lie controlled vocabularies which qualify the {\it topic} of the documents. These topics are used when submitting a document to a digital mathematics library and to perform searches in a library. The latter are refined by the use of these topics as they allow a precise classification of the mathematics area this document addresses. However, there is a major risk that users employ too precise topics to specify their queries: they may be employing a topic that is only "close-by" but missing to match the right resource. We call this the {\it topic trap}. Indeed, since 2009, this issue has appeared frequently on the i2geo.net platform. Other mathematics portals experience the same phenomenon. An approach to solve this issue is to introduce tolerance in the way queries are understood by the user. In particular, the approach of including fuzzy matches but this introduces noise which may prevent the user of understanding the function of the search engine. In this paper, we propose a way to escape the topic trap by employing the navigation between related topics and the count of search results for each topic. This supports the user in that search for close-by topics is a click away from a previous search. This approach was realized with the i2geo search engine and is described in detail where the relation of being {\it related} is computed by employing textual analysis of the definitions of the concepts fetched from the Wikipedia encyclopedia.Comment: 12 pages, Conference on Intelligent Computer Mathematics 2013 Bath, U

Spectrum of π\pi Electrons in Graphene as an Alternant Macromolecule and Its Specific Features in Quantum Conductance

An exact description of $\pi$ electrons based on the tight-binding model of graphene as an alternant, plane macromolecule is presented. The model molecule can contain an arbitrary number of benzene rings and has armchair- and zigzag-shaped edges. This suggests an instructive alternative to the most commonly used approach, where the reference is made to the honeycomb lattice periodic in its A and B sublattices. Several advantages of the macromolecule model are demonstrated. The newly derived analytical relations detail our understanding of $\pi$ electron nature in achiral graphene ribbons and carbon tubes and classify these structures as quantum wires.Comment: 13 pages 8 figures, revised in line with referee's comment