Density Operators for Fermions

The mathematical methods that have been used to analyze the statistical properties of boson fields, and in particular the coherence of photons in quantum optics, have their counterparts for Fermi fields. The coherent states, the displacement operators, the P-representation, and the other operator expansions all possess surprisingly close fermionic analogues. These methods for describing the statistical properties of fermions are based upon a practical calculus of anti-commuting variables. They are used to calculate correlation functions and counting distributions for general systems of fermions.Comment: 45 pages, late

Scaling detection in time series: diffusion entropy analysis

The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where ordinary statistical properties hold true even if strange kinetics are involved. We illustrate a method of statistical analysis based on the Shannon entropy of the diffusion process generated by the time series, called Diffusion Entropy Analysis (DEA). We adopt artificial Gauss and L\'{e}vy time series, as prototypes of ordinary and anomalus statistics, respectively, and we analyse them with the DEA and four ordinary methods of analysis, some of which are very popular. We show that the DEA determines the correct scaling exponent even when the statistical properties, as well as the dynamic properties, are anomalous. The other four methods produce correct results in the Gauss case but fail to detect the correct scaling in the case of L\'{e}vy statistics.Comment: 21 pages,10 figures, 1 tabl

A class of fast exact Bayesian filters in dynamical models with jumps

In this paper, we focus on the statistical filtering problem in dynamical models with jumps. When a particular application relies on physical properties which are modeled by linear and Gaussian probability density functions with jumps, an usualmethod consists in approximating the optimal Bayesian estimate (in the sense of the Minimum Mean Square Error (MMSE)) in a linear and Gaussian Jump Markov State Space System (JMSS). Practical solutions include algorithms based on numerical approximations or based on Sequential Monte Carlo (SMC) methods. In this paper, we propose a class of alternative methods which consists in building statistical models which share the same physical properties of interest but in which the computation of the optimal MMSE estimate can be done at a computational cost which is linear in the number of observations.Comment: 21 pages, 7 figure

Modelling of Diesel fuel properties through its surrogates using Perturbed-Chain, Statistical Associating Fluid Theory

The Perturbed-Chain, Statistical Associating Fluid Theory equation of state is utilised to model the effect of pressure and temperature on the density, volatility and viscosity of four Diesel surrogates; these calculated properties are then compared to the properties of several Diesel fuels. Perturbed-Chain, Statistical Associating Fluid Theory calculations are performed using different sources for the pure component parameters. One source utilises literature values obtained from fitting vapour pressure and saturated liquid density data or from correlations based on these parameters. The second source utilises a group contribution method based on the chemical structure of each compound. Both modelling methods deliver similar estimations for surrogate density and volatility that are in close agreement with experimental results obtained at ambient pressure. Surrogate viscosity is calculated using the entropy scaling model with a new mixing rule for calculating mixture model parameters. The closest match of the surrogates to Diesel fuel properties provides mean deviations of 1.7% in density, 2.9% in volatility and 8.3% in viscosity. The Perturbed-Chain, Statistical Associating Fluid Theory results are compared to calculations using the Peng–Robinson equation of state; the greater performance of the Perturbed-Chain, Statistical Associating Fluid Theory approach for calculating fluid properties is demonstrated. Finally, an eight-component surrogate, with properties at high pressure and temperature predicted with the group contribution Perturbed-Chain, Statistical Associating Fluid Theory method, yields the best match for Diesel properties with a combined mean absolute deviation of 7.1% from experimental data found in the literature for conditions up to 373°K and 500 MPa. These results demonstrate the predictive capability of a state-of-the-art equation of state for Diesel fuels at extreme engine operating conditions

Turning Statistical Physics Models Into Materials Design Engines

Despite the success statistical physics has enjoyed at predicting the properties of materials for given parameters, the inverse problem, identifying which material parameters produce given, desired properties, is only beginning to be addressed. Recently, several methods have emerged across disciplines that draw upon optimization and simulation to create computer programs that tailor material responses to specified behaviors. However, so far the methods developed either involve black-box techniques, in which the optimizer operates without explicit knowledge of the material's configuration space, or they require carefully tuned algorithms with applicability limited to a narrow subclass of materials. Here we introduce a formalism that can generate optimizers automatically by extending statistical mechanics into the realm of design. The strength of this new approach lies in its capability to transform statistical models that describe materials into optimizers to tailor them. By comparing against standard black-box optimization methods, we demonstrate how optimizers generated by this formalism can be faster and more effective, while remaining straightforward to implement. The scope of our approach includes new possibilities for solving a variety of complex optimization and design problems concerning materials both in and out of equilibrium

Quantifying Bar Strength: Morphology Meets Methodology

A set of objective bar-classification methods have been applied to the Ohio State Bright Spiral Galaxy Survey (Eskridge et al. 2002). Bivariate comparisons between methods show that all methods agree in a statistical sense. Thus the distribution of bar strengths in a sample of galaxies can be robustly determined. There are very substantial outliers in all bivariate comparisons. Examination of the outliers reveals that the scatter in the bivariate comparisons correlates with galaxy morphology. Thus multiple measures of bar strength provide a means of studying the range of physical properties of galaxy bars in an objective statistical sense.Comment: LaTeX with Kluwer style file, 5 pages with 3 embedded figures. edited by Block, D.L., Freeman, K.C., Puerari, I., & Groess,

Generalized statistical mechanics and fully developed turbulence

The statistical properties of fully developed hydrodynamic turbulence can be successfully described using methods from nonextensive statistical mechanics. The predicted probability densities and scaling exponents precisely coincide with what is measured in various turbulence experiments. As a dynamical basis for nonextensive behaviour we consider nonlinear Langevin equations with fluctuating friction forces, where Tsallis statistics can be rigorously proved.Comment: 10 pages, 4 figures. To appear in Physica A (Proceedings of Statphys 21

On determination of statistical properties of spectra from parametric level dynamics

We analyze an approach aiming at determining statistical properties of spectra of time-periodic quantum chaotic system based on the parameter dynamics of their quasienergies. In particular we show that application of the methods of statistical physics, proposed previously in the literature, taking into account appropriate integrals of motion of the parametric dynamics is fully justified, even if the used integrals of motion do not determine the invariant manifold in a unique way. The indetermination of the manifold is removed by applying Dirac's theory of constrained Hamiltonian systems and imposing appropriate primary, first-class constraints and a gauge transformation generated by them in the standard way. The obtained results close the gap in the whole reasoning aiming at understanding statistical properties of spectra in terms of parametric dynamics.Comment: 9 pages without figure

Does consistent aggregation really matter?

Consistent aggregation ensures that behavioural properties which apply to disaggregate relationships apply also to aggregate relationships. The agricultural economics literature which has tested for consistent aggregation or measured statistical bias and/or inferential errors due to aggregation is reviewed. Tests for aggregation bias and errors of inference are conducted using indices previously tested for consistent aggregation. Failure to reject consistent aggregation in a partition did not entirely mitigate erroneous inference due to aggregation. However, inferential errors due to aggregation were small relative to errors due to incorrect functional form or failure to account for time series properties of data.Research Methods/ Statistical Methods,

Statistical properties of an ensemble of vortices interacting with a turbulent field

We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by path-integral methods. The function space is the statistical ensemble composed of two parts, the first one representing the vortices influenced by the turbulence and the second one the turbulent field scattered by the randomly placed vortices.Comment: Third version; Important corrections in the normalization for the gas of vortices, et