Quantum Monte Carlo in the Interaction Representation --- Application to a Spin-Peierls Model

A quantum Monte Carlo algorithm is constructed starting from the standard perturbation expansion in the interaction representation. The resulting configuration space is strongly related to that of the Stochastic Series Expansion (SSE) method, which is based on a direct power series expansion of exp(-beta*H). Sampling procedures previously developed for the SSE method can therefore be used also in the interaction representation formulation. The new method is first tested on the S=1/2 Heisenberg chain. Then, as an application to a model of great current interest, a Heisenberg chain including phonon degrees of freedom is studied. Einstein phonons are coupled to the spins via a linear modulation of the nearest-neighbor exchange. The simulation algorithm is implemented in the phonon occupation number basis, without Hilbert space truncations, and is exact. Results are presented for the magnetic properties of the system in a wide temperature regime, including the T-->0 limit where the chain undergoes a spin-Peierls transition. Some aspects of the phonon dynamics are also discussed. The results suggest that the effects of dynamic phonons in spin-Peierls compounds such as GeCuO3 and NaV2O5 must be included in order to obtain a correct quantitative description of their magnetic properties, both above and below the dimerization temperature.

Singing Through Struggle: Music as a Mode of Cultural Exchange in African American Border City Churches After Emancipation, 1862-1890

This project investigates how religious music, invested with symbolic and cultural meaning, provided African Americans in border city churches with a way to negotiate conflict, assert individual values, and establish a collective identity in the post- emancipation era. In order to focus on the encounter between former slaves and free Blacks, the dissertation examines black churches that received large numbers of southern migrants during and after the Civil War. Primarily a work of history, the study also employs insights and conceptual frameworks from other disciplines including anthropology and ritual studies, African American studies, aesthetic theory, and musicology. It is a work of historical reconstruction in the tradition of scholarship that some have called "lived religion." Chapter 1 introduces the dissertation topic and explains how it contributes to scholarship. Chapter 2 examines social and religious conditions African Americans faced in Baltimore, MD, Philadelphia, PA, and Washington, DC to show why the Black Church played a key role in African Americans' adjustment to post-emancipation life. Chapter 3 compares religious slave music and free black church music to identify differences and continuities between them, as well as their functions in religious settings. Chapters 4, 5, and 6 present case studies on Bethel African Methodist Episcopal Church (Baltimore), Zoar Methodist Episcopal Church (Philadelphia), and St. Luke’s Protestant Episcopal Church (Washington, DC), respectively. Informed by fresh archival materials, the dissertation shows how each congregation used its musical life to uphold values like education and community, to come to terms with a shared experience, and to confront or avert authority when cultural priorities were threatened. By arguing over musical choices or performance practices, or agreeing on mutually appealing musical forms like the gospel songs of the Sunday school movement, African Americans forged lively faith communities and distinctive cultures in otherwise adverse environments. The study concludes that religious music was a crucial form of African American discourse and expression in the post-emancipation era. In the Black Church, it nurtured an atmosphere of exchange, gave structure and voice to conflict, helped create a public sphere, and upheld the values of black people.

Exact Geosedics and Shortest Paths on Polyhedral Surface

We present two algorithms for computing distances along a non-convex polyhedral surface. The first algorithm computes exact minimal-geodesic distances and the second algorithm combines these distances to compute exact shortest-path distances along the surface. Both algorithms have been extended to compute the exact minimalgeodesic paths and shortest paths. These algorithms have been implemented and validated on surfaces for which the correct solutions are known, in order to verify the accuracy and to measure the run-time performance, which is cubic or less for each algorithm. The exact-distance computations carried out by these algorithms are feasible for large-scale surfaces containing tens of thousands of vertices, and are a necessary component of near-isometric surface flattening methods that accurately transform curved manifolds into flat representations.