Minimising biases in Full Configuration Interaction Quantum Monte Carlo

We show that Full Configuration Interaction Quantum Monte Carlo (FCIQMC) is a Markov Chain in its present form. We construct the Markov matrix of FCIQMC for a two determinant system and hence compute the stationary distribution. These solutions are used to quantify the dependence of the population dynamics on the parameters defining the Markov chain. Despite the simplicity of a system with only two determinants, it still reveals a population control bias inherent to the FCIQMC algorithm. We investigate the effect of simulation parameters on the population control bias for the neon atom and suggest simulation setups to in general minimise the bias. We show a reweighting scheme to remove the bias caused by population control commonly used in Diffusion Monte Carlo [J. Chem. Phys. 99, 2865 (1993)] is effective and recommend its use as a post processing step.Comment: Supplementary material available as 'Ancillary Files

Fees and Surcharging in automatic teller machine networks: Non-bank ATM providers versus large banks

This paper develops a spacial model of ATM networks to explore the implications for banks and non-banks of interchange fees, foreign fees and surcharges applied to transactions by customers at other than an own-bank ATM. Surcharging raises the price (foreign fee plus surcharge) paid by customers above the joint profit-maximizing level achieved by setting the interchange fee at marginal cost and not surcharging. Similar size banks would agree not to surcharge, but such an agreement is typically not possible between a bank and a non-bank. A high cost of teller transactions modifies the tendency towards high ATM fees.

Vertical Foreclosure and International Trade Policy

We examine conditions under which a low cost vertically integrated manufacturer has an incentive to export an intermediate product to its higher cost (vertically integrated) rival rather than to vertically foreclose, fully cutting off supplies. The nature of supply conditions in the importing country, the size of an import tariff on the final good and optimal policy by the exporting country are all shown to be important for this decision. The exporting country may gain by taxing exports of the final (Cournot) product even though, under Cournot competition, an export subsidy is optimal in the absence of a market for intermediates. In this case, optimal policy also requires an export tax on intermediates, but the higher tax on final goods serves to divert sales to the more profitable market for intermediates increasing the extent of vertical supply. It is optimal to tax the export of both goods or to subsidize the export of both goods. It is never optimal to tax one and subsidize the other.

Wetting layer thickness and early evolution of epitaxially strained thin films

We propose a physical model which explains the existence of finite thickness wetting layers in epitaxially strained films. The finite wetting layer is shown to be stable due to the variation of the non-linear elastic free energy with film thickness. We show that anisotropic surface tension gives rise to a metastable enlarged wetting layer. The perturbation amplitude needed to destabilize this wetting layer decreases with increasing lattice mismatch. We observe the development of faceted islands in unstable films.Comment: 4 pages, 3 eps figure

Open-source development experiences in scientific software: the HANDE quantum Monte Carlo project

The HANDE quantum Monte Carlo project offers accessible stochastic algorithms for general use for scientists in the field of quantum chemistry. HANDE is an ambitious and general high-performance code developed by a geographically-dispersed team with a variety of backgrounds in computational science. In the course of preparing a public, open-source release, we have taken this opportunity to step back and look at what we have done and what we hope to do in the future. We pay particular attention to development processes, the approach taken to train students joining the project, and how a flat hierarchical structure aids communicationComment: 6 pages. Submission to WSSSPE

Astronomy using basic Mark 2 very long baseline interferometry

Two experiments were performed in April and September 1976 to determine precise positions of radio sources using conventional Mark 2 VLBI techniques. Four stations in the continental United States observed at a wavelength of 18 cm. The recording bandwidth was 2 MHz. The preliminary results using analyses of fringe rate and delay are discussed and the source positions compared with the results of other measurements

The effect of quantization on the FCIQMC sign problem

The sign problem in Full Configuration Interaction Quantum Monte Carlo (FCIQMC) without annihilation can be understood as an instability of the psi-particle population to the ground state of the matrix obtained by making all off-diagonal elements of the Hamiltonian negative. Such a matrix, and hence the sign problem, is basis dependent. In this paper we discuss the properties of a physically important basis choice: first versus second quantization. For a given choice of single-particle orbitals, we identify the conditions under which the fermion sign problem in the second quantized basis of antisymmetric Slater determinants is identical to the sign problem in the first quantized basis of unsymmetrized Hartree products. We also show that, when the two differ, the fermion sign problem is always less severe in the second quantized basis. This supports the idea that FCIQMC, even in the absence of annihilation, improves the sign problem relative to first quantized methods. Finally, we point out some theoretically interesting classes of Hamiltonians where first and second quantized sign problems differ, and others where they do not.Comment: 4 pages w/ 2 page appendix, 2 figures, 1 tabl