Coulomb drag in double quantum wells with a perpendicular magnetic field

Momentum transfer due to electron-electron interaction (Coulomb drag) between two quantum wells, separated by a distance $d$, in the presence of a perpendicular magnetic field, is studied at low temperatures. We find besides the well known Shubnikov-de Haas oscillations, which also appear in the drag effect, the momentum transfer is markedly enhanced by the magnetic field.Comment: 8 pages, Revtex, 4 Postscript figures are available upon request, Accepted by Mod. Phys. Lett.

The Pfaffian solution of a dimer-monomer problem: Single monomer on the boundary

We consider the dimer-monomer problem for the rectangular lattice. By mapping the problem into one of close-packed dimers on an extended lattice, we rederive the Tzeng-Wu solution for a single monomer on the boundary by evaluating a Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by identifying it as the product of the nonzero eigenvalues of the Kasteleyn matrix.Comment: 4 Pages to appear in the Physical Review E (2006

On the duality relation for correlation functions of the Potts model

We prove a recent conjecture on the duality relation for correlation functions of the Potts model for boundary spins of a planar lattice. Specifically, we deduce the explicit expression for the duality of the n-site correlation functions, and establish sum rule identities in the form of the M\"obius inversion of a partially ordered set. The strategy of the proof is by first formulating the problem for the more general chiral Potts model. The extension of our consideration to the many-component Potts models is also given.Comment: 17 pages in RevTex, 5 figures, submitted to J. Phys.

SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization

In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common nonsmooth functions arising in the applications such as the Euclidean norm, the maximum eigenvalue function and the least squares functions with $\ell_1$-regularization or elastic net regularization used in statistics and compressed sensing. We show that, under commonly used strict feasibility conditions, the optimal value and an optimal solution of SOS-convex semi-algebraic programs can be found by solving a single semi-definite programming problem (SDP). We achieve the results by using tools from semi-algebraic geometry, convex-concave minimax theorem and a recently established Jensen inequality type result for SOS-convex polynomials. As an application, we outline how the derived results can be applied to show that robust SOS-convex optimization problems under restricted spectrahedron data uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP relaxation result for restricted ellipsoidal data uncertainty and answers the open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a robust solution from the semi-definite programming relaxation in this broader setting