A model of adaptive decision-making from representation of information environment by quantum fields.

We present the mathematical model of decision-making (DM) of agents acting in a complex and uncertain environment (combining huge variety of economical, financial, behavioural and geopolitical factors). To describe interaction of agents with it, we apply the formalism of quantum field theory (QTF). Quantum fields are a purely informational nature. The QFT model can be treated as a far relative of the expected utility theory, where the role of utility is played by adaptivity to an environment (bath). However, this sort of utility-adaptivity cannot be represented simply as a numerical function. The operator representation in Hilbert space is used and adaptivity is described as in quantum dynamics. We are especially interested in stabilization of solutions for sufficiently large time. The outputs of this stabilization process, probabilities for possible choices, are treated in the framework of classical DM. To connect classical and quantum DM, we appeal to Quantum Bayesianism. We demonstrate the quantum-like interference effect in DM, which is exhibited as a violation of the formula of total probability, and hence the classical Bayesian inference scheme.This article is part of the themed issue 'Second quantum revolution: foundational questions'.

Quantum counting: Operator methods for discrete population dynamics with applications to cell division.

The set of natural numbers may be identified with the spectrum of eigenvalues of an operator (quantum counting), and the dynamical equations of populations of discrete, countable items may be formulated using operator methods. These equations take the form of time dependent operator equations, involving Hamiltonian operators, from which the statistical time dependence of population numbers may be determined. The quantum operator method is illustrated by a novel approach to cell population dynamics. This involves Hamiltonians that mimic the process of stimulated cell division. We evaluate two different models, one in which the stimuli are expended in the division process and one in which the stimuli act as true catalysts. While the former model exhibits only bounded cell population variations, the latter exhibits two distinct regimes; one has bounded population fluctuations about a mean level and in the other, the population can undergo growth to levels that are orders of magnitude above threshold levels, through an instability that could be interpreted as a cancerous growth phase.