Another look at the Landau gauge three-gluon vertex

We revisit the computation of the three-gluon vertex in the Landau gauge using lattice QCD simulations with large physical volumes of ~ (6.5 fm)4 and ~ (8 fm) 4 and large statistical ensembles. For the kinematical configuration analysed, that is described by a unique form factor, an evaluation of the lattice artefacts is also performed. Particular attention is given to the low energy behavior of vertex and its connection with evidence (or lack of it) of infrared ghost dominance.

On the Non-Uniqueness of Statistical Ensembles Defining a Density Operator and a Class of Mixed Quantum States with Integrable Wigner Distribution

It is standard to assume that the Wigner distribution of a mixed quantum state consisting of square-integrable functions is a quasi-probability distribution, i.e., that its integral is one and that the marginal properties are satisfied. However, this is generally not true. We introduced a class of quantum states for which this property is satisfied; these states are dubbed “Feichtinger states” because they are defined in terms of a class of functional spaces (modulation spaces) introduced in the 1980s by H. Feichtinger. The properties of these states were studied, giving us the opportunity to prove an extension to the general case of a result due to Jaynes on the non-uniqueness of the statistical ensemble, generating a density operator.

Particle ratios within EPOS, UrQMD and thermal models at AGS, SPS and RHIC energies

The particle ratios [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] measured at AGS, SPS and RHIC energies are compared with large statistical ensembles of 100,000 events deduced from the CRMC EPOS [Formula: see text] and the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) hybrid model. In the UrQMD hybrid model two types of phase transitions are taken into account. All these data are then confronted with the ideal Hadron Resonance Gas Model. The two types of phase transitions are apparently indistinguishable. Apart from [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text], the UrQMD hybrid model agrees well with the CRMC EPOS [Formula: see text]. We also conclude that the CRMC EPOS [Formula: see text] seems to largely underestimate [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text].

NMR-Based Study of the Pore Types’ Contribution to the Elastic Response of the Reservoir Rock

Seismic data and nuclear magnetic resonance (NMR) data are two of the highly trustable kinds of information in hydrocarbon reservoir engineering. Reservoir fluids influence the elastic wave velocity and also determine the NMR response of the reservoir. The current study investigates different pore types, i.e., micro, meso, and macropores’ contribution to the elastic wave velocity using the laboratory NMR and elastic experiments on coal core samples under different fluid saturations. Once a meaningful relationship was observed in the lab, the idea was applied in the field scale and the NMR transverse relaxation time (T2) curves were synthesized artificially. This task was done by dividing the area under the T2 curve into eight porosity bins and estimating each bin’s value from the seismic attributes using neural networks (NN). Moreover, the functionality of two statistical ensembles, i.e., Bag and LSBoost, was investigated as an alternative tool to conventional estimation techniques of the petrophysical characteristics; and the results were compared with those from a deep learning network. Herein, NMR permeability was used as the estimation target and porosity was used as a benchmark to assess the reliability of the models. The final results indicated that by using the incremental porosity under the T2 curve, this curve could be synthesized using the seismic attributes. The results also proved the functionality of the selected statistical ensembles as reliable tools in the petrophysical characterization of the hydrocarbon reservoirs.

The Fundamental Equations of Change in Statistical Ensembles and Biological Populations

A recent article in Nature Physics unified key results from thermodynamics, statistics, and information theory. The unification arose from a general equation for the rate of change in the information content of a system. The general equation describes the change in the moments of an observable quantity over a probability distribution. One term in the equation describes the change in the probability distribution. The other term describes the change in the observable values for a given state. We show the equivalence of this general equation for moment dynamics with the widely known Price equation from evolutionary theory, named after George Price. We introduce the Price equation from its biological roots, review a mathematically abstract form of the equation, and discuss the potential for this equation to unify diverse mathematical theories from different disciplines. The new work in Nature Physics and many applications in biology show that this equation also provides the basis for deriving many novel theoretical results within each discipline.

Density Operator Approach to Turbulent Flows in Plasma and Atmospheric Fluids

We formulate a statistical wave-mechanical approach to describe dissipation and instabilities in two-dimensional turbulent flows of magnetized plasmas and atmospheric fluids, such as drift and Rossby waves. This is made possible by the existence of Hilbert space, associated with the electric potential of plasma or stream function of atmospheric fluid. We therefore regard such turbulent flows as macroscopic wave-mechanical phenomena, driven by the non-Hermitian Hamiltonian operator we derive, whose anti-Hermitian component is attributed to an effect of the environment. Introducing a wave-mechanical density operator for the statistical ensembles of waves, we formulate master equations and define observables: such as the enstrophy and energy of both the waves and zonal flow as statistical averages. We establish that our open system can generally follow two types of time evolution, depending on whether the environment hinders or assists the system’s stability and integrity. We also consider a phase-space formulation of the theory, including the geometrical-optic limit and beyond, and study the conservation laws of physical observables. It is thus shown that the approach predicts various mechanisms of energy and enstrophy exchange between drift waves and zonal flow, which were hitherto overlooked in models based on wave kinetic equations.

Notes on statistical ensembles in the Cell Model

Properties of basic statistical ensembles in the Cell Model are discussed. The simplest version of the model with a fixed total number of particles is considered. The microcanonical ensembles of distinguishable and indistinguishable particles, with and without a limit on the maximum number of particles in a single cell, are discussed. The joint probability distributions of particle multiplicities in cells for different ensembles are derived, and their second moments are calculated. The results for infinite volume limit are calculated. The obtained results resemble those in the statistical physics of bosons, fermions and boltzmanions.