Scarring Effects on Tunneling in Chaotic Double-Well Potentials

The connection between scarring and tunneling in chaotic double-well potentials is studied in detail through the distribution of level splittings. The mean level splitting is found to have oscillations as a function of energy, as expected if scarring plays a role in determining the size of the splittings, and the spacing between peaks is observed to be periodic of period {$2\pi\hbar$} in action. Moreover, the size of the oscillations is directly correlated with the strength of scarring. These results are interpreted within the theoretical framework of Creagh and Whelan. The semiclassical limit and finite-{$\hbar$} effects are discussed, and connections are made with reaction rates and resonance widths in metastable wells.Comment: 22 pages, including 11 figure

Poynting Vector Flow in a Circular Circuit

A circuit is considered in the shape of a ring, with a battery of negligible size and a wire of uniform resistance. A linear charge distribution along the wire maintains an electrostatic field and a steady current, which produces a constant magnetic field. Earlier studies of the Poynting vector and the rate of flow of energy considered only idealized geometries in which the Poynting vector was confined to the space within the circuit. But in more realistic cases the Poynting vector is nonzero outside as well as inside the circuit. An expression is obtained for the Poynting vector in terms of products of integrals, which are evaluated numerically to show the energy flow. Limiting expressions are obtained analytically. It is shown that the total power generated by the battery equals the energy flowing into the wire per unit time.Comment: 19 pages, 8 figure

Beyond the First Recurrence in Scar Phenomena

The scarring effect of short unstable periodic orbits up to times of the order of the first recurrence is well understood. Much less is known, however, about what happens past this short-time limit. By considering the evolution of a dynamically averaged wave packet, we show that the dynamics for longer times is controlled by only a few related short periodic orbits and their interplay.Comment: 4 pages, 4 Postscript figures, submitted to Phys. Rev. Let

A model for global biomass burning in preindustrial time: LPJ-LMfire (v1.0)

Fire is the primary disturbance factor in many terrestrial ecosystems. Wildfire alters vegetation structure and composition, affects carbon storage and biogeochemical cycling, and results in the release of climatically relevant trace gases including CO2, CO, CH4, NOx, and aerosols. One way of assessing the impacts of global wildfire on centennial to multi-millennial timescales is to use process-based fire models linked to dynamic global vegetation models (DGVMs). Here we present an update to the LPJ-DGVM and a new fire module based on SPITFIRE that includes several improvements to the way in which fire occurrence, behaviour, and the effects of fire on vegetation are simulated. The new LPJ-LMfire model includes explicit calculation of natural ignitions, the representation of multi-day burning and coalescence of fires, and the calculation of rates of spread in different vegetation types. We describe a new representation of anthropogenic biomass burning under preindustrial conditions that distinguishes the different relationships between humans and fire among hunter-gatherers, pastoralists, and farmers. We evaluate our model simulations against remote-sensing-based estimates of burned area at regional and global scale. While wildfire in much of the modern world is largely influenced by anthropogenic suppression and ignitions, in those parts of the world where natural fire is still the dominant process (e.g. in remote areas of the boreal forest and subarctic), our results demonstrate a significant improvement in simulated burned area over the original SPITFIRE. The new fire model we present here is particularly suited for the investigation of climate–human–fire relationships on multi-millennial timescales prior to the Industrial Revolution

Impacts of Changes in Land Use and Land Cover on Atmospheric Chemistry and Air Quality over the 21st Century

The effects of future land use and land cover change on the chemical composition of the atmosphere and air quality are largely unknown. To investigate the potential effects associated with future changes in vegetation driven by atmospheric CO2 concentrations, climate, and anthropogenic land use over the 21st century, we performed a series of model experiments combining a general circulation model with a dynamic global vegetation model and an atmospheric chemical-transport model. Our results indicate that climate- and CO2-induced changes in vegetation composition and density between 2100 and 2000 could lead to decreases in summer afternoon surface ozone of up to 10 ppb over large areas of the northern mid-latitudes. This is largely driven by the substantial increases in ozone dry deposition associated with increases in vegetation density in a warmer climate with higher atmospheric CO2 abundance. Climate-driven vegetation changes over the period 2000–2100 lead to general increases in isoprene emissions, globally by 15% in 2050 and 36% in 2100. These increases in isoprene emissions result in decreases in surface ozone concentrations where the NOx levels are low, such as in remote tropical rainforests. However, over polluted regions, such as the northeastern United States, ozone concentrations are calculated to increase with higher isoprene emissions in the future. Increases in biogenic emissions also lead to higher concentrations of secondary organic aerosols, which increase globally by 10% in 2050 and 20% in 2100. Summertime surface concentrations of secondary organic aerosols are calculated to increase by up to 1 μg m−3 and double for large areas in Eurasia over the period of 2000–2100. When we use a scenario of future anthropogenic land use change, we find less increase in global isoprene emissions due to replacement of higher-emitting forests by lower-emitting cropland. The global atmospheric burden of secondary organic aerosols changes little by 2100 when we account for future land use change, but both secondary organic aerosols and ozone show large regional changes at the surface.Engineering and Applied Science

The NN scattering 3S1-3D1 mixing angle at NNLO

The 3S1-3D1 mixing angle for nucleon-nucleon scattering, epsilon_1, is calculated to next-to-next-to-leading order in an effective field theory with perturbative pions. Without pions, the low energy theory fits the observed epsilon_1 well for momenta less than $\sim 50$ MeV. Including pions perturbatively significantly improves the agreement with data for momenta up to $\sim 150$ MeV with one less parameter. Furthermore, for these momenta the accuracy of our calculation is similar to an effective field theory calculation in which the pion is treated non-perturbatively. This gives phenomenological support for a perturbative treatment of pions in low energy two-nucleon processes. We explain why it is necessary to perform spin and isospin traces in d dimensions when regulating divergences with dimensional regularization in higher partial wave amplitudes.Comment: 17 pages, journal versio

Pseudorandomness for Regular Branching Programs via Fourier Analysis

We present an explicit pseudorandom generator for oblivious, read-once, permutation branching programs of constant width that can read their input bits in any order. The seed length is $O(\log^2 n)$, where $n$ is the length of the branching program. The previous best seed length known for this model was $n^{1/2+o(1)}$, which follows as a special case of a generator due to Impagliazzo, Meka, and Zuckerman (FOCS 2012) (which gives a seed length of $s^{1/2+o(1)}$ for arbitrary branching programs of size $s$). Our techniques also give seed length $n^{1/2+o(1)}$ for general oblivious, read-once branching programs of width $2^{n^{o(1)}}$, which is incomparable to the results of Impagliazzo et al.Our pseudorandom generator is similar to the one used by Gopalan et al. (FOCS 2012) for read-once CNFs, but the analysis is quite different; ours is based on Fourier analysis of branching programs. In particular, we show that an oblivious, read-once, regular branching program of width $w$ has Fourier mass at most $(2w^2)^k$ at level $k$, independent of the length of the program.Comment: RANDOM 201