Related papers: Formalizing Elements of Probabilistic Mechanics
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
Multi-dimensional quantum walks can exhibit highly non-trivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a 2D optical quantum walk on a…
The dynamics of a test particle interacting with diffusing impurities in one dimension is investigated analytically and numerically. In the absence of an applied external force, the dynamics of the particle can be characterized by a…
In this paper, we study discrete-time quantum walks on one-dimensional lattices. We find that the coherent dynamics depends on the initial states and coin parameters. For infinite size of lattice, we derive an explicit expression for the…
A discrete-time totally asymmetric simple exclusion process on a lattice with open boundaries is considered. There are particles of different types. The type of a particle is characterized by the probability that a particle moves to a…
We propose that a quantum particle in a potential in one space dimension can be described by a probabilistic cellular automaton. While the simple updating rule of the automaton is deterministic, the probabilistic description is introduced…
This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large…
On the basis of information theory, a new formalism of classical non-relativistic mechanics of a mass point is proposed. The particle trajectories of a general dynamical system defined on an (1+n)-dimensional smooth manifold are treated…
In the worldline formalism, scalar Quantum Electrodynamics on a 2-dimensional lattice is related to the areas of closed loops on this lattice. We exploit this relationship in order to determine the general structure of the moments of the…
In this paper we study a random walk in a one-dimensional dynamic random environment consisting of a collection of independent particles performing simple symmetric random walks in a Poisson equilibrium with density $\rho \in (0,\infty)$.…
This note describes recent results on the localization properties of Random Quantum Walks on the d-dimensional lattice in a regime analogous to the large disorder regime by means of the Fractional Moments Method adapted to the unitary…
Depending on how the dynamical activity of a particle in a random environment is influenced by an external field $E$, its differential mobility at intermediate $E$ can turn negative. We discuss the case where for slowly changing random…
The foundations of Statistical Mechanics can be recovered almost in their entirety from the Principle of Maximum Entropy. In this work we show that its non-equilibrium generalization, the Principle of Maximum Caliber (Jaynes, 1980), when…
Statistical thermodynamics delivers the probability distribution of the equilibrium state of matter through the constrained maximization of a special functional, entropy. Its elegance and enormous success have led to numerous attempts to…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
We propose an experimental realization of discrete quantum random walks using neutral atoms trapped in optical lattices. The random walk is taking place in position space and experimental implementation with present day technology --even…
We present an introduction to the study of a relativistic particle moving under the influence of its own Frenet-Serret curvatures. With the aim of introducing the notation and conventions used in this paper, we first recall the action of a…
We study the dynamics of a particle in continuous time and space, the displacement of which is governed by an internal degree of freedom (spin). In one definite limit, the so-called quantum random walk is recovered but, although quite…
We construct a real-time lattice-gauge-theory-type action for a spin-1/2 matter field of a single particle on a (1+1)-dimensional spacetime lattice. The framework is based on a discrete-time quantum walk, and is hence inherently unitary and…
Motivated by various recent experimental findings, we propose a dynamical model of intermittently self-propelled particles: active particles that recurrently switch between two modes of motion, namely an active run-state and a turn state,…