Related papers: Bose-Einstein and Fermi-Dirac distributions in non…
In this paper, we present an exactly solvable phase transition model in which the phase transition is purely statistically derived. The phase transition in this model is a generalized Bose-Einstein condensation. The exact expression of the…
We propose and study a generalized quantum statistical framework, referred to as \emph{alpha statistics}, that continuously interpolates between Bose--Einstein and Fermi--Dirac statistics and naturally extends into the hyperbosonic regime…
Kappa distributions are widely used in space plasma physics to model velocity distribution functions with heavy tails. Parameter estimation in these distributions is, however, complicated by the fact that the kappa distribution does not…
Highly oscillatory differential equations present significant challenges in numerical treatments. The Modulated Fourier Expansion (MFE), used as an ansatz, is a commonly employed tool as a numerical approximation method. In this article,…
Numerical methods for the description of nonequilibrium many-particle quantum systems such as equation of motion techniques often cannot compute the full statistics of observables but only moments of it, such as mean, variance and…
The analytic continuation of imaginary-time quantum Monte Carlo data to extract real-frequency spectra remains a key problem in connecting theory with experiment. Here we present a fast and efficient stochastic optimization method (FESOM)…
We present a novel analytical approach for the calculation of the mean density of states in many-body systems made of confined indistinguishable and non-interacting particles. Our method makes explicit the intrinsic geometry inherent in the…
We study the expectation-maximization (EM) algorithm for general latent-variable models under (i) distributional misspecification and (ii) nonidentifiability induced by a group action. We formulate EM on the quotient parameter space and…
The method of maximum entropy (ME) is extended to address the following problem: Once one accepts that the ME distribution is to be preferred over all others, the question is to what extent are distributions with lower entropy supposed to…
We introduce the multivariate decomposition finite element method for elliptic PDEs with lognormal diffusion coefficient $a=\exp(Z)$ where $Z$ is a Gaussian random field defined by an infinite series expansion $Z(\boldsymbol{y}) =…
Unless constrained by symmetry, measurement of an observable on an ensemble of identical quantum systems returns a distribution of values which are encoded in the full counting statistics. While the mean value of this distribution is…
The use of Feshbach resonances for tuning the interparticle interaction in ultracold Fermi gases has led to remarkable developments, in particular to the creation and Bose-Einstein condensation of weakly bound diatomic molecules of…
The expectation-maximization (EM) algorithm is a powerful computational technique for finding the maximum likelihood estimates for parametric models when the data are not fully observed. The EM is best suited for situations where the…
Gibbsian statistical mechanics is extended into the domain of non-negligible {though non-specified} correlations in phase space while respecting the fundamental laws of thermodynamics. The appropriate Gibbsian probability distribution is…
Generalized probability distributions for Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac statistics, with unequal source probabilities $q_i$ for each level $i$, are obtained by combinatorial reasoning. For equiprobable degenerate…
Exact formulas are derived for the probability density functions of the sum and difference of two independent non-central gamma distributed random variables, with both series and integral representations of the density presented. These…
We present two approximate Bayesian inference methods for parameter estimation in partial differential equation (PDE) models with space-dependent and state-dependent parameters. We demonstrate that these methods provide accurate and…
In this work we propose an efficient and accurate multi-scale optical simulation algorithm by applying a numerical version of slowly varying envelope approximation in FEM. Specifically, we employ the fast iterative method to quickly compute…
We discuss relevant aspects of the exact q-thermostatistical treatment for an ideal Fermi system. The grand canonical exact generalized partition function is given for arbitrary values of the nonextensivity index q, and the ensuing…
A generalized finite element method is proposed for solving a heterogeneous reaction-diffusion equation with a singular perturbation parameter $\varepsilon$, based on locally approximating the solution on each subdomain by solution of a…