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

Intermediate Judgments Inhibit Belief Updating: Zeno’s Paradox in Decision

Rational agents should update their beliefs in the light of newevidence. Equally, changes in belief should depend only onthe quality of the evidence, and not on factors such as the or-der in which the evidence is acquired, or whether intermedi-ate judgements are requested during evidence acquisition. Incontrast we show that requests for intermediate judgments caninhibit belief updating for real decision makers, which repre-sents a new type of decision making fallacy. This behaviour isparadoxical from the point of view of classical Bayesian mod-els, but we show that it is consistent with an a priori, parameterfree prediction of a cognitive model based on quantum theory

Moral Dynamics In Everyday Life: How Does Morality Evolve In Time?

Recent research on moral dynamics (the processes and phenomena –collective or individual– by which moral behavior and moral attitudes emerge, evolve, spread, erode or disappear) shows that an individual’s ethical mind-set (i.e., outcome-based vs. rule-based) moderates the impact of an initial ethical or unethical act regarding the likelihood of behaving ethically on a subsequent occasion. More specifically, an outcome-based mind-set facilitates Moral Balancing (behaving ethically or unethically decreases the likelihood of engaging in the same type of behavior later), whereas a rule-based mind-set facilitates Moral Consistency (engaging in an ethical or unethical behavior increases the likelihood of engaging in the same type of behavior later). Our objective was to look at the evolution of moral choice across a series of scenarios and so explore if these moral patterns (Balancing vs. Consistency) are maintained over time. The results of three studies showed that Moral Balancing is not maintained over time. On the other hand, Moral Consistency could be maintained over time, if the mind-set was reinforced before making a new moral judgment (but not otherwise)

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

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