27,634 research outputs found
Semiclassics around a phase space caustic: an illustration using the Nelson Hamiltonian
The semiclassical formula for the coherent-state propagator is written in
terms of complex classical trajectories of an equivalent classical system.
Depending on the parameters involved, more than one trajectory may contribute
to the calculation. Eventually, however, two contributing trajectories
coalesce, characterizing what is called phase space caustic. In this case, the
usual semiclassical formula for the propagator diverges, so that a uniform
approximation is required to avoid this singularity. In this paper, we present
a non-trivial application illustrating this scenario, and showing the accuracy
of the uniform formula that we have previously derived.Comment: 6 pages, 2 figure
Rural to Urban Population Density Scaling of Crime and Property Transactions in English and Welsh Parliamentary Constituencies
Urban population scaling of resource use, creativity metrics, and human behaviors has been widely studied. These studies have not looked in detail at the full range of human environments which represent a continuum from the most rural to heavily urban. We examined monthly police crime reports and property transaction values across all 573 Parliamentary Constituencies in England and Wales, finding that scaling models based on population density provided a far superior framework to traditional population scaling. We found four types of scaling: i ) non-urban scaling in which a single power law explained the relationship between the metrics and population density from the most rural to heavily urban environments, ii ) accelerated scaling in which high population density was associated with an increase in the power-law exponent, iii ) inhibited scaling where the urban environment resulted in a reduction in the power-law exponent but remained positive, and iv ) collapsed scaling where transition to the high density environment resulted in a negative scaling exponent. Urban scaling transitions, when observed, took place universally between 10 and 70 people per hectare. This study significantly refines our understanding of urban scaling, making clear that some of what has been previously ascribed to urban environments may simply be the high density portion of non-urban scaling. It also makes clear that some metrics undergo specific transitions in urban environments and these transitions can include negative scaling exponents indicative of collapse. This study gives promise of far more sophisticated scale adjusted metrics and indicates that studies of urban scaling represent a high density subsection of overall scaling relationships which continue into rural environments
The Electronic States of Two Oppositely doped Mott Insulators Bilayers
We study the effect of Coulomb interaction between two oppositely doped
low-dimensional tJ model systems. We exactly show that, in the one-dimensional
case, an arbitrarily weak interaction leads to the formation of charge neutral
electron-hole pairs. We then use two different mean-field theories to address
the two-dimensional case, where inter-layer excitons also form and condense. We
propose that this results in new features which have no analog in single
layers, such as the emergence of an insulating spin liquid phase. Our simple
bilayer model might have relevance to the physics of doped Mott insulator
interfaces and of the new four layer Ba2CaCu4O8 compound.Comment: 4 pages, 1 figur
Nonlinear gyrofluid computation of edge localised ideal ballooning modes
Three dimensional electromagnetic gyrofluid simulations of the ideal
ballooning mode blowout scenario for tokamak edge localized modes (ELMs) are
presented. Special emphasis is placed on energetic diagnosis, examining changes
in the growth rate in the linear, overshoot, and decay phases. The saturation
process is energy transfer to self generated edge turbulence which exhibits an
ion temperature gradient (ITG) mode structure. Convergence in the decay phase
is found only if the spectrum reaches the ion gyroradius. The equilibrium is a
self consistent background whose evolution is taken into account. Approximately
two thirds of the total energy in the edge layer is liberated in the blowout.
Parameter dependence with respect to plasma pressure and the ion gyroradius is
studied. Despite the violent nature of the short-lived process, the transition
to nonlinearity is very similar to that found in generic tokamak edge
turbulence.Comment: The following article has been submitted to Physics of Plasmas. After
it is published, it will be found at http://pop.aip.org
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