Related papers: Shannon Entropy and Many-Electron Correlations: Th…
Entropic measures provide analytic tools to help us understand correlation in quantum systems. In our previous work, we calculated linear entropy and von Neumann entropy as entanglement measures for the ground state and lower lying excited…
The correlation energy of the homogeneous three-dimensional interacting electron gas is calculated using the variational and fixed-node diffusion Monte Carlo methods, with trial functions that include backflow and three-body correlations.…
Shannon entropies of one- and two-electron atomic structure factors in the position and momentum representations are used to examine the behavior of the off-diagonal elements of density matrices with respect to the uncertainty principle and…
Aim of this short note is to study Shannon's entropy power along entropic interpolations, thus generalizing Costa's concavity theorem. We shall provide two proofs of independent interest: the former by $\Gamma$-calculus, hence applicable to…
The uniform electron gas is a key model system in the description of matter, including dense plasmas and solid state systems. However, the simultaneous occurence of quantum, correlation, and thermal effects makes the theoretical description…
Entropy is critically examined as a fundamental concept in contemporary science and informatics. Although the typical Shannon entropy provides a proper framework for describing the canonical ensemble, it fails to represent adequately the…
We propose a simple analytic representation of the correlation energy for the two-dimensional electron gas, as a function of the density and the spin polarization. This new parametrization includes most of the known high- and low- density…
A correlated many-body calculation is presented to characterize the Shannon information entropy of trapped interacting bosons. We reformulate the one-body Shannon information entropy in terms of the one-body probability density. The minimum…
We present a variational Monte Carlo study of a model one dimensional electron gas on the continuum, with long-range interaction (1/r decay). At low density the reduced dimensionality brings about pseudonodes of the many-body wavefunction,…
Statements of Shannon's Noiseless Coding Theorem by various authors, including the original, are reviewed and clarified. Traditional statements of the theorem are often unclear as to when it applies. A new notation is introduced and the…
We use variational quantum Monte Carlo to calculate the density-functional exchange-correlation hole n_{xc}, the exchange-correlation energy density e_{xc}, and the total exchange-correlation energy E_{xc}, of several electron gas systems…
Electron correlation effects are essential for an accurate ab initio description of molecules. A quantitative a priori knowledge of the single- or multi-reference nature of electronic structures as well as of the dominant contributions to…
Quantum entanglement is a concept commonly used with reference to the existence of certain correlations in quantum systems that have no classical interpretation. It is a useful resource to enhance the mutual information of memory channels…
The influence of correlations of uniform Fermi systems (nuclear matter, electron gas and liquid $^3$He) on Shannon's information entropy, $S$, is studied. $S$ is the sum of the information entropies in position and momentum spaces. It is…
The effective electron-electron interaction in the electron gas depends on both the density and spin local field factors. Variational Diagrammatic Quantum Monte Carlo calculations of the spin local field factor are reported and used to…
We explore the relation between entanglement entropy of quantum many body systems and the distribution of corresponding, properly selected, observables. Such a relation is necessary to actually measure the entanglement entropy. We show that…
The paper examines relationships between the conditional Shannon entropy and the expectation of $\ell_{\alpha}$-norm for joint probability distributions. More precisely, we investigate the tight bounds of the expectation of…
The purpose of this note is to give the general solution of two functional equations connected to the Shannon entropy and also to the Tsallis entropy. As a result of this, we present the regular solution of these equations, as well.…
We present a quantum information theory that allows for a consistent description of entanglement. It parallels classical (Shannon) information theory but is based entirely on density matrices (rather than probability distributions) for the…
The paper deals with the generalization of both Boltzmann entropy and distribution in the light of most-probable interpretation of statistical equilibrium. The statistical analysis of the generalized entropy and distribution leads to some…