A Green-function approach to transport phenomena in quantum pumps

We present a general treatment to study transport phenomena in systems described by tight-binding Hamiltonians coupled to reservoirs and with one or more time-periodic potentials. We apply this treatment to the study of transport phenomena in a double barrier structure with one and two harmonic potentials. Among other properties, we discuss the origin of the sign of the net current.Comment: To appear in PR

Contrast salience across three-dimensional chromoluminance space

AbstractWe have extended previously studies of relative contrast salience [Switkes & Crognale, 1999. Comparison of color and luminance contrast: apples versus oranges? Vision Res. 39 (10), 1823–1831] to chromaticities intermediate to cardinal chromatic axes. We find that: (i) observers can reliably match the perceptual contrast of gratings differing in chromoluminance irrespective of whether they lie along canonical axes or intermediate axes; (ii) the relative perceptual contrast of gratings in the isoluminant plane correlates well with a metric based on an ideal observer but added luminance results in a perceptual contrast lower than would be predicted by this model; (iii) contrast matches in the isoluminant plane can be modeled by simple combinations of the cone contrasts for the LM and S pathways; (iv) unipolar, non-opponent, mechanisms may subserve the perception of contrast; and (v) the relative salience of suprathreshold chromatic gratings varies in accord with contrast thresholds but the low spatial frequency increase in luminance contrast threshold is not manifest in a reduced suprathreshold salience for luminance gratings

Symmetry and environment effects on rectification mechanisms in quantum pumps

We consider a paradigmatic model of quantum pumps and discuss its rectification properties in the framework of a symmetry analysis proposed for ratchet systems. We discuss the role of the environment in breaking time-reversal symmetry and the possibility of a finite directed current in the Hamiltonian limit of annular systems.Comment: To appear as Rapid Communication in PR

Heat production and energy balance in nanoengines driven by time-dependent fields

We present a formalism to study the heat transport and the power developed by the local driving fields on a quantum system coupled to macroscopic reservoirs. We show that, quite generally, two important mechanisms can take place: (i) directed heat transport between reservoirs induced by the ac potentials and (ii) at slow driving, two oscillating out of phase forces perform work against each other, while the energy dissipated into the reservoirs is negligibleComment: 5 pages, 4 figure

Human Impact on Planetary Temperature and Glacial Volume: Extending a Toy Climate Model to a New Millennium

Starting with a toy climate model from the literature, we employ a system of two nonlinear differential equations to model the reciprocal effects of the average temperature and the percentage of glacial volume on Earth. In the literature, this model is used to demonstrate the potential for a stable periodic orbit over a long time span in the form of an attracting limit cycle. In the roughly twenty five years since this model appeared in the literature, the effects of global warming and human-impacted climate change have become much more well known and apparent. We demonstrate modification of initial conditions to understand how human activity could affect the model results. Although we too see the attracting limit cycle that yields a periodic orbit, we demonstrate that small perturbations in initial conditions can lead to extreme outcomes due to the presence of a nearby saddle point. We simulate the results over time to to highlight the critical nature of perturbations that in effect change the initial conditions and to determine how soon drastic climate events might take place

Rolling Dice on a Date

When a young mathematician faces the prospect of a date, all kinds of mathematics ensue. Here we explore her innovative way to keep the conversation going through rolling dice to decide which conversation starter to utilize. In the course of our exploration, we solve an interesting generating function problem

Congressional Districting: "Rocks-Pebbles-Sand"

As a case study into an algorithmic approach to congressional districting, North Carolina provides a lot to explore. Statistical modeling has called into question whether recent North Carolina district plans are unbiased. In particular, the literature suggests that the district plan used in the 2016 U.S. House of Representatives election yields outlier results that are statistically unlikely to be obtained without the application of bias. Therefore, methods for creating strong and fair district plans are needed. Informed by previous districting models and algorithms, we build a model and algorithm to produce an ensemble of viable Congressional district plans. Our work contributes a ``Rocks-Pebbles-Sand'' concept and procedure facilitating reasonable population equity with a small overall number of county splits among districts. Additionally, our methodology minimizes the initial need for granular, precinct-level data, thereby reducing the risk of covert gerrymandering. This case study indicates plausibility of an approach built upon an easy-to-understand intuition.Comment: 26 pages, 14 figures, 10 table

Control of Decoherence and Correlation in Single Quantum Dissipative Oscillator Systems

A single quantum dissipative oscillator described by the Lindblad equation serves as a model for a nanosystem. This model is solved exactly by using the ambiguity function. The solution shows the features of decoherence (spatial extent of quantum behavior), correlation (spatial scale over which the system localizes to its physical dimensions), and mixing (mixed- state spatial correlation). A new relation between these length scales is obtained here. By varying the parameters contained in the Lindblad equation, it is shown that decoherence and correlation can be controlled. We indicate possible interpretation of the Lindblad parameters in the context of experiments using engineered reservoirs.Comment: 10 pages, 2 figure