Transforming fixed-length self-avoiding walks into radial SLE_8/3

We conjecture a relationship between the scaling limit of the fixed-length ensemble of self-avoiding walks in the upper half plane and radial SLE with kappa=8/3 in this half plane from 0 to i. The relationship is that if we take a curve from the fixed-length scaling limit of the SAW, weight it by a suitable power of the distance to the endpoint of the curve and then apply the conformal map of the half plane that takes the endpoint to i, then we get the same probability measure on curves as radial SLE. In addition to a non-rigorous derivation of this conjecture, we support it with Monte Carlo simulations of the SAW. Using the conjectured relationship between the SAW and radial SLE, our simulations give estimates for both the interior and boundary scaling exponents. The values we obtain are within a few hundredths of a percent of the conjectured values

Coplanar Circumbinary Debris Disks

We present resolved Herschel images of circumbinary debris disks in the alpha CrB (HD139006) and beta Tri (HD13161) systems. We find that both disks are consistent with being aligned with the binary orbital planes. Though secular perturbations from the binary can align the disk, in both cases the alignment time at the distances at which the disk is resolved is greater than the stellar age, so we conclude that the coplanarity was primordial. Neither disk can be modelled as a narrow ring, requiring extended radial distributions. To satisfy both the Herschel and mid-IR images of the alpha CrB disk, we construct a model that extends from 1-300AU, whose radial profile is broadly consistent with a picture where planetesimal collisions are excited by secular perturbations from the binary. However, this model is also consistent with stirring by other mechanisms, such as the formation of Pluto-sized objects. The beta Tri disk model extends from 50-400AU. A model with depleted (rather than empty) inner regions also reproduces the observations and is consistent with binary and other stirring mechanisms. As part of the modelling process, we find that the Herschel PACS beam varies by as much as 10% at 70um and a few % at 100um. The 70um variation can therefore hinder image interpretation, particularly for poorly resolved objects. The number of systems in which circumbinary debris disk orientations have been compared with the binary plane is now four. More systems are needed, but a picture in which disks around very close binaries (alpha CrB, beta Tri, and HD 98800, with periods of a few weeks to a year) are aligned, and disks around wider binaries (99 Her, with a 50 yr period) are misaligned, may be emerging. This picture is qualitatively consistent with the expectation that the protoplanetary disks from which the debris emerged are more likely to be aligned if their binaries have shorter periods.Comment: accepted to MNRA

Monte Carlo Tests of SLE Predictions for the 2D Self-Avoiding Walk

The conjecture that the scaling limit of the two-dimensional self-avoiding walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE) with $\kappa=8/3$ leads to explicit predictions about the SAW. A remarkable feature of these predictions is that they yield not just critical exponents, but probability distributions for certain random variables associated with the self-avoiding walk. We test two of these predictions with Monte Carlo simulations and find excellent agreement, thus providing numerical support to the conjecture that the scaling limit of the SAW is SLE$_{8/3}$.Comment: TeX file using APS REVTeX 4.0. 10 pages, 5 figures (encapsulated postscript

Identification of proteins in the postsynaptic density fraction by mass spectrometry

Our understanding of the organization of postsynaptic signaling systems at excitatory synapses has been aided by the identification of proteins in the postsynaptic density (PSD) fraction, a subcellular fraction enriched in structures with the morphology of PSDs. In this study, we have completed the identification of most major proteins in the PSD fraction with the use of an analytical method based on mass spectrometry coupled with searching of the protein sequence databases. At least one protein in each of 26 prominent protein bands from the PSD fraction has now been identified. We found 7 proteins not previously known to be constituents of the PSD fraction and 24 that had previously been associated with the PSD by other methods. The newly identified proteins include the heavy chain of myosin-Va (dilute myosin), a motor protein thought to be involved in vesicle trafficking, and the mammalian homolog of the yeast septin protein cdc10, which is important for bud formation in yeast. Both myosin-Va and cdc10 are threefold to fivefold enriched in the PSD fraction over brain homogenates. Immunocytochemical localization of myosin-Va in cultured hippocampal neurons shows that it partially colocalizes with PSD-95 at synapses and is also diffusely localized in cell bodies, dendrites, and axons. Cdc10 has a punctate distribution in cell bodies and dendrites, with some of the puncta colocalizing with PSD-95. The results support a role for myosin-Va in transport of materials into spines and for septins in the formation or maintenance of spines

Mott transition in lattice boson models

We use mathematically rigorous perturbation theory to study the transition between the Mott insulator and the conjectured Bose-Einstein condensate in a hard-core Bose-Hubbard model. The critical line is established to lowest order in the tunneling amplitude.Comment: 20 page

First passage times and distances along critical curves

We propose a model for anomalous transport in inhomogeneous environments, such as fractured rocks, in which particles move only along pre-existing self-similar curves (cracks). The stochastic Loewner equation is used to efficiently generate such curves with tunable fractal dimension $d_f$. We numerically compute the probability of first passage (in length or time) from one point on the edge of the semi-infinite plane to any point on the semi-circle of radius $R$. The scaled probability distributions have a variance which increases with $d_f$, a non-monotonic skewness, and tails that decay faster than a simple exponential. The latter is in sharp contrast to predictions based on fractional dynamics and provides an experimental signature for our model.Comment: 5 pages, 5 figure

Quantum interference of electromagnetic fields from remote quantum memories

We observe quantum, Hong-Ou-Mandel, interference of fields produced by two remote atomic memories. High-visibility interference is obtained by utilizing the finite atomic memory time in four-photon delayed coincidence measurements. Interference of fields from remote atomic memories is a crucial element in protocols for scalable generation of multi-node remote qubit entanglement.Comment: 4 pages, 3 figure

Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems

Gapped ground states of quantum spin systems have been referred to in the physics literature as being `in the same phase' if there exists a family of Hamiltonians H(s), with finite range interactions depending continuously on $s \in [0,1]$, such that for each $s$, H(s) has a non-vanishing gap above its ground state and with the two initial states being the ground states of H(0) and H(1), respectively. In this work, we give precise conditions under which any two gapped ground states of a given quantum spin system that 'belong to the same phase' are automorphically equivalent and show that this equivalence can be implemented as a flow generated by an $s$-dependent interaction which decays faster than any power law (in fact, almost exponentially). The flow is constructed using Hastings' 'quasi-adiabatic evolution' technique, of which we give a proof extended to infinite-dimensional Hilbert spaces. In addition, we derive a general result about the locality properties of the effect of perturbations of the dynamics for quantum systems with a quasi-local structure and prove that the flow, which we call the {\em spectral flow}, connecting the gapped ground states in the same phase, satisfies a Lieb-Robinson bound. As a result, we obtain that, in the thermodynamic limit, the spectral flow converges to a co-cycle of automorphisms of the algebra of quasi-local observables of the infinite spin system. This proves that the ground state phase structure is preserved along the curve of models $H(s), 0\leq s\leq 1$.Comment: Updated acknowledgments and new email address of S

Charge-ordered ferromagnetic phase in manganites

A mechanism for charge-ordered ferromagnetic phase in manganites is proposed. The mechanism is based on the double exchange in the presence of diagonal disorder. It is modeled by a combination of the Ising double-exchange and the Falicov-Kimball model. Within the dynamical mean-field theory the charge and spin correlation function are explicitely calculated. It is shown that the system exhibits two successive phase transitions. The first one is the ferromagnetic phase transition, and the second one is a charge ordering. As a result a charge-ordered ferromagnetic phase is stabilized at low temperature.Comment: To appear in Phys. Rev.