A unified diagrammatic approach to topological fixed point models

We introduce a systematic mathematical language for describing fixed point models and apply it to the study to topological phases of matter. The framework established is reminiscent to that of state-sum models and lattice topological quantum field theories, but is formalized and unified in terms of tensor networks. In contrast to existing tensor network ansatzes for the study of ground states of topologically ordered phases, the tensor networks in our formalism directly represent discrete path integrals in Euclidean space-time. This language is more immediately related to the Hamiltonian defining the model than other approaches, via a Trotterization of the respective imaginary time evolution. We illustrate our formalism at hand of simple examples, and demonstrate its full power by expressing known families of models in 2+1 dimensions in their most general form, namely string-net models and Kitaev quantum doubles based on weak Hopf algebras. To elucidate the versatility of our formalism, we also show how fermionic phases of matter can be described and provide a framework for topological fixed point models in 3+1 dimensions.Comment: 86 pages and many diagrams, small change

Topological dualities via tensor networks

The ground state of the toric code, that of the two-dimensional class D superconductor, and the partition sum of the two-dimensional Ising model are dual to each other. This duality is remarkable inasmuch as it connects systems commonly associated to different areas of physics -- that of long range entangled topological order, (topological) band insulators, and classical statistical mechanics, respectively. Connecting fermionic and bosonic systems, the duality construction is intrinsically non-local, a complication that has been addressed in a plethora of different approaches, including dimensional reduction to one dimension, conformal field theory methods, and operator algebra. In this work, we propose a unified approach to this duality, whose main protagonist is a tensor network (TN) assuming the role of an intermediate translator. Introducing a fourth node into the net of dualities offers several advantages: the formulation is integrative in that all links of the duality are treated on an equal footing, (unlike in field theoretical approaches) it is formulated with lattice precision, a feature that becomes key in the mapping of correlation functions, and their possible numerical implementation. Finally, the passage from bosons to fermions is formulated entirely within the two-dimensional TN framework where it assumes an intuitive and technically convenient form. We illustrate the predictive potential of the formalism by exploring the fate of phase transitions, point and line defects, topological boundary modes, and other structures under the mapping between system classes. Having condensed matter readerships in mind, we introduce the construction pedagogically in a manner assuming only minimal familiarity with the concept of TNs.Comment: 19 pages, 19 figure

Comparing the Use and Survival Outcome of Stereotactic Radiosurgery and Stereotactic Radiation Therapy

Brain metastases are common in many types of cancer. Treatment for this condition is usually through surgical resection, whole brain radiation treatment (WBRT), stereotactic radiosurgery (SRS), or stereotactic radiation therapy (SRT). SRS (15 to 24 Gy in 1 fraction) and SRT (21, 24 or 30 Gy in 3 fractions or 25, 30 Gy in 5 fractions) have similar biological equivalent doses but differ in the number of treatments the radiation is delivered over. The objective of this study is to use national cancer database (NCDB) to examine the factors associated with receiving SRS as compared to SRT, and to compare overall survival between patients who received SRS to those who received SRT after adjusting for all potential prognostic factors. The two treatments were not found to have a significant difference in survival.https://digitalcommons.unmc.edu/surp2020/1001/thumbnail.jp

Leydig cells express neural cell adhesion molecules in vivo and in vitro

The neural cell adhesion molecule (NCAM) polypeptides are expressed by numerous tissues during embryonic development, where they are involved in cell-cell interactions. In the adult, NCAM expression is confined to a few cell types, including neurons and peptide-hormone-producing cells. Here we demonstrate that the Leydig cells of the adult rat, mouse, and hamster testes express NCAM as well. Western blotting showed that an NCAM of approximately 120 kDa was present in the adult testes of all three species investigated. This form was also found in freshly isolated mouse Leydig cells and in Leydig cells after 2 days in culture. After 4 days in culture, mouse Leydig cells expressed additional NCAM isoforms of approximately 140 and 180 kDa, indicating changes in alternative splicing of NCAM primary transcripts. Also, NCAM mRNA of all isoforms, as detected by S1-nuclease protection assays, increased with time in culture. The expression of the cell adhesion molecule NCAM by adult Leydig cells may explain the aggregation of Leydig cells in clusters in rodent testes, which could be a prerequisite for functional coordination of groups of Leydig cells. Furthermore, the presence of this neural and endocrine marker may indicate a closer relationship between Leydig cells and neural and peptide-hormone-producing cells than is considered to exist at the present time

Intensity interferometry of single x-ray pulses from a synchrotron storage ring

We report on measurements of second-order intensity correlations at the high brilliance storage ring PETRA III using a prototype of the newly developed Adaptive Gain Integrating Pixel Detector (AGIPD). The detector recorded individual synchrotron radiation pulses with an x-ray photon energy of 14.4 keV and repetition rate of about 5 MHz. The second-order intensity correlation function was measured simultaneously at different spatial separations that allowed to determine the transverse coherence length at these x-ray energies. The measured values are in a good agreement with theoretical simulations based on the Gaussian Schell-model.Comment: 16 pages, 6 figures, 42 reference