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By analyzing the relationships between a socioeconomical system modeled through evolutionary game theory and a physical system modeled through quantum mechanics we show how although both systems are described through two theories apparently…
Elementary Cycles are intrinsic periodic phenomena, classical in the essence, whose classical relativistic dynamics reproduce the complete coherence (perfect recurrences) typically associated to the pure quantum behaviours of elementary…
We explore connections between von Neumann's mean ergodic theorem and concepts of model theory. As an application we present a proof Wiener's generalization of von Neumann's result in which the group acting on the Hilbert space…
More than 15 years ago, a new approach to quantum mechanics was suggested, in which Hermiticity of the Hamiltonian was to be replaced by invariance under a discrete symmetry, the product of parity and time-reversal symmetry, $\mathcal{PT}$.…
We define a new quantum Hermitian operator (namely, the energy variance operator) which is simply duplicated from the statistical definition of energy variance in classical physics. Its expectation value yields the standard deviation of the…
On the occasion of the 100th anniversary of the beginning of the revolutionary contributions to physics by Einstein, I am happy to respond to a problem posed by him in 1905. He said: In this paper it will be shown that according to the…
On a new approach to quantum gravity called Electro-Magnetic Quantum Gravity (EMQG) which is manifestly compatible with Cellular Automata (CA) theory and is based on a new theory of inertia (ref. 5) proposed by R. Haisch, A. Rueda, and H.…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
The Standard Model of particle physics is built on the principle of local gauge symmetry. This work provides a pedagogical introduction for advanced undergraduates by using quantum electrodynamics (QED) as the simplest example of a gauge…
Based on the view that thermal equilibrium should be characterized through macroscopic observations, we develop a general theory about typicality of thermal equilibrium and the approach to thermal equilibrium in macroscopic quantum systems.…
We study the ergodic properties of quantized ergodic maps of the torus. It is known that these satisfy quantum ergodicity: For almost all eigenstates, the expectation values of quantum observables converge to the classical phase-space…
We find a new effect for the behaviour of Von Neumann entropy. For this we derive the framework for describing Von Neumann entropy in non-Hermitian quantum systems and then apply it to a simple interacting PT symmetric bosonic system. We…
The quantization of the electrical charge in the electrodynamics and of the hypercharge in the standard model are imposed in the theory based not on theoretical arguments but on the experimental observations. In this paper we propose a…
The notion of Shannon entropy is crucial for the theory of classical information. In quantum information theory, an analogous key role is played by the von Neumann entropy: quantum information processing is closely related to entropy…
Elementary Cycles Theory is a self-consistent, unified formulation of quantum and relativistic physics. Here we introduce its basic quantum aspects. On one hand, Newton's law of inertia states that every isolated particle has persistent…
The stochastic processes underlying the growth and stability of biological and psychological systems reveal themselves when far from equilibrium. Far from equilibrium, nonergodicity reigns. Nonergodicity implies that the average outcome for…
In this paper two hypotheses are developed. The first hypothesis is the existence of random phenomena/experiments in which the events cannot generally be assigned a definite probability but that nevertheless admit a class of nearly certain…
Three problems stand in the way of deriving classical theories from quantum mechanics: those of realist interpretation, of classical properties and of quantum measurement. Recently, we have identified some tacit assumptions that lie at the…
If a cat, a cannonball, and an economics textbook are all dropped from the same height, they fall to the ground with exactly the same acceleration under the influence of gravity. This equality of gravitational accelerations of different…
Boltzmann introduced in the 1870's a logarithmic measure for the connection between the thermodynamical entropy and the probabilities of the microscopic configurations of the system. His entropic functional for classical systems was…