32 research outputs found
The propagator for the step potential using the path decomposition expansion
We present a direct path integral derivation of the propagator in the
presence of a step potential. The derivation makes use of the Path
Decomposition Expansion (PDX), and also of the definition of the propagator as
a limit of lattice paths.Comment: To appear in DICE 2008 conference proceeding
Aspects of Time in Quantum Theory
We consider a number of aspects of the problem of defining time observables in quantum
theory. Time observables are interesting quantities in quantum theory because they often
cannot be associated with self-adjoint operators. Their definition therefore touches on
foundational issues in quantum theory.
Various operational approaches to defining time observables have been proposed in the
past. Two of the most common are those based on pulsed measurements in the form of strings
of projection operators and continuous measurements in the form of complex potentials. One
of the major achievements of this thesis is to prove that these two operational approaches
are equivalent.
However operational approaches are somewhat unsatisfying by themselves. To provide a
definition of time observables which is not linked to a particular measurement scheme we
employ the decoherent, or consistent, histories approach to quantum theory. We focus on the
arrival time, one particular example of a time observable, and we use the relationship between
pulsed and continuous measurements to relate the decoherent histories approach to one based
on complex potentials. This lets us compute the arrival time probability distribution in
decoherent histories and we show that it agrees with semiclassical expectations in the right
limit. We do this both for a free particle and for a particle coupled to an environment.
Finally, we consider how the results discussed in this thesis relate to those derived by
coupling a particle to a model clock. We show that for a general class of clock models the
probabilities thus measured can be simply related to the ideal ones computed via decoherent
histories
A review of the decoherent histories approach to the arrival time problem in quantum theory
We review recent progress in understanding the arrival time problem in
quantum mechanics, from the point of view of the decoherent histories approach
to quantum theory. We begin by discussing the arrival time problem, focussing
in particular on the role of the probability current in the expected classical
solution. After a brief introduction to decoherent histories we review the use
of complex potentials in the construction of appropriate class operators. We
then discuss the arrival time problem for a particle coupled to an environment,
and review how the arrival time probability can be expressed in terms of a POVM
in this case. We turn finally to the question of decoherence of the
corresponding histories, and we show that this can be achieved for simple
states in the case of a free particle, and for general states for a particle
coupled to an environment.Comment: 10 pages. To appear in DICE 2010 conference proceeding
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Advanced tools and concepts for quantum cognition: A tutorial
This tutorial is intended to provide an introduction to some advanced tools and concepts needed to construct more realistic quantum models of cognition and decision. The aim is to cover, in a format suitable for researchers with some limited exposure to quantum models of cognition, the ideas of density matrices, POVM type measurements and open system dynamics. The central theme we explore is how we might introduce noise into our quantum models, and the effect this has on model behavior. These important ideas are likely to be very useful for constructing more realistic cognitive models, but they are generally not covered by introductory accounts of quantum theory. We hope that this tutorial will help to introduce these tools to other researchers interested in constructing quantum models of cognition
Modeling verbal short-term memory: A walk around the neighborhood.
When remembering over the short-term, long-term knowledge has a large effect on the number of correctly recalled items and little impact on memory for order. This is true, for example, when the effects of semantic category are examined. Contrary to what these findings suggest, Poirier et al. in 2015 proposed that memory for order relies on the level of activation within long-term networks. Importantly, although their view has been criticized, they showed that manipulating semantic associations led to item migrations that were atypical. In this article, we show that similar migrations can be obtained with another knowledge-based factor: orthographic neighborhood. In three experiments, we manipulated the orthographic neighborhood of to-be-recalled items. The latter is a sublexical factor; as such, it is much less likely than semantic relatedness to involve demand characteristics or grouping strategies. The first experiment established that the neighborhood manipulation produced the pattern of item migrations previously observed with semantic relatedness, confirming that the migration effect can generalize to other variables. The last two experiments suggested that migrations were due to the features shared across list items rather than to item co-activation (as in Poirier et al.). The results were successfully modeled by calling upon the Revised Feature Model, where recall depends on selecting a retrieval candidate based on the features of the cueing information. Overall, our findings underline the usefulness of a model where retrieval is determined by relative distinctiveness and underline that multiple mechanisms can lead to order errors in recall
The propagator for the step potential and delta function potential using the path decomposition expansion
We present a derivation of the propagator for a particle in the presence of
the step and delta function potentials. These propagators are known, but we
present a direct path integral derivation, based on the path decomposition
expansion and the Brownian motion definition of the path integral. The
derivation exploits properties of the Catalan numbers, which enumerate certain
classes of lattice paths.Comment: 11 pages, 3 figure
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A quantum theory account of order effects and conjunction fallacies in political judgments
Are our everyday judgments about the world around us normative? Decades of research in the judgment and decision-making literature suggest the answer is no. If people's judgments do not follow normative rules, then what rules if any do they follow? Quantum probability theory is a promising new approach to modeling human behavior that is at odds with normative, classical rules. One key advantage of using quantum theory is that it explains multiple types of judgment errors using the same basic machinery, unifying what have previously been thought of as disparate phenomena. In this article, we test predictions from quantum theory related to the co-occurrence of two classic judgment phenomena, order effects and conjunction fallacies, using judgments about real-world events (related to the U.S. presidential primaries). We also show that our data obeys two a priori and parameter free constraints derived from quantum theory. Further, we examine two factors that moderate the effects, cognitive thinking style (as measured by the Cognitive Reflection Test) and political ideology