We obtain exact results for correlation functions of primary operators in the two-dimensional conformal field theory of a scalar field interacting with a critical periodic boundary potential. Amplitudes involving arbitrary bulk discrete primary fields are given in terms of SU(2) rotation coefficients while boundary amplitudes involving discrete boundary fields are independent of the boundary in...

Based on the technique of quasiclassical Green’s functions, we construct a theoretical framework for describing heterostructures consisting of superconductors and/or spin-polarized materials. The necessary boundary conditions at the interfaces separating different metals are formulated in terms of hopping amplitudes in a t-matrix approximation. The theory is applicable for an interface with arb...

We construct a matrix model equivalent (exactly, not asymptotically), to the random plane partition model, with almost arbitrary boundary conditions. Equivalently, it is also a random matrix model for a TASEP with arbitrary boundary conditions. Using the known solution of matrix models, this method allows to find the large size asymptotic expansion of plane partitions, to ALL orders. It also al...

We consider the SUq(N) invariant spin chain with diagonal and non-diagonal integrable boundary terms. The algebraic study of spin chains with different types of boundary terms is used to motivate a set of spectral equivalences between integrable chains with purely diagonal boundary terms and ones with an arbitrary non-diagonal term at one end. For each choice of diagonal boundary terms there is...

The Dirichlet boundary-value problem and isoperimetric inequalities for positive definite regular solutions of the vacuum Einstein equations are studied in arbitrary dimensions for the class of metrics with boundaries admitting a U(1) action. In the case of trivial bundles, apart from the flat space solution with periodic identification, such solutions include the Euclideanised Schwarzschild me...

(Dated: February 2, 2008) We develop a systematic approach to calculating the electrostatic force between point charges in an arbitrary geometry with arbitrary boundary conditions. When the boundary is present, the simple expression for the force acting on a charge as “the charge times the field it is placed in” becomes ill-defined. However, this rule can be salvaged if the field in question is...

The swept volume problem is practical, dif®cult and interesting enough to have received a great deal of attention over the years, and the literature contains much discussion of methods for computing swept volumes in many situations. The method presented here permits an arbitrary polyhedral object (given in a typical boundary representation) to be swept through an arbitrary trajectory. A polyhed...