Nonlinear nanomechanical resonators for quantum optoelectromechanics

We present a scheme for tuning and controlling nano mechanical resonators by subjecting them to electrostatic gradient fields, provided by nearby tip electrodes. We show that this approach enables access to a novel regime of optomechanics, where the intrinsic nonlinearity of the nanoresonator can be explored. In this regime, one or several laser driven cavity modes coupled to the nanoresonator and suitably adjusted gradient fields allow to control the motional state of the nanoresonator at the single phonon level. Some applications of this platform have been presented previously [New J. Phys. 14, 023042 (2012), Phys. Rev. Lett. 110, 120503 (2013)]. Here, we provide a detailed description of the corresponding setup and its optomechanical coupling mechanisms, together with an in-depth analysis of possible sources of damping or decoherence and a discussion of the readout of the nanoresonator state.Comment: 15 pages, 6 figure

Effects of classification context on categorization in natural categories

The patterns of classification of borderline instances of eight common taxonomic categories were examined under three different instructional conditions to test two predictions: first, that lack of a specified context contributes to vagueness in categorization, and second, that altering the purpose of classification can lead to greater or lesser dependence on similarity in classification. The instructional conditions contrasted purely pragmatic with more technical/quasi-legal contexts as purposes for classification, and these were compared with a no-context control. The measures of category vagueness were between-subjects disagreement and within-subjects consistency, and the measures of similarity based categorization were category breadth and the correlation of instance categorization probability with mean rated typicality, independently measured in a neutral context. Contrary to predictions, none of the measures of vagueness, reliability, category breadth, or correlation with typicality were generally affected by the instructional setting as a function of pragmatic versus technical purposes. Only one subcondition, in which a situational context was implied in addition to a purposive context, produced a significant change in categorization. Further experiments demonstrated that the effect of context was not increased when participants talked their way through the task, and that a technical context did not elicit more all-or-none categorization than did a pragmatic context. These findings place an important boundary condition on the effects of instructional context on conceptual categorization

Quantum Structure in Cognition: Why and How Concepts are Entangled

One of us has recently elaborated a theory for modelling concepts that uses the state context property (SCoP) formalism, i.e. a generalization of the quantum formalism. This formalism incorporates context into the mathematical structure used to represent a concept, and thereby models how context influences the typicality of a single exemplar and the applicability of a single property of a concept, which provides a solution of the 'Pet-Fish problem' and other difficulties occurring in concept theory. Then, a quantum model has been worked out which reproduces the membership weights of several exemplars of concepts and their combinations. We show in this paper that a further relevant effect appears in a natural way whenever two or more concepts combine, namely, 'entanglement'. The presence of entanglement is explicitly revealed by considering a specific example with two concepts, constructing some Bell's inequalities for this example, testing them in a real experiment with test subjects, and finally proving that Bell's inequalities are violated in this case. We show that the intrinsic and unavoidable character of entanglement can be explained in terms of the weights of the exemplars of the combined concept with respect to the weights of the exemplars of the component concepts.Comment: 10 page

Assessing Semantic Similarities among Geospatial Feature Class Definitions

The assessment of semantic similarity among objects is a basic requirement for semantic interoperability. This paper presents an innovative approach to semantic similarity assessment by combining the advantages of two different strategies: featurematching process and semantic distance calculation. The model involves a knowledge base of spatial concepts that consists of semantic relations (is-a and part-whole) and distinguishing features (functions, parts, and attributes). By taking into consideration cognitive properties of similarity assessments, this model expects to represent a cognitively plausible and computationally achievable method for measuring the degree of interoperability

Feature integration in natural language concepts

Two experiments measured the joint influence of three key sets of semantic features on the frequency with which artifacts (Experiment 1) or plants and creatures (Experiment 2) were categorized in familiar categories. For artifacts, current function outweighed both originally intended function and current appearance. For biological kinds, appearance and behavior, an inner biological function, and appearance and behavior of offspring all had similarly strong effects on categorization. The data were analyzed to determine whether an independent cue model or an interactive model best accounted for how the effects of the three feature sets combined. Feature integration was found to be additive for artifacts but interactive for biological kinds. In keeping with this, membership in contrasting artifact categories tended to be superadditive, indicating overlapping categories, whereas for biological kinds, it was subadditive, indicating conceptual gaps between categories. It is argued that the results underline a key domain difference between artifact and biological concepts

Classical Logical versus Quantum Conceptual Thought: Examples in Economics, Decision theory and Concept Theory

Inspired by a quantum mechanical formalism to model concepts and their disjunctions and conjunctions, we put forward in this paper a specific hypothesis. Namely that within human thought two superposed layers can be distinguished: (i) a layer given form by an underlying classical deterministic process, incorporating essentially logical thought and its indeterministic version modeled by classical probability theory; (ii) a layer given form under influence of the totality of the surrounding conceptual landscape, where the different concepts figure as individual entities rather than (logical) combinations of others, with measurable quantities such as 'typicality', 'membership', 'representativeness', 'similarity', 'applicability', 'preference' or 'utility' carrying the influences. We call the process in this second layer 'quantum conceptual thought', which is indeterministic in essence, and contains holistic aspects, but is equally well, although very differently, organized than logical thought. A substantial part of the 'quantum conceptual thought process' can be modeled by quantum mechanical probabilistic and mathematical structures. We consider examples of three specific domains of research where the effects of the presence of quantum conceptual thought and its deviations from classical logical thought have been noticed and studied, i.e. economics, decision theory, and concept theories and which provide experimental evidence for our hypothesis.Comment: 14 page

Iterative algorithm versus analytic solutions of the parametrically driven dissipative quantum harmonic oscillator

We consider the Brownian motion of a quantum mechanical particle in a one-dimensional parabolic potential with periodically modulated curvature under the influence of a thermal heat bath. Analytic expressions for the time-dependent position and momentum variances are compared with results of an iterative algorithm, the so-called quasiadiabatic propagator path integral algorithm (QUAPI). We obtain good agreement over an extended range of parameters for this spatially continuous quantum system. These findings indicate the reliability of the algorithm also in cases for which analytic results may not be available a priori.Comment: 15 pages including 11 figures, one reference added, minor typos correcte

Cumulant Expansions and the Spin-Boson Problem

The dynamics of the dissipative two-level system at zero temperature is studied using three different cumulant expansion techniques. The relative merits and drawbacks of each technique are discussed. It is found that a new technique, the non-crossing cumulant expansion, appears to embody the virtues of the more standard cumulant methods.Comment: 26 pages, LaTe