Related papers: Measured quantum probability distribution function…

The Wigner function is a quantum analogue of the classical joined distribution of position and momentum. As such is should be a good tool to study quantum-classical correspondence. In this paper, the classical limit of the Wigner function…

Quantum particles in a potential are described by classical statistical probabilities. We formulate a basic time evolution law for the probability distribution of classical position and momentum such that all known quantum phenomena follow,…

We study entanglement dynamics in quantum Brownian motion (QBM) models. Our main tool is the Wigner function propagator. Time evolution in the Wigner picture is physically intuitive and it leads to a simple derivation of a master equation…

Full formal descriptions of algorithms making use of quantum principles must take into account both quantum and classical computing components and assemble them so that they communicate and cooperate.Moreover, to model concurrent and…

A new formulation of quantum mechanics is proposed based on a new principle that can be considered a generalization of the Born rule. The principle is composed of a mathematical expression and an associated interpretation, and establishes a…

A set of probabilities along with corresponding quantiles are often used to define predictive distributions or probabilistic forecasts. These quantile predictions offer easily interpreted uncertainty of an event, and quantiles are generally…

We construct a model of Brownian Motion on a pseudo-Riemannian manifold associated with general relativity. There are two aspects of the problem: The first is to define a sequence of stopping times associated with the Brownian "kicks" or…

We introduce the notion of {\em covariance measure structure} for square integrable stochastic processes. We define Wiener integral, we develop a suitable formalism for stochastic calculus of variations and we make Gaussian assumptions only…

In previous articles we presented a derivation of Born's rule and unitary transforms in Quantum Mechanics (QM), from a simple set of axioms built upon a physical phenomenology of quantization. Physically, the structure of QM results of an…

We review the main features of the Weyl-Wigner formulation of noncommutative quantum mechanics. In particular, we present a $\star$-product and a Moyal bracket suitable for this theory as well as the concept of noncommutative Wigner…

Starting from the famous Pauli problem on the possibility to associate quantum states with probabilities, the formulation of quantum mechanics in which quantum states are described by fair probability distributions (tomograms, i.e.…

Weak measurements of photon position can be used to obtain direct experimental evidence of the wavefunction of a photon between generation and ultimate detection. Significantly, these measurement results can also be understood as complex…

The recently proposed probability representation of quantum mechanics is generalized to quantum field theory. We introduce a probability distribution functional for field configurations and find an evolution equation for such a…

The motion of a quantum particle hopping on a simple cubic lattice under the influence of thermal noise and of a static random potential is expected to be diffusive, i.e., the particle is expected to exhibit `quantum Brownian motion', no…

The density distribution function of the integral of the exponential Brownian motion is determined explicitly in the form of a rapidly convergent series.

A simple model of quantum particle is proposed in which the particle in a {\it macroscopic} rest frame is represented by a {\it microscopic d}-dimensional oscillator, {\it s=(d-1)/2} being the spin of the particle. The state vectors are…

This paper is about quantum heat defined as the change in energy of a bath during a process. The presentation takes into account recent developments in classical strong-coupling thermodynamics, and addresses a version of quantum heat which…

We construct a class of one-dimensional diffusion processes on the particles of branching Brownian motion that are symmetric with respect to the limits of random martingale measures. These measures are associated with the extended extremal…

Quantum mechanics predicts the joint probability distribution of the outcomes of simultaneous measurements of commuting observables, but, in the state of the art, has lacked the operational definition of simultaneous measurements. The…

It has recently been shown that it is possible to represent the complete quantum state of any system as a phase-space quasi-probability distribution (Wigner function) [Phys Rev Lett 117, 180401]. Such functions take the form of expectation…