Nernst effect and diamagnetism in phase fluctuating superconductors

We study superconducting systems in the regime where superconductivity is destroyed by phase fluctuations. We find that the Nernst effect has a much sharper temperature decay than predicted by Gaussian fluctuations, with an onset temperature that tracks Tc rather than the pairing temperature. We find a close quantitative connection with diamagnetism--the ratio of magnetization to transverse thermoelectric conductivity reaches a fixed value at high temperatures. We interpret measurements on underdoped cuprates in terms of a dilute vortex liquid over a wide temperature range above Tc.     

Exponential time integration for fast finite element solutions of some financial engineering problems

We consider exponential time integration schemes for fast numerical pricing of European, American, barrier and butterfly options when the stock price follows a dynamics described by a jump-diffusion process. The resulting pricing equation which is in the form of a partial integro-differential equation is approximated in space using finite elements. Our methods require the computation of a single matrix exponential and we demonstrate using a wide range of numerical tests that the combination of exponential integrators and finite element discretisations with quadratic basis functions leads to highly accurate algorithms for cases when the jump magnitude is Gaussian. Comparison with other time-stepping methods are also carried out to illustrate the effectiveness of our methods.     

Entanglement entropy of critical spin liquids

Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we calculate their bipartite entanglement entropy that characterizes their quantum structure. In particular we calculate the Renyi entropy S(2) on model wave functions obtained by Gutzwiller projection of a Fermi sea. Although the wave functions are not sign positive, S(2) can be calculated on relatively large systems (>324 spins) using the variational Monte Carlo technique. On the triangular lattice we find that entanglement entropy of the projected Fermi sea state violates the boundary law, with S(2) enhanced by a logarithmic factor. This is an unusual result for a bosonic wave function reflecting the presence of emergent fermions. These techniques can be extended to study a wide class of other phases.     

Analysis of algebraic systems arising from fourth‐order compact discretizations of convection‐diffusion equations

We study the properties of coefficient matrices arising from high‐order compact discretizations of convection‐diffusion problems. Asymptotic convergence factors of the convex hull of the spectrum and the field of values of the coefficient matrix for a one‐dimensional problem are derived, and the convergence factor of the convex hull of the spectrum is shown to be inadequate for predicting the convergence rate of GMRES. For a two‐dimensional constant‐coefficient problem, we derive the eigenvalues of the nine‐point matrix, and we show that the matrix is positive definite for all values of the cell‐Reynolds number. Using a recent technique for deriving analytic expressions for discrete solutions produced by the fourth‐order scheme, we show by analyzing the terms in the discrete solutions that they are oscillation‐free for all values of the cell Reynolds number. Our theoretical results support observations made through numerical experiments by other researchers on the non‐oscillatory nature of the discrete solution produced by fourth‐order compact approximations to the convection‐diffusion equation. © 2002 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 18: 155–178, 2002; DOI 10.1002/num.1041     

Combustion wave propagation in mixtures of JSC-1A lunar regolith simulant with magnesium

Combustion of lunar regolith mixed with energetic additives is a potential method for production of construction materials in future moon missions. Recently, self-sustained combustion in the mixtures of JSC-1A lunar regolith and magnesium has been demonstrated. However, the concentration of magnesium in those mixtures was as high as 26 wt%. Note that magnesium must be either transported from Earth or recovered from lunar minerals or used structures. The present paper focuses on the minimization of magnesium content in JSC-1A/Mg mixtures. The mixtures were compacted into pellets and ignited in argon environment. Initial attempts to decrease magnesium concentration resulted in the observations of a spinning combustion wave at 23 wt% Mg. The observed spin combustion involved periodical motion of two counterpropagating hot spots along a helical path on the sample surface. These observations, including features such as formation of a faster hot spot after collision of the counterpropagating spots, confirm theoretical predictions for spin combustion in solid–solid mixtures. High-energy mechanical milling of JSC-1A in a planetary ball mill significantly increased its reactivity and improved combustion of its mixtures with magnesium. Mixtures of the obtained powder (the median diameter of about 3 μm) with 26 wt% Mg exhibit easy ignition and vigorous combustion. The minimum concentration of magnesium required for self-sustained propagation of a planar combustion front is as low as 13 wt%.     

Spin-charge separated solitons in a topological band insulator

In this Letter we construct a simple, controllable, two-dimensional model based on a topological band insulator. It has many attractive properties. (1) We obtain spin-charge separated solitons that are associated with dynamic pi fluxes. (2) These solitons obey Bose statistics and their condensation triggers a phase transition from a spin Hall insulator to an easy-plane ferromagnet. (3) It suggests an alternative way to classify the Z2 topological band insulator without resorting to the sample boundary.     

Bismuth compounds in organic synthesis. A one-pot synthesis of homoallyl ethers and homoallyl acetates from aldehydes catalyzed by bismuth triflate

[reaction: see text] Three one-pot methods for the conversion of aldehydes to homoallyl ethers catalyzed by Bi(OTf)(3).xH(2)O (1 < x < 4) have been developed. The one-pot synthesis of homoallyl ethers can be achieved either by in situ generation of the acetal followed by its reaction with allyltrialkylsilane or by a three-component synthesis in which the aldehyde, trimethylorthoformate or an alkoxytrimethylsilane and allyltrimethylsilane are mixed together in the presence of bismuth triflate (0.1-1.0 mol %). In addition, a three-component synthesis of homoallyl acetates, which is achieved by reacting the aldehyde, acetic anhydride, and allyltrimethylsilane in the presence of bismuth triflate (3.0-5.0 mol %), has been developed. The use of a relatively nontoxic, easy to handle, and inexpensive catalyst adds to the versatility of these methods.     

A fast high-order finite difference algorithm for pricing American options

We describe an improvement of Han and Wu’s algorithm [H. Han, X.Wu, A fast numerical method for the Black–Scholes equation of American options, SIAM J. Numer. Anal. 41 (6) (2003) 2081–2095] for American options. A high-order optimal compact scheme is used to discretise the transformed Black–Scholes PDE under a singularity separating framework. A more accurate free boundary location based on the smooth pasting condition and the use of a non-uniform grid with a modified tridiagonal solver lead to an efficient implementation of the free boundary value problem. Extensive numerical experiments show that the new finite difference algorithm converges rapidly and numerical solutions with good accuracy are obtained. Comparisons with some recently proposed methods for the American options problem are carried out to show the advantage of our numerical method.     

Ultracold atoms in a tunable optical kagome lattice

We realize a two-dimensional kagome lattice for ultracold atoms by overlaying two commensurate triangular optical lattices generated by light at the wavelengths of 532 and 1064 nm. Stabilizing and tuning the relative position of the two lattices, we explore different lattice geometries including a kagome, a one-dimensional stripe, and a decorated triangular lattice. We characterize these geometries using Kapitza-Dirac diffraction and by analyzing the Bloch-state composition of a superfluid released suddenly from the lattice. The Bloch-state analysis also allows us to determine the ground-state distribution within the superlattice unit cell. The lattices implemented in this work offer a near-ideal realization of a paradigmatic model of many-body quantum physics, which can serve as a platform for future studies of geometric frustration.