Exploring Nonlinear Logistic Behavior in Quantum Dynamics

by Open Science Repository Physics
(September 2014)

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To explore quantum and classical connection from a new perspective, a quantum population dynamics (QPoD) model common to several sciences is investigated. From postulates of causality and finiteness a classical quantum entity, a quanta, is defined with unitary extension and intensity. Applying the logistic relation to a quantum population of non-local two-state oscillators results in a quantum-classical equation linking wave and particle dynamics with an explicit account of decoherence. Varying over ~124 orders of magnitude, the coupling constant acts like a delta Dirac function between regimes. The quantum regime is conform to Schrödinger and Dirac equations according to respective Hamiltonian while the classical mode suppresses the quantum wave function and follows the Hamilton-Jacobi equation. Besides the quantum wave solutions, in the classical range, the general equation admits Fermi-Dirac and Bose-Einstein solution, relating to thermodynamics. Inertial mass is found in terms of the quantum entropy gradient. The most compact quantum cluster forming a crystal produces a unique flat space filling lattice cells of one simple tetrahedron and one composite truncated tetrahedron corresponding respectively to a fermionic cell and a bosonic cell. From this lattice geometry alone, the mass ratios of all fermion are expressed uniquely in terms of vertices and faces, matching charges properties of three generations and three families. Except for a minor degeneracy correction, the solution is shown to follow the logistic dynamics. The resulting mass equation is a function of dimensionless natural numbers. Many properties of the Standard Model are recovered from geometry at the Planck scale, respecting naturalness, uniqueness and minimality. QPoD may help addressing questions about the nature of spacetime and the physical structure of particles.

Keywords: nonlinear dynamics, chaos, foundation of quantum mechanics, modeling, philosophy of science.

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Exploring Nonlinear Logistic Behavior in Quantum Dynamics