Quantum brownian motion on a triangular lattice and c=2 boundary conformal field theory

We study a single particle diffusing on a triangular lattice and interacting with a heat bath, using boundary conformal field theory (CFT) and exact integrability techniques. We derive a correspondence between the phase diagram of this problem and that recently obtained for the 2-dimensional 3-state Potts model with a boundary. Exact results are obtained on phases with intermediate mobilities. These correspond to nontrivial boundary states in a conformal field theory with 2 free bosons which we explicitly construct for the first time. These conformally invariant boundary conditions are not simply products of Dirichlet and Neumann ones and unlike those trivial boundary conditions, are not invariant under a Heisenberg algebra.     

Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

Vacuum quantum effect for curved boundaries in static Robertson–Walker space–time

The energy–momentum tensor for a massless conformally coupled scalar field in the region between two curved boundaries in k=−1 static Robertson–Walker space–time is investigated. We assume that the scalar field satisfies the Dirichlet boundary condition on the boundaries. k=−1 Robertson–Walker space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy–momentum tensor for conformally invariant field in Robertson–Walker space from the corresponding Rindler counterpart by the conformal transformation.     

Transforming Fixed-Length Self-avoiding Walks into Radial SLE<Subscript>8/3</Subscript>

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_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 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_8/3. 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_8/3, 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.     

SLE on Doubly-Connected Domains and the Winding of Loop-Erased Random Walks

Two-dimensional loop-erased random walks (LERWs) are random planar curves whose scaling limit is known to be a Schramm-Loewner evolution SLE _κ with parameter κ=2. In this note, some properties of an SLE _κ trace on doubly-connected domains are studied and a connection to passive scalar diffusion in a Burgers flow is emphasised. In particular, the endpoint probability distribution and winding probabilities for SLE₂ on a cylinder, starting from one boundary component and stopped when hitting the other, are found. A relation of the result to conditioned one-dimensional Brownian motion is pointed out. Moreover, this result permits to study the statistics of the winding number for SLE₂ with fixed endpoints. A solution for the endpoint distribution of SLE₄ on the cylinder is obtained and a relation to reflected Brownian motion pointed out.     

On the surface contribution to the grand-canonical pressure of free quantum gases

The surface term in the thermodynamic pressure of free quantum gases is proved to exist and is evaluated. Detailed proofs are given for parallelepipedic domains with Dirichlet, periodic, and Neumann boundary conditions and for more general domains with Dirichlet boundary conditions.     

The Yang-Mills Heat Semigroup on Three-Manifolds with Boundary

Long time existence and uniqueness of solutions to the Yang-Mills heat equation is proven over a compact 3-manifold with smooth boundary. The initial data is taken to be a Lie algebra valued connection form in the Sobolev space H ₁. Three kinds of boundary conditions are explored, Dirichlet type, Neumann type and Marini boundary conditions. The last is a nonlinear boundary condition, specified by setting the normal component of the curvature to zero on the boundary. The Yang-Mills heat equation is a weakly parabolic nonlinear equation. We use gauge symmetry breaking to convert it to a parabolic equation and then gauge transform the solution of the parabolic equation back to a solution of the original equation. Apriori estimates are developed by first establishing a gauge invariant version of the Gaffney-Friedrichs inequality. A gauge invariant regularization procedure for solutions is also established. Uniqueness holds upon imposition of boundary conditions on only two of the three components of the connection form because of weak parabolicity. This work is motivated by possible applications to quantum field theory.     

Conformal Field Theories of Stochastic Loewner Evolutions

Stochastic Loewner evolutions (SLE) are random growth processes of sets, called hulls, embedded in the two dimensional upper half plane. We elaborate and develop a relation between SLE evolutions and conformal field theories (CFT) which is based on a group theoretical formulation of SLE processes and on the identification of the proper hull boundary states. This allows us to define an infinite set of SLE zero modes, or martingales, whose existence is a consequence of the existence of a null vector in the appropriate Virasoro modules. This identification leads, for instance, to linear systems for generalized crossing probabilities whose coefficients are multipoint CFT correlation functions. It provides a direct link between conformal correlation functions and probabilities of stopping time events in SLE evolutions. We point out a relation between SLE processes and two dimensional gravity and conjecture a reconstruction procedure of conformal field theories from SLE data. Member of the CNRS     

On Conformally Invariant CLE Explorations

We study some conformally invariant dynamic ways to construct the Conformal Loop Ensembles with simple loops introduced in earlier papers by Sheffield, and by Sheffield and Werner. One outcome is a conformally invariant way to measure a distance of a CLE₄ loop to the boundary “within” the CLE₄, when one identifies all points of each loop.     

Exact partition function and boundary state of 2D massive Ising field theory with boundary magnetic field

We compute the exact partition function, the universal ground-state degeneracy and boundary state of the 2D Ising model with boundary magnetic field at off-critical temperatures. The model has a domain that exhibits states localized near the boundaries. We study this domain of boundary bound state and derive exact expressions for the “g function” and boundary state for all temperatures and boundary magnetic fields. In the massless limit we recover the boundary renormalization group flow between the conformally invariant free and fixed boundary conditions.     

Supersymmetric Boundary Conditions in \mathcal{N}=4 Super Yang-Mills Theory

We study boundary conditions in ${\mathcal{N}}=4$ super Yang-Mills theory that preserve one-half the supersymmetry. The obvious Dirichlet boundary conditions can be modified to allow some of the scalar fields to have a “pole” at the boundary. The obvious Neumann boundary conditions can be modified by coupling to additional fields supported at the boundary. The obvious boundary conditions associated with orientifolds can also be generalized. In preparation for a separate study of how electric-magnetic duality acts on these boundary conditions, we explore moduli spaces of solutions of Nahm’s equations that appear in the presence of a boundary. Though our main interest is in boundary conditions that are Lorentz-invariant (to the extent possible in the presence of a boundary), we also explore non-Lorentz-invariant but half-BPS deformations of Neumann boundary conditions. We make preliminary comments on the action of electric-magnetic duality, deferring a more serious study to a later paper.     

Coercive field enhancement in microstructured (La<Subscript>0.4</Subscript>Pr<Subscript>0.6</Subscript>)<Subscript>0.67</Subscript>Ca<Subscript>0.33</Subscript>MnO<Subscript>3</Subscript> thin films

The perovskite material (La_0.4Pr_0.6)_0.67Ca_0.33MnO₃ (LPCMO) has complex electronic and magnetic behavior based on phase competition between ferromagnetic metallic (FMM) and insulating phases with similar free energies. Experimental evidence has indicated that in-plane stress anisotropy influences these phases and can affect electronic and magnetic properties. Here we investigate the roles that both stress and shape anisotropies may play in controlling the coercive field of the material. LPCMO thin films of various thicknesses (20, 25, and 30 nm) were deposited on (110) NdGaO₃ (NGO) substrates using pulsed laser deposition and the coercive fields were measured. Photolithography was then used to fabricate microstructured arrays of LPCMO on the NGO substrates for each of the films. The coercive fields of these arrays of LPCMO were compared to the behavior of the corresponding unpatterned LPCMO thin films across a range of temperatures. Microstructure arrays for the thicker (25 and 30 nm) films showed a substantial increase in the coercive field after forming the arrays, whereas a thinner film (20 nm) showed almost no change in the coercive field. Stress anisotropy continues to play a dominant role in the behavior of LPCMO thin films and dimensionality of the magnetic domains also influences the results. The films show 2D behavior when film thickness approaches the size of the critical radius for single-to-multidomain transitions. Making thicker films allows for 3D behavior and a role for shape anisotropy to influence the coercive fields.     

On SLE Martingales in Boundary WZW Models

Following Bettelheim et al. (Phys Rev Lett 95:251601, 2005), we consider the boundary WZW model on a half-plane with a cut growing according to the Schramm–Loewner stochastic evolution and the boundary fields inserted at the tip of the cut and at infinity. We study necessary and sufficient conditions for boundary correlation functions to be SLE martingales. Necessary conditions come from the requirement for the boundary field at the tip of the cut to have a depth two null vector. Sufficient conditions are established using Knizhnik–Zamolodchikov equations for boundary correlators. Combining these two approaches, we show that in the case of G = SU(2) the boundary correlator is an SLE martingale if and only if the boundary field carries spin 1/2. In the case of G = SU(n) and the level k = 1, there are several situations when boundary one-point correlators are SLE _κ -martingales. If the boundary field is labelled by the defining n-dimensional representation of SU(n), we obtain \varkappa = 2{\varkappa=2} . For n even, by choosing the boundary field labelled by the (unique) self-adjoint fundamental representation, we get \varkappa = 8/(n + 2){\varkappa=8/(n {+} 2)} . We also study the situation when the distance between the two boundary fields is finite, and we show that in this case the SLE_\varkappa{{\rm SLE}_\varkappa} evolution is replaced by SLE_\varkappa,r{{\rm SLE}_{\varkappa,\rho}} with r = \varkappa -6{\rho=\varkappa -6} .     

Neumann Casimir effect: A singular boundary-interaction approach

Dirichlet boundary conditions on a surface can be imposed on a scalar field, by coupling it quadratically to a δ-like potential, the strength of which tends to infinity. Neumann conditions, on the other hand, require the introduction of an even more singular term, which renders the reflection and transmission coefficients ill-defined because of UV divergences. We present a possible procedure to tame those divergences, by introducing a minimum length scale, related to the nonzero ‘width’ of a nonlocal term. We then use this setup to reach (either exact or imperfect) Neumann conditions, by taking the appropriate limits. After defining meaningful reflection coefficients, we calculate the Casimir energies for flat parallel mirrors, presenting also the extension of the procedure to the case of arbitrary surfaces. Finally, we discuss briefly how to generalize the worldline approach to the nonlocal case, what is potentially useful in order to compute Casimir energies in theories containing nonlocal potentials; in particular, those which we use to reproduce Neumann boundary conditions.     

Distribution of Resonances and Decay Rate of the Local Energy for the Elastic Wave Equation

We study resonances (scattering poles) associated to the elasticity operator in the exterior of an arbitrary obstacle with Neumann or Dirichlet boundary conditions. We prove that there exists an exponentially small neighborhood of the real axis free of resonances. Consequently we prove that for regular data, the energy for the elastic wave equation decays at least as fast as the inverse of the logarithm of time. According to Stefanov–Vodev ([SV1, SV2]), our results are optimal in the case of a Neumann boundary condition, even when the obstacle is a ball of ℝ³. The main difference between our case and the case of the scalar Laplacian (see Burq [Bu]) is the phenomenon of Rayleigh surface waves, which are connected to the failure of the Lopatinskii condition. Received: 22 February 2000 / Accepted: 28 June 2000     

String Non(anti)commutativity for Neveu-Schwarz Boundary Conditions

The appearance of non(anti)commutativity in superstring theory, satisfying the Neveu-Schwarz boundary conditions is discussed in this paper. Both an open free superstring and also one moving in a background antisymmetric tensor field are analyzed to illustrate the point that string non(anti)commutativity is a consequence of the nontrivial boundary conditions. The method used here is quite different from several other approaches where boundary conditions were treated as constraints. An interesting observation of this study is that, one requires that the bosonic sector satisfies Dirichlet boundary conditions at one end and Neumann at the other in the case of the bosonic variables X ^μ being antiperiodic. The non(anti)commutative structures derived in this paper also leads to the closure of the super constraint algebra which is essential for the internal consistency of our analysis.     

Experimental study on doubly QML Nd:Lu<Subscript>0.15</Subscript>Y<Subscript>0.85</Subscript>VO<Subscript>4</Subscript> laser with AO modulator and central SESAM

By using double-mixed crystal Nd:Lu_0.15Y_0.85VO₄ as laser medium, a diode-pumped doubly Q-switched and mode-locked (QML) Nd:Lu_0.15Y_0.85VO₄ laser with acousto-optic (AO) modulator and central semiconductor saturable absorption mirror (SESAM) is realized for the first time. The Q-switched envelope modulation depth is nearly 100%.The average output power and the pulse width of the Q-switched envelope etc. for different AO modulator repetition rates have been measured. The experimental result show that Nd:Lu_0.15Y_0.85VO₄ crystal is an excellent laser medium for doubly QML lasers.     

Effect of boundary conditions on the operator content of two-dimensional conformally invariant theories

The operator content of unitary conformally invariant theories with c<1 is further analysed by deriving the spectrum of the transfer matrix for finite width strips and a variety of boundary conditions: antiperiodic, cyclic, twisted, free, fixed and a mixture of the last two. Complete results are obtained for the Ising model and for the three-state Potts model, as illustrations of the method. They demonstrate how the internal symmetries of these theories are tied in with their conformal properties.