Related papers: Estimation of a classical parameter with gaussian …
Physics is based on probabilities as fundamental entities of a mathematical description. Expectation values of observables are computed according to the classical statistical rule. The overall probability distribution for one world covers…
Quantum metrology employs entanglement to enhance measurement precision. The focus and progress so far have primarily centered on estimating a single parameter. In diverse application scenarios, the estimation of more than one single…
A perturbation method to analytically describe the dynamics of a classical spinning particle, based on the Mathisson-Papapetrou-Dixon (MPD) equations of motion, is presented. By a power series expansion with respect to the particle's spin…
We briefly review the use of the order parameter probability distribution function as a useful tool to obtain the critical properties of statistical mechanical models using computer Monte Carlo simulations. Some simple discrete spin…
The estimation of cosmological parameters from precision observables is an important industry with crucial ramifications for particle physics. This article discusses the statistical methods presently used in cosmological data analysis,…
Quantum optical metrology aims to identify ultimate sensitivity bounds for the estimation of parameters encoded into quantum states of the electromagnetic field. In many practical applications, including imaging, microscopy, and remote…
The paper presents a statistical model which reproduces the results of Monte Carlo simulations to estimate the parameters of the gravitational wave signal from a coalesing binary system. The model however is quite general and would be…
Using Grassmann variant of classical mechanics, we construct Lagrangian dynamics of classical spinning particle in (possibly non-abelian) gauge fields. Quantization of this model is briefly discussed.
Quantum dynamics of the collective mode and individual particles on a ring is studied as the simplest model of projective quantum measurement. In this model, the collective mode measures an individual single quantum system. The heart of the…
Non-commutative quantum physics at the atom scale can arise from coarse graining of a classical statistical ensemble at the Planck scale. Position and momentum of an isolated particle are classical observables which remain computable in…
Einstein's General Theory of Relativity predicts that accelerating mass distributions produce gravitational radiation, analogous to electromagnetic radiation from accelerating charges. These gravitational waves have not been directly…
Utilising dynamic electromagnetic field control over charged particles serves as the basis for a quantum machine learning platform that operates on observables rather than directly on states. Such a platform can be physically realised in…
A systematic method is developed to study classical motion of a mass point in gravitational gauge field. First, the formulation of gauge theory of gravity in arbitrary curvilinear coordinates is given. Then in spherical coordinates system,…
The effective dynamics of a slow classical system coupled to a fast chaotic environment is described by means of a Master equation. We show how this approach permits a very simple derivation of geometric magnetism.
Gravitational radiation from known astrophysical sources is conventionally treated classically. This treatment corresponds, implicitly, to the hypothesis that a particular class of quantum-mechanical states -- the so-called coherent states…
A theoretical scheme, based on a probabilistic generalization of the Hamilton's principle, is elaborated to obtain an unified description of more general dynamical behaviors determined both from a lagrangian function and by mechanisms not…
This work provides a computationally efficient and statistically consistent moment-based estimator for mixtures of spherical Gaussians. Under the condition that component means are in general position, a simple spectral decomposition…
The magnetic field generated by an electron bound in a spherically symmetric potential is calculated for eigenstates of the orbital and total angular momentum. General expressions are presented for the current density in such states and the…
If we admit that quantum mechanics (QM) is universal theory, then QM should contain also some description of classical mechanical systems. The presented text contains description of two different ways how the mathematical description of…
We consider ensemble averaged theories with discrete random variables. We propose a suitable measure to do the ensemble average. We also provide a mathematical description of such ensemble averages of theories in terms of Poisson point…