An analysis of selected Indiana coals by the particle count method

Indiana Geological Survey Report of Progress 6The bituminous coals of Indiana show a characteristic bright and dull banding which is due to alternating bands of five distinct physical constituents, namely, vitrain, clarain, durain, fusain, and mineral matter. A petrographic analysis of Indiana Coals V, VI, and VII was made to determine whether any appreciable variation in the content of these ingredients occurred. The “particle count method” was used in analyzing the coals. In order to establish a standard for comparing Coals V, VI, and VII, an index number was determined for each sample by dividing the combined clarain-durain content by the vitrain content. These index numbers are the most reliable and satisfactory basis for the comparison of coals, and they maybe used to some extent in coal correlation. Because vitrain has the most desirable combustion properties, a coal that has a high vitrain content may be more desirable commercially. Coals VI and VII were found to have a distinctly higher vitrain content than Coal V. Localities of high-vitrain content within the various coal beds in Indiana are outlined in this report. Suggestions for further use of the particle count method in coal analysis are made.Indiana Department of Conservatio

Target Space Entanglement Entropy

We define a notion of target space entanglement entropy. Rather than partitioning the base space on which the theory is defined, we consider partitions of the target space. This is the physical case of interest for first-quantized theories, such as worldsheet string theory. We associate to each subregion of the target space a suitably chosen sub-algebra of observables $\mathcal{A}$. The entanglement entropy is calculated as the entropy of the density matrix restricted to $\mathcal{A}$. As an example, we illustrate our framework by computing spatial entanglement in first-quantized many-body quantum mechanics. The algebra $\mathcal{A}$ is chosen to reproduce the entanglement entropy obtained by embedding the state in the fixed particle sub-sector of the second-quantized Hilbert space. We then generalize our construction to the quantum field-theoretical setting

A converse to Lieb-Robinson bounds in one dimension using index theory

Unitary dynamics with a strict causal cone (or "light cone") have been studied extensively, under the name of quantum cellular automata (QCAs). In particular, QCAs in one dimension have been completely classified by an index theory. Physical systems often exhibit only approximate causal cones; Hamiltonian evolutions on the lattice satisfy Lieb-Robinson bounds rather than strict locality. This motivates us to study approximately locality preserving unitaries (ALPUs). We show that the index theory is robust and completely extends to one-dimensional ALPUs. As a consequence, we achieve a converse to the Lieb-Robinson bounds: any ALPU of index zero can be exactly generated by some time-dependent, quasi-local Hamiltonian in constant time. For the special case of finite chains with open boundaries, any unitary satisfying the Lieb-Robinson bound may be generated by such a Hamiltonian. We also discuss some results on the stability of operator algebras which may be of independent interest.Comment: 55 pages, 8 figure

The ℏ→0\hbar\to 0 limit of open quantum systems with general Lindbladians: vanishing noise ensures classicality beyond the Ehrenfest time

Quantum and classical systems evolving under the same formal Hamiltonian $H$ may exhibit dramatically different behavior after the Ehrenfest timescale $t_E \sim \log(\hbar^{-1})$, even as $\hbar \to 0$. Coupling the system to a Markovian environment results in a Lindblad equation for the quantum evolution. Its classical counterpart is given by the Fokker-Planck equation on phase space, which describes Hamiltonian flow with friction and diffusive noise. The quantum and classical evolutions may be compared via the Wigner-Weyl representation. Due to decoherence, they are conjectured to match closely for times far beyond the Ehrenfest timescale as $\hbar \to 0$. We prove a version of this correspondence, bounding the error between the quantum and classical evolutions for any sufficiently regular Hamiltonian $H(x,p)$ and Lindblad functions $L_k(x,p)$. The error is small when the strength of the diffusion $D$ associated to the Lindblad functions satisfies $D \gg \hbar^{4/3}$, in particular allowing vanishing noise in the classical limit. We use a time-dependent semiclassical mixture of variably squeezed Gaussian states evolving by a local harmonic approximation to the Lindblad dynamics. Both the exact quantum trajectory and its classical counterpart can be expressed as perturbations of this semiclassical mixture, with the errors bounded using Duhamel's principle. We present heuristic arguments suggesting the $4/3$ exponent is optimal and defines a boundary in the sense that asymptotically weaker diffusion permits a breakdown of quantum-classical correspondence at the Ehrenfest timescale. Our presentation aims to be comprehensive and accessible to both mathematicians and physicists. In a shorter companion paper, we treat the special case of Hamiltonians of the form $H=p^2/2m + V(x)$ and linear Lindblad operators, with explicit bounds that can be applied directly to physical systems.Comment: 53 pages + appendices, 2 figures. Companion to arXiv:2306.1371

The QAOA gets stuck starting from a good classical string

The Quantum Approximate Optimization Algorithm (QAOA) is designed to maximize a cost function over bit strings. While the initial state is traditionally a superposition over all strings, it is natural to try expediting the QAOA: first use a classical algorithm to produce some good string, and then run the ordinary QAOA starting in the computational basis state associated with that string. Here we report numerical experiments that this method of initializing the QAOA fails dramatically, exhibiting little to no improvement of the cost function. We investigate criteria for the rare instances in which there is any improvement at all, and we provide a statistical argument for the more typical case of no improvement. The statistical argument holds for any string that locally mimics the thermal ensemble at the appropriate temperature. Our numerical experiments indicate this property holds for typical good strings. We emphasize that our negative results only apply to our simple incarnation of the warm-start QAOA and may not apply to other approaches in the literature. We hope that our theoretical analysis will inform future algorithm design.Comment: 26 pages, 1 figure, 6 table

Beyond ‘peer pressure’: rethinking drug use and ‘youth culture’

The study of drug use by young people in the West has been transformed over the last decade by the development of sociological approaches to drug use which take serious account of the cultural context in which young people encounter drugs. One consequence is that the notion of ‘peer pressure’, as the primary articulation of the engagement between youth culture and drug use, has been displaced by that of ‘normalisation’, which envisages ‘recreational’ drug use as one expression of consumer-based youth cultural lifestyles. In stark contrast, academic discussion of drug use in Russia remains primarily concerned with the prevalence and health consequences of (intravenous) drug use while explanations of rising rates of drug use focus on structural factors related to the expansion of drugs supply and, to a lesser extent, post-Soviet social and economic dislocation. In this article, original empirical research in Russia is used to develop an understanding of young people's drug use that synthesises structural and cultural explanations of it. It does this by situating young people's narratives of their drugs choices in the context of local drugs markets and broader socio-economic processes. However, it attempts to go beyond seeing structural location as simply a ‘constraint’ on individual choice by adopting an understanding of ‘youth culture’ as a range of youth cultural practices and formations that simultaneously embody, reproduce and negotiate the structural locations of their subjects

Omnivorousness in sport: The importance of social capital and networks

There has been for some time a significant and growing body of research around the relationship between sport and social capital. Similarly, within sociology there has been a corpus of work that has acknowledged the emergence of the omnivore–univore relationship. Surprisingly, relatively few studies examining sport and social capital have taken the omnivore–univore framework as a basis for understanding the relationship between sport and social capital. This gap in the sociology of sport literature and knowledge is rectified by this study that takes not Putnam, Coleman or Bourdieu, but Lin’s social network approach to social capital. The implications of this article are that researchers investigating sport and social capital need to understand more about how social networks and places for sport work to create social capital and, in particular, influence participating in sporting activities. The results indicate that social networks both facilitate and constrain sports participation; whilst family and friendship networks are central in active lifestyles, those who are less active have limited networks