Decision Making for Inconsistent Expert Judgments Using Negative Probabilities

In this paper we provide a simple random-variable example of inconsistent information, and analyze it using three different approaches: Bayesian, quantum-like, and negative probabilities. We then show that, at least for this particular example, both the Bayesian and the quantum-like approaches have less normative power than the negative probabilities one.Comment: 14 pages, revised version to appear in the Proceedings of the QI2013 (Quantum Interactions) conferenc

On the notion of composite system

The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.Comment: 9 pages. Comments are welcom

Quantum Darwinism

Quantum Darwinism describes the proliferation, in the environment, of multiple records of selected states of a quantum system. It explains how the fragility of a state of a single quantum system can lead to the classical robustness of states of their correlated multitude; shows how effective `wave-packet collapse' arises as a result of proliferation throughout the environment of imprints of the states of quantum system; and provides a framework for the derivation of Born's rule, which relates probability of detecting states to their amplitude. Taken together, these three advances mark considerable progress towards settling the quantum measurement problem

Off-shell superconformal nonlinear sigma-models in three dimensions

We develop superspace techniques to construct general off-shell N=1,2,3,4 superconformal sigma-models in three space-time dimensions. The most general N=3 and N=4 superconformal sigma-models are constructed in terms of N=2 chiral superfields. Several superspace proofs of the folklore statement that N=3 supersymmetry implies N=4 are presented both in the on-shell and off-shell settings. We also elaborate on (super)twistor realisations for (super)manifolds on which the three-dimensional N-extended superconformal groups act transitively and which include Minkowski space as a subspace.Comment: 67 pages; V2: typos corrected, one reference added, version to appear on JHE

Random-phase approximation and its applications in computational chemistry and materials science

The random-phase approximation (RPA) as an approach for computing the electronic correlation energy is reviewed. After a brief account of its basic concept and historical development, the paper is devoted to the theoretical formulations of RPA, and its applications to realistic systems. With several illustrating applications, we discuss the implications of RPA for computational chemistry and materials science. The computational cost of RPA is also addressed which is critical for its widespread use in future applications. In addition, current correction schemes going beyond RPA and directions of further development will be discussed.Comment: 25 pages, 11 figures, published online in J. Mater. Sci. (2012

Megascopic Quantum Phenomena. A Critical Study of Physical Interpretations

A megascopic revalidation is offered providing responses and resolutions of current inconsistencies and existing contradictions in present-day quantum theory. As the core of this study we present an independent proof of the Goldstone theorem for a quantum field formulation of molecules and solids. Along with phonons two types of new quasiparticles appear: rotons and translons. In full analogy with Lorentz covariance, combining space and time coordinates, a new covariance is necessary, binding together the internal and external degrees of freedom, without explicitly separating the centre-of-mass, which normally applies in both classical and quantum formulations. The generally accepted view regarding the lack of a simple correspondence between the Goldstone modes and broken symmetries, has significant consequences: an ambiguous BCS theory as well as a subsequent Higgs mechanism. The application of the archetype of the classical spontaneous symmetry breaking, i.e. the Mexican hat, as compared to standard quantum relations, i.e. the Jahn-Teller effect, superconductivity or the Higgs mechanism, becomes a disparity. In short, symmetry broken states have a microscopic causal origin, but transitions between them have a teleological component. The different treatments of the problem of the centre of gravity in quantum mechanics and in field theories imply a second type of Bohr complementarity on the many-body level opening the door for megascopic representations of all basic microscopic quantum axioms with further readings for teleonomic megascopic quantum phenomena, which have no microscopic rationale: isomeric transitions, Jahn-Teller effect, chemical reactions, Einstein-de Haas effect, superconductivity-superfluidity, and brittle fracture.Comment: 117 pages, 17 sections, final revised version from 20 May 2019 but uploaded after the DOI was know