Related papers: Probabilistic cellular automaton for quantum parti…
A deterministic model with a large number of continuous and discrete degrees of freedom is described, and a statistical treatment is proposed. The model exactly obeys a Schrodinger equation, which has to be interpreted exactly according to…
A new formulation of quantum mechanics based on differential commutator brackets is developed. We have found a wave equation representing the fermionic particle. In this formalism, the continuity equation mixes the Klein-Gordon and…
We analyze the problem of one dimensional quantum particle falling in a constant gravitational field, also known as the {\it bouncing ball}, employing a semiclassical approach known as momentous effective quantum mechanics. In this…
The chaotic diffusion for particles moving in a time dependent potential well is described by using two different procedures: (i) via direct evolution of the mapping describing the dynamics and ; (ii) by the solution of the diffusion…
Optimal simultaneous control of position and momentum can be achieved by maximizing the probabilities of finding their experimentally observed values within two well-defined intervals. The assumption that particles move along straight lines…
The goal of this paper is to apply the collection of mathematical tools known as the "method of arbitrary functions" to analyze how probability arises from quantum dynamics. We argue that in a toy model of quantum measurement the Born rule…
We investigate dynamical many-body systems capable of universal computation, which leads to their properties being unpredictable unless the dynamics is simulated from the beginning to the end. Unpredictable behavior can be quantitatively…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
Sequential Monte Carlo methods, also known as particle methods, are a popular set of techniques for approximating high-dimensional probability distributions and their normalizing constants. These methods have found numerous applications in…
The transport of ultra-cold atoms in magneto-optical potentials provides a clean setting in which to investigate the distinct predictions of classical versus quantum dynamics for a system with coupled degrees of freedom. In this system,…
The transport equation of active motion is generalised to consider time-fractional dynamics for describing the anomalous diffusion of self-propelled particles observed in many different systems. In the present study, we consider an…
The work introduces a 3D cellular automaton model for the spatial and crystallographic prediction of spherulite growth phenomena in polymers at the mesoscopic scale. The automaton is discrete in time, real space, and orientation space. The…
We show that all non-relativistic quantum processes, whether open or closed, are either unitary or probabilistic unitary, i.e., probabilistic combination of unitary evolutions. This means that for open quantum systems, its continuous…
Quantum annealing is a generic name of quantum algorithms to use quantum-mechanical fluctuations to search for the solution of optimization problem. It shares the basic idea with quantum adiabatic evolution studied actively in quantum…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
A new kind of cellular automaton (CA) for the study of the dynamics of urban systems is proposed. The state of a cell is not described using a finite set, but by means of continuum variables. A population sector is included, taking into…
Gravitational clustering of a random distribution of point masses is dominated by the effective short-range interactions due to large-scale isotropy. We introduce a one-dimensional cellular automaton to reproduce this effect in the most…
The one-parameter two-dimensional cellular automaton with the Margolus neighbourhood is analyzed based on the considering the projection of the stochastic movements of a single particle. Introducing the auxiliary random variable associated…
We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states. Unlike the conventional one this model…