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A quantum theoretical explanation for probability judgment errors
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning
Optomechanical-like coupling between superconducting resonators
We propose and analyze a circuit that implements a nonlinear coupling between
two superconducting microwave resonators. The resonators are coupled through a
superconducting quantum interference device (SQUID) that terminates one of the
resonators. This produces a nonlinear interaction on the standard
optomechanical form, where the quadrature of one resonator couples to the
photon number of the other resonator. The circuit therefore allows for
all-electrical realizations of analogs to optomechanical systems, with coupling
that can be both strong and tunable. We estimate the coupling strengths that
should be attainable with the proposed device, and we find that the device is a
promising candidate for realizing the single-photon strong-coupling regime. As
a potential application, we discuss implementations of networks of
nonlinearly-coupled microwave resonators, which could be used in
microwave-photon based quantum simulation.Comment: 10 pages, 7 figure
Variational approximation of flux in conforming finite element methods for elliptic partial differential equations: a model problem
We consider the approximation of elliptic boundary value problems by conforming finite element methods. A model problem, the Poisson equation with Dirichlet boundary conditions, is used to examine the convergence behavior of flux defined on an internal boundary which splits the domain in two. A variational definition of flux, designed to satisfy local conservation laws, is shown to lead to improved rates of convergence
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