Good just isn't Good enough. Best System Probabilities and the Foundations of Statistical Mechanics

Statistical physicists assume a probability distribution over micro-states to explain thermodynamic behavior. The question of this paper is whether these probabilities are part of a best system and can thus be interpreted as Humean chances. I consider two strategies, viz. a globalist as suggested by Loewer, and a localist as advocated by Frigg and Hoefer. Both strategies fail because the system they are part of have rivals that are roughly equally good, while ontic probabilities should be part of a clearly winning system. I conclude with the diagnosis that well-defined micro-probabilities under-estimate the robust character of explanations in statistical physics.

Pseudospectra in non-Hermitian quantum mechanics

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

Comparative Analysis of Evolving Software Systems Using the Gini Coefficient

Software metrics offer us the promise of distilling useful information from vast amounts of software in order to track development progress, to gain insights into the nature of the software, and to identify potential problems. Unfortunately, however, many software metrics exhibit highly skewed, non-Gaussian distributions. As a consequence, usual ways of interpreting these metrics --- for example, in terms of "average" values --- can be highly misleading. Many metrics, it turns out, are distributed like wealth --- with high concentrations of values in selected locations. We propose to analyze software metrics using the Gini coefficient, a higher-order statistic widely used in economics to study the distribution of wealth. Our approach allows us not only to observe changes in software systems efficiently, but also to assess project risks and monitor the development process itself. We apply the Gini coefficient to numerous metrics over a range of software projects, and we show that many metrics not only display remarkably high Gini values, but that these values are remarkably consistent as a project evolves over time.

The (2 + 1)-d U (1) quantum link model masquerading as deconfined criticality

The (2 + 1)-d U(1) quantum link model is a gauge theory, amenable to quantum simulation, with a spontaneously broken SO(2) symmetry emerging at a quantum phase transition. Its low-energy physics is described by a (2 + 1)-d RP(1) effective field theory, perturbed by an SO(2) breaking operator, which prevents the interpretation of the emergent pseudo-Goldstone boson as a dual photon. At the quantum phase transition, the model mimics some features of deconfined quantum criticality, but remains linearly confining. Deconfinement only sets in at high temperature.

A stochastic principle behind polar properties of condensed molecular matter

A statistical mechanics view leads to the conclusion that polar molecules allowed to populate a degree of freedom for orientational disorder in a condensed phase thermalize into a bi-polar state featuring zero net polarity. In cases of orientational disorder polar order of condensed molecular matter can only exist in corresponding sectors of opposite average polarities. Channel type inclusion compounds, single component molecular crystals, solid solutions, optically anomalous crystals, inorganic ionic crystals, biomimetic crystals and biological tissues investigated by scanning pyroelectric and phase sensitive second harmonic generation microscopy all showed domains of opposite polarities in their final grown state. For reported polar molecular crystal structures it is assumed that kinetic hindrance along one direction of the polar axis is preventing the formation of a bi-polar state, thus allowing for a kinetically controlled mono-domain state. In this review we summarize theoretical and experimental findings leading to far reaching conclusions on the polar state of solid molecular matter. “… no stationary state … of a system has an electrical dipole moment.” P. W. Anderson, Science, 1972, 177, 393.

Symmetry and the polar state of condensed molecular matter

Polar molecular crystals seem to contradict a quantum mechanical statement, according to which no stationary state of a system features a permanent electrical polarization. By stationary we understand here an ensemble for which thermal averaging applies. In the language of statistical mechanics we have thus to ask for the thermal expectation value of the polarization in molecular crystals. Nucleation aggregates and growing crystal surfaces can provide a single degree of freedom for polar molecules required to average the polarization. By means of group theoretical reasoning and Monte Carlo simulations we show that such systems thermalize into a bi-polar state featuring zero bulk polarity. A two domain, i.e. bipolar state is obtained because boundaries are setting up opposing effective electrical fields. Described phenomena can be understood as a process of partial ergodicity-restoring. Experimentally, a bi-polar state of molecular crystals was demonstrated using phase sensitive second harmonic generation and scanning pyroelectric microscopy