Related papers: Position and momentum tomography
The use of momentum in stochastic gradient methods has become a widespread practice in machine learning. Different variants of momentum, including heavy-ball momentum, Nesterov's accelerated gradient (NAG), and quasi-hyperbolic momentum…
We present an analytic method for computing the moments of a sum of independent and identically distributed random variables. The limiting behavior of these sums is very important to statistical theory, and the moment expressions that we…
Transverse-momentum dependent parton distributions (TMDs) are studied in the framework of quark models. In particular, quark model relations among TMDs are reviewed and their physical origin is discussed in terms of rotational-symmetry…
This study introduces an innovative local statistical moment approach for estimating Kramers-Moyal coefficients, effectively bridging the gap between nonparametric and parametric methodologies. These coefficients play a crucial role in…
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…
Applying random matrix theory to quantum transport in chaotic cavities, we develop a novel approach to computation of the moments of the conductance and shot-noise (including their joint moments) of arbitrary order and at any number of open…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
Models of stochastic image deformation allow study of time-continuous stochastic effects transforming images by deforming the image domain. Applications include longitudinal medical image analysis with both population trends and random…
We investigate the utility of Einstein-Podolsky-Rosen correlations of the position and momentum of photon pairs from parametric down-conversion in the implementation of a secure quantum key distribution protocol. We show that security is…
We examine the procedure to construct the variables of use for the momentum representation in quantum mechanics. The momentum variables must be chosen properly conjugate to the corresponding position space variables, such that valid…
In this paper, we present a systematic stability analysis of the quadrature-based moment method (QBMM) for the one-dimensional Boltzmann equation with BGK or Shakhov models. As reported in recent literature, the method has revealed its…
The density matrix of a two-level system (spin, atom) is usually determined by measuring the three non-commuting components of the Pauli vector. This density matrix can also be obtained via the measurement data of two commuting variables,…
The problem to establish not only the asymptotic distribution results for statistical estimators but also the moment convergence of the estimators has been recognized as an important issue in advanced theories of statistics. One of the main…
Given $0<q<1,$ every absolutely continuous distribution can be described in two different ways: in terms of a probability density function and also in terms of a $q$-density. Correspondingly, it has a sequence of moments and a sequence of…
We present a new method which uses Feynman-like diagrams to calculate the statistical quantities of embedded many-body random matrix problems. The method provides a promising alternative to existing techniques and offers many important…
An analysis is made of a moving disturbance using a directed cyclic graph. A statistical approach is used to calculate the alternative positions in space and state of the disturbance with a defined observed time. The probability for a…
For a particle moving in a one-dimensional space an under a periodic external force, its quantization is study using the Hamiltonian (generalized linear momentum quantization) and constant of motion (velocity quantization) approaches. it is…
Predicting the stationary behavior of observables in isolated many-body quantum systems is a central challenge in quantum statistical mechanics. While one can often use the Gibbs ensemble, which is simple to compute, there are many…
The atom-optics kicked rotor can be used to prepare specific momentum distributions on a discrete basis set. We implement a continuous-time quantum walk and a quantum search protocol in this momentum basis. In particular we propose ways to…
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,…