175 research outputs found
On the Relationship Between Complex Potentials and Strings of Projection Operators
It is of interest in a variety of contexts, and in particular in the arrival
time problem, to consider the quantum state obtained through unitary evolution
of an initial state regularly interspersed with periodic projections onto the
positive -axis (pulsed measurements). Echanobe, del Campo and Muga have
given a compelling but heuristic argument that the state thus obtained is
approximately equivalent to the state obtained by evolving in the presence of a
certain complex potential of step-function form. In this paper, with the help
of the path decomposition expansion of the associated propagators, we give a
detailed derivation of this approximate equivalence. The propagator for the
complex potential is known so the bulk of the derivation consists of an
approximate evaluation of the propagator for the free particle interspersed
with periodic position projections. This approximate equivalence may be used to
show that to produce significant reflection, the projections must act at time
spacing less than 1/E, where E is the energy scale of the initial state.Comment: 29 pages, LaTex, 4 figures. Substantial revision
Analytic Examples, Measurement Models and Classical Limit of Quantum Backflow
We investigate the backflow effect in elementary quantum mechanics - the
phenomenon in which a state consisting entirely of positive momenta may have
negative current and the probability flows in the opposite direction to the
momentum. We compute the current and flux for states consisting of
superpositions of gaussian wave packets. These are experimentally realizable
but the amount of backflow is small. Inspired by the numerical results of Penz
et al (M.Penz, G.Gr\"ubl, S.Kreidl and P.Wagner, J.Phys. A39, 423 (2006)), we
find two non-trivial wave functions whose current at any time may be computed
analytically and which have periods of significant backflow, in one case with a
backwards flux equal to about 70 percent of the maximum possible backflow, a
dimensionless number , discovered by Bracken and Melloy
(A.J.Bracken and G.F.Melloy, J.Phys. A27, 2197 (1994)). This number has the
unusual property of being independent of (and also of all other
parameters of the model), despite corresponding to an obviously
quantum-mechanical effect, and we shed some light on this surprising property
by considering the classical limit of backflow. We discuss some specific
measurement models in which backflow may be identified in certain measurable
probabilities.Comment: 33 pages, 14 figures. Minor revisions. Published versio
Quantum Arrival Time For Open Systems
We extend previous work on the arrival time problem in quantum mechanics, in
the framework of decoherent histories, to the case of a particle coupled to an
environment. The usual arrival time probabilities are related to the
probability current, so we explore the properties of the current for general
open systems that can be written in terms of a master equation of Lindblad
form. We specialise to the case of quantum Brownian motion, and show that after
a time of order the localisation time the current becomes positive. We show
that the arrival time probabilities can then be written in terms of a POVM,
which we compute. We perform a decoherent histories analysis including the
effects of the environment and show that time of arrival probabilities are
decoherent for a generic state after a time much greater than the localisation
time, but that there is a fundamental limitation on the accuracy, ,
with which they can be specified which obeys . We confirm
that the arrival time probabilities computed in this way agree with those
computed via the current, provided there is decoherence. We thus find that the
decoherent histories formulation of quantum mechanics provides a consistent
explanation for the emergence of the probability current as the classical
arrival time distribution, and a systematic rule for deciding when
probabilities may be assigned.Comment: 30 pages, 1 figure. Published versio
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
Recommended from our members
Perspectives on Correctness in Probabilistic Inference from Psychology
Research into decision making has enabled us to appreciate that the notion of correctness is multifaceted. Different normative framework for correctness can lead to different insights about correct behavior. We illustrate the shifts for correctness insights with two tasks, the Wason selection task and the conjunction fallacy task; these tasks have had key roles in the development of logical reasoning and decision making research respectively. The Wason selection task arguably has played an important part in the transition from understanding correctness using classical logic to classical probability theory (and information theory). The conjunction fallacy has enabled a similar shift from baseline classical probability theory to quantum probability. The focus of this overview is the latter, as it represents a novel way for understanding probabilistic inference in psychology. We conclude with some of the current challenges concerning the application of quantum probability theory in psychology in general and specifically for the problem of understanding correctness in decision making
Recommended from our members
Contemporary morality: moral judgments in digital contexts
Nowadays, several of the situations in which we have to make decisions are in digital form. In a first experiment (N=1010) we showed that people’s moral judgments depend on the Digital Context (Smartphone vs. PC) in which a dilemma is presented, becoming more utilitarian (vs. deontological) when using Smartphones in high conflict moral dilemmas. To provide additional evidence, we ran a second (N=250) and a third experiment (N=300), where we introduced time constraints and we manipulated time instructions. Our results provide an extended perspective on Dual-Process Models of Moral Judgment, as we showed that the use of smartphones, often assumed to be hurried which would be consistent with gut-feeling decision-making, increased the likelihood of utilitarian responses and decreased deontological ones. We suggest that the increase in utilitarian judgments is a result of inducing high construal, increasing psychological distance and giving rise to an abstract representation of actions. A fourth experiment (N=1211), where we measured psychological distance, provided some first evidence for our hypotheses. This is one of the first studies to look at the impact of the digital age on moral judgments and the results presented have consequences for understanding moral choice in our increasingly virtualized world
Recommended from our members
Patterns and evolution of moral behavior: moral dynamics in everyday life
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 on 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 again 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 on). The objective was to look at the evolution of moral choice across a series of scenarios, that is, to 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)
Quantum Arrival and Dwell Times via Idealised Clocks
A number of approaches to the problem of defining arrival and dwell time
probabilities in quantum theory make use of idealised models of clocks. An
interesting question is the extent to which the probabilities obtained in this
way are related to standard semiclassical results. In this paper we explore
this question using a reasonably general clock model, solved using path
integral methods. We find that in the weak coupling regime where the energy of
the clock is much less than the energy of the particle it is measuring, the
probability for the clock pointer can be expressed in terms of the probability
current in the case of arrival times, and the dwell time operator in the case
of dwell times, the expected semiclassical results. In the regime of strong
system-clock coupling, we find that the arrival time probability is
proportional to the kinetic energy density, consistent with an earlier model
involving a complex potential. We argue that, properly normalized, this may be
the generically expected result in this regime. We show that these conclusions
are largely independent of the form of the clock Hamiltonian.Comment: 19 pages, 4 figures. Published versio
Recommended from our members
The triangle inequality constraint in similarity judgments
Since Tversky's (1977) seminal investigation, the triangle inequality, along with symmetry and minimality, have had a central role in investigations of the fundamental constraints on human similarity judgments. The meaning of minimality and symmetry in similarity judgments has been straightforward, but this is not the case for the triangle inequality. Expressed in terms of dissimilarities, and assuming a simple, linear function between dissimilarities and distances, the triangle inequality constraint implies that human behaviour should be consistent with Dissimilarity (A,B) + Dissimilarity (B,C) ≥ Dissimilarity (A,C), where A, B, and C are any three stimuli. We show how we can translate this constraint into one for similarities, using Shepard's (1987) generalization law, and so derive the multiplicative triangle inequality for similarities, Sim(A,C)≥Sim(A,B)(dot operator)Sim(B,C) where 0≤Sim(x,y)≤1. Can humans violate the multiplicative triangle inequality? An empirical demonstration shows that they can
Recommended from our members
The Environmental Agency's Assessment of the Post-Closure Safety Case for the BNFL DRIGG Low Level Radioactive Waste Disposal Facility
The Environment Agency is responsible, in England and Wales, for authorization of radioactive waste disposal under the Radioactive Substances Act 1993. British Nuclear Fuels plc (BNFL) is currently authorized by the Environment Agency to dispose of solid low level radioactive waste at its site at Drigg, near Sellafield, NW England. As part of a planned review of this authorization, the Environment Agency is currently undertaking an assessment of BNFL's Post-Closure Safety Case Development Programme for the Drigg disposal facility. This paper presents an outline of the review methodology developed and implemented by the Environment Agency specifically for the planned review of BNFL's Post-Closure Safety Case. The paper also provides an overview of the Environment Agency's progress in its on-going assessment programme
- …