Three-body Unitarity in the Finite Volume

The physical interpretation of lattice QCD simulations, performed in a small volume, requires an extrapolation to the infinite volume. A method is proposed to perform such an extrapolation for three interacting particles at energies above threshold. For this, a recently formulated relativistic $3\to 3$ amplitude based on the isobar formulation is adapted to the finite volume. The guiding principle is two- and three-body unitarity that imposes the imaginary parts of the amplitude in the infinite volume. In turn, these imaginary parts dictate the leading power-law finite-volume effects. It is demonstrated that finite-volume poles arising from the singular interaction, from the external two-body sub-amplitudes, and from the disconnected topology cancel exactly leaving only the genuine three-body eigenvalues. The corresponding quantization condition is derived for the case of three identical scalar-isoscalar particles and its numerical implementation is demonstrated.Comment: 9 pages, 3 figure

Partial decode-forward for quantum relay channels

A relay channel is one in which a Source and Destination use an intermediate Relay station in order to improve communication rates. We propose the study of relay channels with classical inputs and quantum outputs and prove that a "partial decode and forward" strategy is achievable. We divide the channel uses into many blocks and build codes in a randomized, block-Markov manner within each block. The Relay performs a standard Holevo-Schumacher-Westmoreland quantum measurement on each block in order to decode part of the Source's message and then forwards this partial message in the next block. The Destination performs a novel "sliding-window" quantum measurement on two adjacent blocks in order to decode the Source's message. This strategy achieves non-trivial rates for classical communication over a quantum relay channel.Comment: 7 pages, submission to the 2012 International Symposium on Information Theory (ISIT 2012), Boston, MA, US

Financing Constraints and the Family Farm: How do Families React?

This paper explores the idea that off-farm income is used for investment in farm assets. Using Alabama farm data for the 1997-2004 period, we find that farm investment is more sensitive to off-farm than to on-farm income, and that this sensitivity is stronger for farms with sales less than $250,000.Farm Management, Q12, Q14, G11,

Properties of Dynamic Earthquake Ruptures With Heterogeneous Stress Drop

Earthquake rupture is a notoriously complex process, at all observable scales. We introduce a simplified semi-dynamic crack model to investigate the connection between the statistical properties of stress and those of macroscopic source parameters such as rupture size, seismic moment, apparent stress drop and radiated energy. Rupture initiation is treated consistently with nucleation on a linear slip-weakening fault, whereas rupture propagation and arrest are treated according to the Griffith criterion. The available stress drop is prescribed as a spatially correlated random field and is shown to potentially sustain a broad range of magnitudes. By decreasing the amplitude of the stress heterogeneities or increasing their correlation length the distribution of earthquake sizes presents a transition from Gutenberg- Richter to characteristic earthquake behavior. This transition is studied through a mean-field analysis. The bifurcation to characteristic earthquake behavior is sharp, reminiscent of a first-order phase transition. A lower roll-off magnitude observed in the Gutenberg-Richter regime is shown to depend on the correlation length of the available stress drop, rather than being a direct signature of the nucleation process. More generally, we highlight the possible role of the stress correlation length scale on deviations from earthquake source self-similarity. The present reduced model is a building block towards understanding the effect of structural and dynamic fault heterogeneities on the scaling of source parameters and on basic properties of seismicity