Mapping the Wigner distribution function of the Morse oscillator into a semi-classical distribution function

The mapping of the Wigner distribution function (WDF) for a given bound-state onto a semiclassical distribution function (SDF) satisfying the Liouville equation introduced previously by us is applied to the ground state of the Morse oscillator. Here we give results showing that the SDF gets closer to the corresponding WDF as the number of levels of the Morse oscillator increases. We find that for a Morse oscillator with one level only, the agreement between the WDF and the mapped SDF is very poor but for a Morse oscillator of ten levels it becomes satisfactory.Comment: Revtex, 27 pages including 13 eps figure

Momentum of an electromagnetic wave in dielectric media

Almost a hundred years ago, two different expressions were proposed for the energy--momentum tensor of an electromagnetic wave in a dielectric. Minkowski's tensor predicted an increase in the linear momentum of the wave on entering a dielectric medium, whereas Abraham's tensor predicted its decrease. Theoretical arguments were advanced in favour of both sides, and experiments proved incapable of distinguishing between the two. Yet more forms were proposed, each with their advocates who considered the form that they were proposing to be the one true tensor. This paper reviews the debate and its eventual conclusion: that no electromagnetic wave energy--momentum tensor is complete on its own. When the appropriate accompanying energy--momentum tensor for the material medium is also considered, experimental predictions of all the various proposed tensors will always be the same, and the preferred form is therefore effectively a matter of personal choice.Comment: 23 pages, 3 figures, RevTeX 4. Removed erroneous factor of mu/mu_0 from Eq.(44

Assessing Human Error Against a Benchmark of Perfection

An increasing number of domains are providing us with detailed trace data on human decisions in settings where we can evaluate the quality of these decisions via an algorithm. Motivated by this development, an emerging line of work has begun to consider whether we can characterize and predict the kinds of decisions where people are likely to make errors. To investigate what a general framework for human error prediction might look like, we focus on a model system with a rich history in the behavioral sciences: the decisions made by chess players as they select moves in a game. We carry out our analysis at a large scale, employing datasets with several million recorded games, and using chess tablebases to acquire a form of ground truth for a subset of chess positions that have been completely solved by computers but remain challenging even for the best players in the world. We organize our analysis around three categories of features that we argue are present in most settings where the analysis of human error is applicable: the skill of the decision-maker, the time available to make the decision, and the inherent difficulty of the decision. We identify rich structure in all three of these categories of features, and find strong evidence that in our domain, features describing the inherent difficulty of an instance are significantly more powerful than features based on skill or time.Comment: KDD 2016; 10 page

Shear flow, viscous heating, and entropy balance from dynamical systems

A consistent description of a shear flow, the accompanied viscous heating, and the associated entropy balance is given in the framework of a deterministic dynamical system, where a multibaker dynamics drives two fields: the velocity and the temperature distributions. In an appropriate macroscopic limit their transport equations go over into the Navier-Stokes and the heat conduction equation of viscous flows. The inclusion of an artificial heat sink can stabilize steady states with constant temperatures. It mimics a thermostating algorithm used in non-equilibrium molecular-dynamics simulations.Comment: LaTeX 2e (epl.cls + sty-files for Europhys Lett included); 7 pages + 1 eps-figur

Dynamical description of vesicle growth and shape change

We systematize and extend the description of vesicle growth and shape change using linear nonequilibrium thermodynamics. By restricting the study to shape changes from spheres to axisymmetric ellipsoids, we are able to give a consistent formulation which includes the lateral tension of the vesicle membrane. This allows us to generalize and correct a previous calculation. Our present calculations suggest that, for small growing vesicles, a prolate ellipsoidal shape should be favored over oblate ellipsoids, whereas for large growing vesicles oblates should be favored over prolates. The validity of this prediction is examined in the light of the various assumptions made in its derivation.Comment: 6 page

Atomic and itinerant effects at the transition metal x-ray absorption K-pre-edge exemplified in the case of V2_2O3_3

X-ray absorption spectroscopy is a well established tool for obtaining information about orbital and spin degrees of freedom in transition metal- and rare earth-compounds. For this purpose usually the dipole transitions of the L- (2p to 3d) and M- (3d to 4f) edges are employed, whereas higher order transitions such as quadrupolar 1s to 3d in the K-edge are rarely studied in that respect. This is due to the fact that usually such quadrupolar transitions are overshadowed by dipole allowed 1s to 4p transitions and, hence, are visible only as minor features in the pre-edge region. Nonetheless, these features carry a lot of valuable information, similar to the dipole L-edge transition, which is not accessible in experiments under pressure due to the absorption of the diamond anvil pressurecell. We recently performed a theoretical and experimental analysis of such a situation for the metal insulator transition of (V(1-x)Crx)2O3. Since the importance of the orbital degrees of freedom in this transition is widely accepted, a thorough understanding of quadrupole transitions of the vanadium K-pre-edge provides crucial information about the underlying physics. Moreover, the lack of inversion symetry at the vanadium site leads to onsite mixing of vanadium 3d- and 4p- states and related quantum mechanical interferences between dipole and quadrupole transitions. Here we present a theoretical analysis of experimental high resolution x-ray absorption spectroscopy at the V pre-K edge measured in partial fluorescence yield mode for single crystals. We carried out density functional as well as configuration interaction calculations in order to capture effects coming from both, itinerant and atomic limits

Statistical mechanics in the context of special relativity II

The special relativity laws emerge as one-parameter (light speed) generalizations of the corresponding laws of classical physics. These generalizations, imposed by the Lorentz transformations, affect both the definition of the various physical observables (e.g. momentum, energy, etc), as well as the mathematical apparatus of the theory. Here, following the general lines of [Phys. Rev. E {\bf 66}, 056125 (2002)], we show that the Lorentz transformations impose also a proper one-parameter generalization of the classical Boltzmann-Gibbs-Shannon entropy. The obtained relativistic entropy permits to construct a coherent and selfconsistent relativistic statistical theory, preserving the main features of the ordinary statistical theory, which recovers in the classical limit. The predicted distribution function is a one-parameter continuous deformation of the classical Maxwell-Boltzmann distribution and has a simple analytic form, showing power law tails in accordance with the experimental evidence. Furthermore the new statistical mechanics can be obtained as stationary case of a generalized kinetic theory governed by an evolution equation obeying the H-theorem and reproducing the Boltzmann equation of the ordinary kinetics in the classical limit.Comment: 14 pages, no figures, proof correction

Anomalous diffusion in viscosity landscapes

Anomalous diffusion is predicted for Brownian particles in inhomogeneous viscosity landscapes by means of scaling arguments, which are substantiated through numerical simulations. Analytical solutions of the related Fokker-Planck equation in limiting cases confirm our results. For an ensemble of particles starting at a spatial minimum (maximum) of the viscous damping we find subdiffusive (superdiffusive) motion. Superdiffusion occurs also for a monotonically varying viscosity profile. We suggest different substances for related experimental investigations.Comment: 15 page

Collisional Semiclassical Aproximations in Phase-Space Representation

The Gaussian Wave-Packet phase-space representation is used to show that the expansion in powers of $\hbar$ of the quantum Liouville propagator leads, in the zeroth order term, to results close to those obtained in the statistical quasiclassical method of Lee and Scully in the Weyl-Wigner picture. It is also verified that propagating the Wigner distribution along the classical trajectories the amount of error is less than that coming from propagating the Gaussian distribution along classical trajectories.Comment: 20 pages, REVTEX, no figures, 3 tables include