2,980 research outputs found
Systems, environments, and soliton rate equations: A non-Kolmogorovian framework for population dynamics
Soliton rate equations are based on non-Kolmogorovian models of probability
and naturally include autocatalytic processes. The formalism is not widely
known but has great unexplored potential for applications to systems
interacting with environments. Beginning with links of contextuality to
non-Kolmogorovity we introduce the general formalism of soliton rate equations
and work out explicit examples of subsystems interacting with environments. Of
particular interest is the case of a soliton autocatalytic rate equation
coupled to a linear conservative environment, a formal way of expressing
seasonal changes. Depending on strength of the system-environment coupling we
observe phenomena analogous to hibernation or even complete blocking of decay
of a population.Comment: 51 pages, 15 eps figure
Entanglement of Conceptual Entities in Quantum Model Theory (QMod)
We have recently elaborated 'Quantum Model Theory' (QMod) to model situations
where the quantum effects of contextuality, interference, superposition,
entanglement and emergence, appear without the entities giving rise to these
situations having necessarily to be of microscopic nature. We have shown that
QMod models without introducing linearity for the set of the states. In this
paper we prove that QMod, although not using linearity for the state space,
provides a method of identification for entangled states and an intuitive
explanation for their occurrence. We illustrate this method for entanglement
identification with concrete examples
Anatomy of Fluorescence: Quantum trajectory statistics from continuously measuring spontaneous emission
We investigate the continuous quantum measurement of a superconducting qubit
undergoing fluorescence. The fluorescence of the qubit is detected via a
phase-preserving heterodyne measurement, giving the fluorescence quadrature
signals as two continuous qubit readout results. By using the stochastic path
integral approach to the measurement physics, we derive most likely paths
between boundary conditions on the state, and compute approximate time
correlation functions between all stochastic variables via diagrammatic
perturbation theory. We focus on paths that increase in energy during the
continuous measurement. Our results are compared to Monte Carlo numerical
simulation of the trajectories, and we find close agreement between direct
simulation and theory. We generalize this analysis to arbitrary diffusive
quantum systems that are continuously monitored.Comment: 15 pages, 5 figures, plenty of diagram
A model of the emergence and evolution of integrated worldviews
It \ud
is proposed that the ability of humans to flourish in diverse \ud
environments and evolve complex cultures reflects the following two \ud
underlying cognitive transitions. The transition from the \ud
coarse-grained associative memory of Homo habilis to the \ud
fine-grained memory of Homo erectus enabled limited \ud
representational redescription of perceptually similar episodes, \ud
abstraction, and analytic thought, the last of which is modeled as \ud
the formation of states and of lattices of properties and contexts \ud
for concepts. The transition to the modern mind of Homo \ud
sapiens is proposed to have resulted from onset of the capacity to \ud
spontaneously and temporarily shift to an associative mode of thought \ud
conducive to interaction amongst seemingly disparate concepts, \ud
modeled as the forging of conjunctions resulting in states of \ud
entanglement. The fruits of associative thought became ingredients \ud
for analytic thought, and vice versa. The ratio of \ud
associative pathways to concepts surpassed a percolation threshold \ud
resulting in the emergence of a self-modifying, integrated internal \ud
model of the world, or worldview
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