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We obtain a generalization of the relativistic diffusion of Schay and Dudley for particles with spin. The diffusion equation is a classical version of an equation for the Wigner function of an elementary particle. The elementary particle is…
We develop a bonded-particle model for magneto-elastic rods that unifies large deformations, contact, and long-range magnetic interactions within a single discrete-element framework. The rod is discretized into orientable particles…
We introduce the probability distributions describing quantum observables in conventional quantum mechanics and clarify their relations to the tomographic probability distributions describing quantum states. We derive the evolution equation…
In this paper we create a model of particle motion on a three-dimensional lattice using discrete random walk with small steps. We rigorously construct a probability space of the particle trajectories. Unlike deterministic approach in…
We discuss the dynamics of single particle by laying a hypothesis that the Hamilton's principle of stationary action is not exact. We then postulate that the deviation of the action with sufficiently short time interval from the stationary…
We extend the Shirafuji model for massless particles with primary spacetime coordinates and composite four-momenta to a model for massive particles with spin and electric charge. The primary variables in the model are the spacetime…
We are presenting an internal trajectory model for a quantum particle in the Schroedinger non-relativistic approximation. This model is based on two new mathematical concepts: a complex analytical mechanics in Minplus complex analysis and a…
The difficulties with which the concept of point-like particles is beset, such as the infinities encountered in the existing theories of elementary particles, suggest a different approach to the study of these particles. Instead of…
We propose a quantum mechanics of extended objects that accounts for the finite extent of a particle defined via its Compton wavelength. The Hilbert space representation theory of such a quantum mechanics is presented and this…
The master equation describing non-equilibrium one-dimensional problems like diffusion limited reactions or critical dynamics of classical spin systems can be written as a Schr\"odinger equation in which the wave function is the probability…
We reduce Dirac's spinor formalism for a spin 1/2 particle to a complex wavefunction description in curved spacetimes. We consider a localized fermionic particle in curved spacetimes and perform an expansion in terms of the acceleration and…
We consider a particular 4-dimensional generalization of the transition from the Heisenberg to the Schr\"odinger picture. The space-time independent expansion with respect to the unitary irreducible representations of the Lorentz group is…
In this paper, a modified formulation of generalized probabilistic theories that will always give rise to the structure of Hilbert space of quantum mechanics, in any finite outcome space, is presented and the guidelines to how to extend…
The Schrodinger equation based on the de Broglie wave is the most fundamental equation of the quantum mechanics. There can be no doubt about it's prediction validity. However, the probabilistic interpretation on the quantum mechanics has…
The correlation between particle and wave descriptions of electron-matter interactions is analyzed by measuring the delocalization of an evanescent field using electron microscopy. Its spatial extension coincides with the energy-dependent,…
In two prior papers of this series, it was proposed that a wavefunction model of a heavy particle and a collection of light particles might generate ``Brownian-Motion-Like" trajectories as well as diffusive motion (displacement proportional…
Wave particle duality remains a central interpretational challenge in quantum theory. In this work, we develop a trajectory-based description of photon dynamics formulated in an extended complex space within the relativistic quantum…
The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length…
The wave-particle duality and its probabilistic interpretation are at the heart of quantum mechanics. Here we show that, in some standard contexts like the double slit experiment, a deterministic interpretation can be provided. This…
Recently, a self-contained trajectory-based formulation of non-relativistic quantum mechanics was developed [Ann. Phys. 315, 505 (2005); Chem. Phys. 370, 4 (2010); J. Chem. Phys. 136, 031102 (2012)], that makes no use of wavefunctions or…