Coarse grained belief propagation for simulation of interacting quantum systems at all temperatures

We continue our numerical study of quantum belief propagation initiated in [Phys. Rev. A, 77 (2008), p. 052318]. We demonstrate how the method can be expressed in terms of an effective thermal potential that materializes when the system presents quantum correlations, but is insensitive to classical correlations. The thermal potential provides an efficient means to assess the precision of belief propagation on graphs with no loops. We illustrate these concepts using the one-dimensional quantum Ising model and compare our results with exact solutions. We also use the method to study the transverse field quantum Ising spin glass for which we obtain a phase diagram that is largely in agreement with the one obtained in [arXiv:0706.4391] using a different approach. Finally, we introduce the coarse grained belief propagation (CGBP) algorithm to improve belief propagation at low temperatures. This method combines the reliability of belief propagation at high temperatures with the ability of entanglement renormalization to efficiently describe low energy subspaces of quantum systems with local interactions. With CGBP, thermodynamic properties of quantum systems can be calculated with a high degree of accuracy at all temperatures.Comment: updated references and acknowledgement

Laparoscopic repair of a large interstitially incarcerated inguinal hernia.

A 68 year old female presented for elective repair of an abdominal wall hernia. Preoperative CT imaging revealed a right inguinal hernia defect with hernia contents coursing cephalad between the external and internal abdominal oblique muscles. This was consistent with an interstitial inguinal hernia, a rare entity outside of post- traumatic hernias. At operation the hernia contents were reduced laparoscopically. The hernia was then repaired by transitioning to the totally extraperitoneal (TEP) approach using a 15cm X 15cm piece of polyester mesh. The patient had an uneventful recovery. Interstitial hernias are rare, difficult to diagnose and potentially dangerous if left untreated. There is no consensus on the ideal repair of these unique hernias. This represents a minimally invasive repair of an unusual hernia, with a novel approach to diagnose and manage the hernia and its redundant sac

Dynamic mean-field and cavity methods for diluted Ising systems

We compare dynamic mean-field and dynamic cavity as methods to describe the stationary states of dilute kinetic Ising models. We compute dynamic mean-field theory by expanding in interaction strength to third order, and compare to the exact dynamic mean-field theory for fully asymmetric networks. We show that in diluted networks the dynamic cavity method generally predicts magnetizations of individual spins better than both first order ("naive") and second order ("TAP") dynamic mean field theory

On the Josephson Coupling between a disk of one superconductor and a surrounding superconducting film of a different symmetry

A cylindrical Josephson junction with a spatially dependent Josephson coupling which averages to zero is studied in order to model the physics of a disk of d-wave superconductor embedded in a superconducting film of a different symmetry. It is found that the system always introduces Josepshon vortices in order to gain energy at the junction. The critical current is calculated. It is argued that a recent experiment claimed to provide evidence for s-wave superconductivity in $YBa_2Cu_3O_7$ may also be consistent with d-wave superconductivity. Figures available from the author on request.Comment: 10 pages, revtex3.0, TM-11111-940321-1

Pearl J. Flemister to Mr. Meredith (2 October 1962)

https://egrove.olemiss.edu/mercorr_pro/1556/thumbnail.jp