Bridge Decomposition of Restriction Measures

Motivated by Kesten's bridge decomposition for two-dimensional self-avoiding walks in the upper half plane, we show that the conjectured scaling limit of the half-plane SAW, the SLE(8/3) process, also has an appropriately defined bridge decomposition. This continuum decomposition turns out to entirely be a consequence of the restriction property of SLE(8/3), and as a result can be generalized to the wider class of restriction measures. Specifically we show that the restriction hulls with index less than one can be decomposed into a Poisson Point Process of irreducible bridges in a way that is similar to Ito's excursion decomposition of a Brownian motion according to its zeros.Comment: 24 pages, 2 figures. Final version incorporates minor revisions suggested by the referee, to appear in Jour. Stat. Phy

Emergent gauge dynamics of highly frustrated magnets

Condensed matter exhibits a wide variety of exotic emergent phenomena such as the fractional quantum Hall effect and the low temperature cooperative behavior of highly frustrated magnets. I consider the classical Hamiltonian dynamics of spins of the latter phenomena using a method introduced by Dirac in the 1950s by assuming they are constrained to their lowest energy configurations as a simplifying measure. Focusing on the kagome antiferromagnet as an example, I find it is a gauge system with topological dynamics and non-locally connected edge states for certain open boundary conditions similar to doubled Chern-Simons electrodynamics expected of a $Z_2$ spin liquid. These dynamics are also similar to electrons in the fractional quantum Hall effect. The classical theory presented here is a first step towards a controlled semi-classical description of the spin liquid phases of many pyrochlore and kagome antiferromagnets and towards a description of the low energy classical dynamics of the corresponding unconstrained Heisenberg models.Comment: Updated with some appendices moved to the main body of the paper and some additional improvements. 21 pages, 5 figure

Harmonic Measure and Winding of Conformally Invariant Curves

The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension of the points where the potential scales with distance $r$ as $H \sim r^{\alpha}$ while the curve logarithmically spirals with a rotation angle phi=lambda ln r. It obeys the scaling law f(\alpha,\lambda)=(1+\lambda^2) f(\bar \alpha)-b\lambda^2 with \bar \alpha=\alpha/(1+\lambda^2) and b=(25-c)/{12}$, and where f(\alpha)\equiv f(\alpha,0) is the pure harmonic measure spectrum, and c the conformal central charge. The results apply to O(N) and Potts models, as well as to {\rm SLE}_{\kappa}.Comment: 3 figure

Multiconfiguration Time-Dependent Hartree-Fock Treatment of Electronic and Nuclear Dynamics in Diatomic Molecules

The multiconfiguration time-dependent Hartree-Fock (MCTDHF) method is formulated for treating the coupled electronic and nuclear dynamics of diatomic molecules without the Born- Oppenheimer approximation. The method treats the full dimensionality of the electronic motion, uses no model interactions, and is in principle capable of an exact nonrelativistic description of diatomics in electromagnetic fields. An expansion of the wave function in terms of configurations of orbitals whose dependence on internuclear distance is only that provided by the underlying prolate spheroidal coordinate system is demonstrated to provide the key simplifications of the working equations that allow their practical solution. Photoionization cross sections are also computed from the MCTDHF wave function in calculations using short pulses.Comment: Submitted to Phys Rev

Distribution of sizes of erased loops of loop-erased random walks in two and three dimensions

We show that in the loop-erased random walk problem, the exponent characterizing probability distribution of areas of erased loops is superuniversal. In d-dimensions, the probability that the erased loop has an area A varies as A^{-2} for large A, independent of d, for 2 <= d <= 4. We estimate the exponents characterizing the distribution of perimeters and areas of erased loops in d = 2 and 3 by large-scale Monte Carlo simulations. Our estimate of the fractal dimension z in two-dimensions is consistent with the known exact value 5/4. In three-dimensions, we get z = 1.6183 +- 0.0004. The exponent for the distribution of durations of avalanche in the three-dimensional abelian sandpile model is determined from this by using scaling relations.Comment: 25 pages, 1 table, 8 figure

Critical Exponents near a Random Fractal Boundary

The critical behaviour of correlation functions near a boundary is modified from that in the bulk. When the boundary is smooth this is known to be characterised by the surface scaling dimension \xt. We consider the case when the boundary is a random fractal, specifically a self-avoiding walk or the frontier of a Brownian walk, in two dimensions, and show that the boundary scaling behaviour of the correlation function is characterised by a set of multifractal boundary exponents, given exactly by conformal invariance arguments to be \lambda_n = 1/48 (\sqrt{1+24n\xt}+11)(\sqrt{1+24n\xt}-1). This result may be interpreted in terms of a scale-dependent distribution of opening angles $\alpha$ of the fractal boundary: on short distance scales these are sharply peaked around $\alpha=\pi/3$. Similar arguments give the multifractal exponents for the case of coupling to a quenched random bulk geometry.Comment: 13 pages. Comments on relation to results in quenched random bulk added, and on relation to other recent work. Typos correcte

Duality of Chordal SLE

We derive some geometric properties of chordal SLE$(\kappa;\vec{\rho})$ processes. Using these results and the method of coupling two SLE processes, we prove that the outer boundary of the final hull of a chordal SLE$(\kappa;\vec{\rho})$ process has the same distribution as the image of a chordal SLE$(\kappa';\vec{\rho'})$ trace, where $\kappa>4$, $\kappa'=16/\kappa$, and the forces $\vec{\rho}$ and $\vec{\rho'}$ are suitably chosen. We find that for $\kappa\ge 8$, the boundary of a standard chordal SLE$(\kappa)$ hull stopped on swallowing a fixed x\in\R\sem\{0\} is the image of some SLE$(16/\kappa;\vec{\rho})$ trace started from $x$. Then we obtain a new proof of the fact that chordal SLE$(\kappa)$ trace is not reversible for $\kappa>8$. We also prove that the reversal of SLE$(4;\vec{\rho})$ trace has the same distribution as the time-change of some SLE$(4;\vec{\rho'})$ trace for certain values of $\vec{\rho}$ and $\vec{\rho'}$.Comment: In this third version, the referee's suggestions are taken into consideration. More details are added. Some typos are corrected. The paper has been accepted by Inventiones Mathematica

Vasopressin pressor effects in critically ill children during evaluation for brain death and organ recovery.

BACKGROUND: Vasopressin (VP) shows promise as a pressor agent in animals and adult human cardiac arrest and resuscitation, but has not been studied for pressor effect in critically ill or arrested children. VP infusion is routine treatment for diabetes insipidus during brain death evaluation and organ recovery. We hypothesized that low dose VP infusion during organ recovery in critically ill children exerts a pressor effect, without major organ toxicity. METHODS: 34 VP-treated and 29 age-matched critically ill controls (C) \u3c or =18 years were retrospectively reviewed during brain death evaluation and organ recovery. VP infusion protocol titrated VP dose clinically to urine output, with high variability. Pressor and inotrope management was titrated clinically to BP, cerebral perfusion and central venous pressures (when available) and peripheral perfusion with similar protocol targets for pre-load in VP and C groups. Outcome measures include dose, type and number of pressors and inotropes. Organ function was assessed at recovery and 48 h post-transplant by independent surgeon and transplant program organ function criteria. Analysis by Odds Ratio (OR), and chi-square. RESULTS: VP dose averaged 0.041+/-0.069 U/kg/h. Average baseline mean arterial pressure (MAP) before VP infusion was 79+/-17 mmHg VP and 76+/-14 mm Hg C (P=0.6). Subsequent average MAP were: 82+/-21 mmHgVP after VP infusion versus 71+/-16 mmHg C (P=0.01) and 80+/-14 mmHg VP versus 68+/-22 mmHg C (P=0.01). Ability to wean/stop pressors and inotropes was: dopamine (14/23) 42% VP versus (10/26) 38% C (P=0.75), dobutamine (4/7) 57% VP versus (0/6) 0% C (P=0.026), epinephrine (4/5) 80% VP versus (0/6) 0% C (P=0.006), norepinephrine/phenylephrine (4/4) 100% VP versus (2/5) 40% C (P=0. 057). Alpha agonist pressor dependence was successfully weaned from 7/9 (78%) VP versus 0/9 (0%) C: odds ratio=7.3, (P CONCLUSIONS: Low dose vasopressin infusion exerts a pressor effect in critically ill children treated for diabetes insipidus during brain death and organ recovery. VP treated patients were 7.3 times more likely to wean from alpha agonists than comparably managed age matched controls, without adverse affect on transplant organ function. We speculate that further prospective assessment of VP safety and efficacy as a pressor adjunct for resuscitation of critically ill children is warranted

Fluctuation force exerted by a planar self-avoiding polymer

Using results from Schramm Loewner evolution (SLE), we give the expression of the fluctuation-induced force exerted by a polymer on a small impenetrable disk, in various 2-dimensional domain geometries. We generalize to two polymers and examine whether the fluctuation force can trap the object into a stable equilibrium. We compute the force exerted on objects at the domain boundary, and the force mediated by the polymer between such objects. The results can straightforwardly be extended to any SLE interface, including Ising, percolation, and loop-erased random walks. Some are relevant for extremal value statistics.Comment: 7 pages, 22 figure