Classical Statistics Inherent in a Quantum Density Matrix

A density matrix formulation of classical bipartite correlations is constructed. This leads to an understanding of the appearance of classical statistical correlations intertwined with the quantum correlations as well as a physical underpinning of these correlations. As a byproduct of this analysis, a physical basis of the classical statistical correlations leading to additive entropy in a bipartite system discussed recently by Tsallis et al emerges as inherent classical spin fluctuations. It is found that in this example, the quantum correlations shrink the region of additivity in phase space.Comment: 10 pages, 3 figure

An improved perturbation approach to the 2D Edwards polymer -- corrections to scaling

We present the results of a new perturbation calculation in polymer statistics which starts from a ground state that already correctly predicts the long chain length behaviour of the mean square end--to--end distance $\langle R_N^2 \rangle\$, namely the solution to the 2~dimensional~(2D) Edwards model. The $\langle R_N^2 \rangle$ thus calculated is shown to be convergent in $N$, the number of steps in the chain, in contrast to previous methods which start from the free random walk solution. This allows us to calculate a new value for the leading correction--to--scaling exponent~$\Delta$. Writing $\langle R_N^2 \rangle = AN^{2\nu}(1+BN^{-\Delta} + CN^{-1}+...)$, where $\nu = 3/4$ in 2D, our result shows that $\Delta = 1/2$. This value is also supported by an analysis of 2D self--avoiding walks on the {\em continuum}.Comment: 17 Pages of Revtex. No figures. Submitted to J. Phys.

The Plains of Mars, European War Prints, 1500-1825

Over fifty original prints by renowned artists from the sixteenth through the early nineteenth century, including Albrecht Dürer, Lucas Cranach, Théodore Géricault, and Francisco de Goya, among many others, are featured inThe Plains of Mars: European War Prints, 1500-1825. On loan from the Sarah Campbell Blaffer Foundation at the Museum of Fine Arts, Houston, the works of art included in this exhibition examine the topics of war and peace, propaganda, heroism, brutal conflicts, and the harrowing aftermath of battle. Spanning from the Renaissance to the Romantic periods and encompassing a wide geographic scope including Italy, Germany, France, Spain, the Low Countries, England, and North America, the prints depict triumphant Renaissance soldiers, devastating scenes of violence, and satirical caricatures of political figures. Also on display is Goya’s compelling “Disasters of War” series, completed in response to the brutality of the Spanish War of Independence. Goya’s prints serve as a powerful testament to the horrors faced by both soldiers and civilians. Under the direction of Professor Felicia Else and Shannon Egan, Melissa Casale ‘19 and Bailey Harper ‘19 have researched and written didactic labels, catalogue essays, and created an interactive digital interface to complement the exhibition. Together, Melissa and Bailey will lead public tours of the exhibition. A Gallery Talk by Prof. Peter Carmichael will draw connections between the depictions of warfare on view in the Gallery with representations of the American Civil War. James Clifton, Director of the Sarah Campbell Blaffer Foundation at the Museum of Fine Arts, Houston, will be delivering a lecture in conjunction with the exhibition. Dr. Clifton, who also serves as curator of Renaissance and Baroque painting at MFAH, curated the exhibition in its first iteration and wrote the exhibition catalogue (published by Yale University Press). Dr. Clifton’s lecture not only will provide an overview of the exhibition, but also will focus on the concept of “mediated war.” A full-color catalogue with images and essays by Bailey Harper ’19 and Melissa Casale ’19, under the supervision of Profs. Felicia Else and Shannon Egan, is planned to accompany the exhibition.https://cupola.gettysburg.edu/artcatalogs/1028/thumbnail.jp

Minimum Requirements for Detecting a Stochastic Gravitational Wave Background Using Pulsars

We assess the detectability of a nanohertz gravitational wave (GW) background with respect to additive red and white noise in the timing of millisecond pulsars. We develop detection criteria based on the cross-correlation function summed over pulsar pairs in a pulsar timing array. The distribution of correlation amplitudes is found to be non-Gaussian and highly skewed, which significantly influences detection and false-alarm probabilities. When only white noise and GWs contribute, our detection results are consistent with those found by others. Red noise, however, drastically alters the results. We discuss methods to meet the challenge of GW detection ("climbing mount significance") by distinguishing between GW-dominated and red or white-noise limited regimes. We characterize detection regimes by evaluating the number of millisecond pulsars that must be monitored in a high-cadence, 5-year timing program for a GW background spectrum $h_c(f) = A f^{-2/3}$ with $A = 10^{-15}$ yr$^{-2/3}$. Unless a sample of 20 super-stable millisecond pulsars can be found --- those with timing residuals from red-noise contributions $\sigma_r \lesssim 20$ ns --- a much larger timing program on $\gtrsim 50 - 100$ MSPs will be needed. For other values of $A$, the constraint is $\sigma_r \lesssim 20 {\rm ns} (A/10^{-15} {\rm yr}^{-2/3})$. Identification of suitable MSPs itself requires an aggressive survey campaign followed by characterization of the level of spin noise in the timing residuals of each object. The search and timing programs will likely require substantial fractions of time on new array telescopes in the southern hemisphere as well as on existing ones.Comment: Submitted to the Astrophysical Journa

Hide and seek on complex networks

Signaling pathways and networks determine the ability to communicate in systems ranging from living cells to human society. We investigate how the network structure constrains communication in social-, man-made and biological networks. We find that human networks of governance and collaboration are predictable on teat-a-teat level, reflecting well defined pathways, but globally inefficient. In contrast, the Internet tends to have better overall communication abilities, more alternative pathways, and is therefore more robust. Between these extremes the molecular network of Saccharomyces cerevisea is more similar to the simpler social systems, whereas the pattern of interactions in the more complex Drosophilia melanogaster, resembles the robust Internet.Comment: 5 pages, 5 figure

Entropic uncertainty relations and entanglement

We discuss the relationship between entropic uncertainty relations and entanglement. We present two methods for deriving separability criteria in terms of entropic uncertainty relations. Especially we show how any entropic uncertainty relation on one part of the system results in a separability condition on the composite system. We investigate the resulting criteria using the Tsallis entropy for two and three qubits.Comment: 8 pages, 3 figures, v2: small change

A Bayesian Analogue of Gleason's Theorem

We introduce a novel notion of probability within quantum history theories and give a Gleasonesque proof for these assignments. This involves introducing a tentative novel axiom of probability. We also discuss how we are to interpret these generalised probabilities as partially ordered notions of preference and we introduce a tentative generalised notion of Shannon entropy. A Bayesian approach to probability theory is adopted throughout, thus the axioms we use will be minimal criteria of rationality rather than ad hoc mathematical axioms.Comment: 14 pages, v2: minor stylistic changes, v3: changes made in-line with to-be-published versio