11,677 research outputs found
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
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
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