Finite temperature correlations in the one-dimensional quantum Ising model

We extend the form-factors approach to the quantum Ising model at finite temperature. The two point function of the energy is obtained in closed form, while the two point function of the spin is written as a Fredholm determinant. Using the approach of \Korbook, we obtain, starting directly from the continuum formulation, a set of six differential equations satisfied by this two point function. Four of these equations involve only spacetime derivatives, of which three are equivalent to the equations obtained earlier in \mccoy,\perk. In addition, we obtain two new equations involving a temperature derivative. Some of these results are generalized to the Ising model on the half line with a magnetic field at the origin.Comment: 37 pages, uses harvmac, minor changes in the last two paragraphs, updating some conjecture

A cryogenic liquid-mirror telescope on the moon to study the early universe

We have studied the feasibility and scientific potential of zenith observing liquid mirror telescopes having 20 to 100 m diameters located on the moon. They would carry out deep infrared surveys to study the distant universe and follow up discoveries made with the 6 m James Webb Space Telescope (JWST), with more detailed images and spectroscopic studies. They could detect objects 100 times fainter than JWST, observing the first, high-red shift stars in the early universe and their assembly into galaxies. We explored the scientific opportunities, key technologies and optimum location of such telescopes. We have demonstrated critical technologies. For example, the primary mirror would necessitate a high-reflectivity liquid that does not evaporate in the lunar vacuum and remains liquid at less than 100K: We have made a crucial demonstration by successfully coating an ionic liquid that has negligible vapor pressure. We also successfully experimented with a liquid mirror spinning on a superconducting bearing, as will be needed for the cryogenic, vacuum environment of the telescope. We have investigated issues related to lunar locations, concluding that locations within a few km of a pole are ideal for deep sky cover and long integration times. We have located ridges and crater rims within 0.5 degrees of the North Pole that are illuminated for at least some sun angles during lunar winter, providing power and temperature control. We also have identified potential problems, like lunar dust. Issues raised by our preliminary study demand additional in-depth analyses. These issues must be fully examined as part of a scientific debate we hope to start with the present article.Comment: 35 pages, 11 figures. To appear in Astrophysical Journal June 20 200

gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions

We consider the non-hermitian 2D Dirac Hamiltonian with (A): real random mass, imaginary scalar potential and imaginary gauge field potentials, and (B) arbitrary complex random potentials of all three kinds. In both cases this Hamiltonian gives rise to a delocalization transition at zero energy with particle-hole symmetry in every realization of disorder. Case (A) is in addition time-reversal invariant, and can also be interpreted as the random-field XY Statistical Mechanics model in two dimensions. The supersymmetric approach to disorder averaging results in current-current perturbations of $gl(N|N)$ super-current algebras. Special properties of the $gl(N|N)$ algebra allow the exact computation of the beta-functions, and of the correlation functions of all currents. One of them is the Edwards-Anderson order parameter. The theory is `nearly conformal' and possesses a scale-invariant subsector which is not a current algebra. For N=1, in addition, we obtain an exact solution of all correlation functions. We also study the delocalization transition of case (B), with broken time reversal symmetry, in the Gade-Wegner (Random-Flux) universality class, using a GL(N|N;C)/U(N|N) sigma model, as well as its PSL(N|N) variant, and a corresponding generalized random XY model. For N=1 the sigma model is shown to be identical to the current-current perturbation. For the delocalization transitions (case (A) and (B)) a density of states, diverging at zero energy, is found.Comment: LaTeX, 40 page

Dynamics at a smeared phase transition

We investigate the effects of rare regions on the dynamics of Ising magnets with planar defects, i.e., disorder perfectly correlated in two dimensions. In these systems, the magnetic phase transition is smeared because static long-range order can develop on isolated rare regions. We first study an infinite-range model by numerically solving local dynamic mean-field equations. Then we use extremal statistics and scaling arguments to discuss the dynamics beyond mean-field theory. In the tail region of the smeared transition the dynamics is even slower than in a conventional Griffiths phase: the spin autocorrelation function decays like a stretched exponential at intermediate times before approaching the exponentially small equilibrium value following a power law at late times.Comment: 10 pages, 8eps figures included, final version as publishe

Lattice fermion models with supersymmetry

We investigate a family of lattice models with manifest N=2 supersymmetry. The models describe fermions on a 1D lattice, subject to the constraint that no more than k consecutive lattice sites may be occupied. We discuss the special properties arising from the supersymmetry, and present Bethe ansatz solutions of the simplest models. We display the connections of the k=1 model with the spin-1/2 antiferromagnetic XXZ chain at \Delta=-1/2, and the k=2 model with both the su(2|1)-symmetric tJ model in the ferromagnetic regime and the integrable spin-1 XXZ chain at \Delta=-1/\sqrt{2}. We argue that these models include critical points described by the superconformal minimal models.Comment: 28 pages. v2: added new result on mapping to XXZ chai

Quantum Sine(h)-Gordon Model and Classical Integrable Equations

We study a family of classical solutions of modified sinh-Gordon equation, $\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\ \re^{-2\eta}=0$with$p(z)=z^{2\alpha}-s^{2\alpha}$. We show that certain connection coefficients for solutions of the associated linear problem coincide with the$Q$-function of the quantum sine-Gordon$(\alpha>0)$or sinh-Gordon$(\alpha<-1)$ models.Comment: 35 pages, 3 figure

Boundary Conditions in Rational Conformal Field Theories

We develop further the theory of Rational Conformal Field Theories (RCFTs) on a cylinder with specified boundary conditions emphasizing the role of a triplet of algebras: the Verlinde, graph fusion and Pasquier algebras. We show that solving Cardy's equation, expressing consistency of a RCFT on a cylinder, is equivalent to finding integer valued matrix representations of the Verlinde algebra. These matrices allow us to naturally associate a graph $G$ to each RCFT such that the conformal boundary conditions are labelled by the nodes of $G$. This approach is carried to completion for $sl(2)$ theories leading to complete sets of conformal boundary conditions, their associated cylinder partition functions and the $A$-$D$-$E$ classification. We also review the current status for WZW $sl(3)$ theories. Finally, a systematic generalization of the formalism of Cardy-Lewellen is developed to allow for multiplicities arising from more general representations of the Verlinde algebra. We obtain information on the bulk-boundary coefficients and reproduce the relevant algebraic structures from the sewing constraints.Comment: 71 pages. Minor changes with respect to 2nd version. Recently published in Nucl.Phys.B but mistakenly as 1st version. Will be republished in Nucl.Phys.B as this (3rd) versio

Structural basis for potency differences between GDF8 and GDF11.

BACKGROUND: Growth/differentiation factor 8 (GDF8) and GDF11 are two highly similar members of the transforming growth factor β (TGFβ) family. While GDF8 has been recognized as a negative regulator of muscle growth and differentiation, there are conflicting studies on the function of GDF11 and whether GDF11 has beneficial effects on age-related dysfunction. To address whether GDF8 and GDF11 are functionally identical, we compared their signaling and structural properties. RESULTS: Here we show that, despite their high similarity, GDF11 is a more potent activator of SMAD2/3 and signals more effectively through the type I activin-like receptor kinase receptors ALK4/5/7 than GDF8. Resolution of the GDF11:FS288 complex, apo-GDF8, and apo-GDF11 crystal structures reveals unique properties of both ligands, specifically in the type I receptor binding site. Lastly, substitution of GDF11 residues into GDF8 confers enhanced activity to GDF8. CONCLUSIONS: These studies identify distinctive structural features of GDF11 that enhance its potency, relative to GDF8; however, the biological consequences of these differences remain to be determined

Arctic passages: liminality, I&#xF1;upiat Eskimo mothers and NW Alaska communities in transition

Background. While the primary goal of the NW Alaska Native maternal transport is safe deliveries for mothers from remote villages, little has been done to question the impact of transport on the mothers and communities involved. This study explores how presence of I&#xF1;upiat values influences the desire of indigenous women of differing eras and NW Alaska villages to participate in biomedical birth, largely made available by a tribal health-sponsored transport system. Objective. This paper portrays how important it is (and why) for Alaska Native families and women of different generations from various areas of I&#xF1;upiat villages of NW Alaska to get to the hospital to give birth. This research asks: How does a community&#x2019;s presence of I&#xF1;upiat values influence women of different eras and locations to participate in a more biomedical mode of birth? Design. Theoretical frameworks of medical anthropology and maternal identity work are used to track the differences in regard to the maternal transport operation for I&#xF1;upiat mothers of the area. Presence of I&#xF1;upiat values in each of the communities is compared by birth era and location for each village. Content analysis is conducted to determine common themes in an inductive, recursive fashion. Results. A connection is shown between a community&#x2019;s manifestation of I&#xF1;upiat cultural expression and mothers&#x2019; acceptance of maternal transport in this study. For this group of I&#xF1;upiat Eskimo mothers, there is interplay between community expression of I&#xF1;upiat values and desire and lengths gone to by women of different eras and locations. Conclusions. The more openly manifested the I&#xF1;upiat values of the community, the more likely alternative birthing practices sought, lessening the reliance on the existing transport policy. Conversely, the more openly western values are manifested in the village of origin, the less likely alternative measures are sought. For this study group, mothers from study villages with openly manifested western values are more likely to easily acquiesce to policy, and &#x201C;make the best&#x201D; of their prenatal travel

Detection of ctDNA in plasma of patients with clinically localised prostate cancer is associated with rapid disease progression.

BACKGROUND DNA originating from degenerate tumour cells can be detected in the circulation in many tumour types, where it can be used as a marker of disease burden as well as to monitor treatment response. Although circulating tumour DNA (ctDNA) measurement has prognostic/predictive value in metastatic prostate cancer, its utility in localised disease is unknown. METHODS We performed whole-genome sequencing of tumour-normal pairs in eight patients with clinically localised disease undergoing prostatectomy, identifying high confidence genomic aberrations. A bespoke DNA capture and amplification panel against the highest prevalence, highest confidence aberrations for each individual was designed and used to interrogate ctDNA isolated from plasma prospectively obtained pre- and post- (24 h and 6 weeks) surgery. In a separate cohort (n = 189), we identified the presence of ctDNA TP53 mutations in preoperative plasma in a retrospective cohort and determined its association with biochemical- and metastasis-free survival. RESULTS Tumour variants in ctDNA were positively identified pre-treatment in two of eight patients, which in both cases remained detectable postoperatively. Patients with tumour variants in ctDNA had extremely rapid disease recurrence and progression compared to those where variants could not be detected. In terms of aberrations targeted, single nucleotide and structural variants outperformed indels and copy number aberrations. Detection of ctDNA TP53 mutations was associated with a significantly shorter metastasis-free survival (6.2 vs. 9.5 years (HR 2.4; 95% CIs 1.2-4.8, p = 0.014). CONCLUSIONS CtDNA is uncommonly detected in localised prostate cancer, but its presence portends more rapidly progressive disease