Notes on coherent backscattering from a random potential

We consider the quantum scattering from a random potential of strength $\lambda^{1/2}$ and with a support on the scale of the mean free path, which is of order $\lambda^{-1}$. On the basis of maximally crossed diagrams we provide a concise formula for the backscattering rate in terms of the Green's function for the kinetic Boltzmann equation. We briefly discuss the extension to wave scattering.Comment: 17 pages. 8 figure

Mass renormalization in nonrelativistic QED

In nonrelativistic QED the charge of an electron equals its bare value, whereas the self-energy and the mass have to be renormalized. In our contribution we study perturbative mass renormalization, including second order in the fine structure constant $\alpha$, in the case of a single, spinless electron. As well known, if $m$ denotes the bare mass and \mass the mass computed from the theory, to order $\alpha$ one has \frac{\mass}{m} =1+\frac{8\alpha}{3\pi} \log(1+\half (\Lambda/m))+O(\alpha^2) which suggests that \mass/m=(\Lambda/m)^{8\alpha/3\pi} for small $\alpha$. If correct, in order $\alpha^2$ the leading term should be \displaystyle \half ((8\alpha/3\pi)\log(\Lambda/m))^2. To check this point we expand \mass/m to order $\alpha^2$. The result is $\sqrt{\Lambda/m}$ as leading term, suggesting a more complicated dependence of $m_{\mathrm{eff}}$ on $m$

Condensation in the zero range process: stationary and dynamical properties

The zero range process is of particular importance as a generic model for domain wall dynamics of one-dimensional systems far from equilibrium. We study this process in one dimension with rates which induce an effective attraction between particles. We rigorously prove that for the stationary probability measure there is a background phase at some critical density and for large system size essentially all excess particles accumulate at a single, randomly located site. Using random walk arguments supported by Monte Carlo simulations, we also study the dynamics of the clustering process with particular attention to the difference between symmetric and asymmetric jump rates. For the late stage of the clustering we derive an effective master equation, governing the occupation number at clustering sites.Comment: 22 pages, 4 figures, to appear in J. Stat. Phys.; improvement of presentation and content of Theorem 2, added reference

Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers

The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to a many body quantum boson system with attractive interactions. Performing the summation over the entire spectrum of excited states the problem is reduced to the Fredholm determinant with the Airy kernel which is known to yield the Tracy-Widom distributionComment: 5 page

Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory

Through a Euclidean path integral we establish that the density fluctuations of a Fermi fluid in one dimension are related to vicinal surfaces and to the stochastic dynamics of particles interacting through long range forces with inverse distance decay. In the surface picture one easily obtains the Haldane relation and identifies the scaling exponents governing the low energy, Luttinger liquid behavior. For the stochastic particle model we develop a hydrodynamic fluctuation theory, through which in some cases the large distance Gaussian fluctuations are proved nonperturbatively

How large are present-day heat flux variations across the surface of Mars?

©2016. American Geophysical UnionThe first in situ Martian heat flux measurement to be carried out by the InSight Discovery‐class mission will provide an important baseline to constrain the present‐day heat budget of the planet and, in turn, the thermochemical evolution of its interior. In this study, we estimate the magnitude of surface heat flux heterogeneities in order to assess how the heat flux at the InSight landing site relates to the average heat flux of Mars. To this end, we model the thermal evolution of Mars in a 3‐D spherical geometry and investigate the resulting surface spatial variations of heat flux at the present day. Our models assume a fixed crust with a variable thickness as inferred from gravity and topography data and with radiogenic heat sources as obtained from gamma ray measurements of the surface. We test several mantle parameters and show that the present‐day surface heat flux pattern is dominated by the imposed crustal structure. The largest surface heat flux peak‐to peak variations lie between 17.2 and 49.9 mW m−2, with the highest values being associated with the occurrence of prominent mantle plumes. However, strong spatial variations introduced by such plumes remain narrowly confined to a few geographical regions and are unlikely to bias the InSight heat flux measurement. We estimated that the average surface heat flux varies between 23.2 and 27.3 mW m−2, while at the InSight location it lies between 18.8 and 24.2 mW m−2. In most models, elastic lithosphere thickness values exceed 250 km at the north pole, while the south pole values lie well above 110 km

Early Thermal Evolution of Planetesimals and its Impact on Processing and Dating of Meteoritic Material

Radioisotopic ages for meteorites and their components provide constraints on the evolution of small bodies: timescales of accretion, thermal and aqueous metamorphism, differentiation, cooling and impact metamorphism. Realising that the decay heat of short-lived nuclides (e.g. 26Al, 60Fe), was the main heat source driving differentiation and metamorphism, thermal modeling of small bodies is of utmost importance to set individual meteorite age data into the general context of the thermal evolution of their parent bodies, and to derive general conclusions about the nature of planetary building blocks in the early solar system. As a general result, modelling easily explains that iron meteorites are older than chondrites, as early formed planetesimals experienced a higher concentration of short-lived nuclides and more severe heating. However, core formation processes may also extend to 10 Ma after formation of Calcium-Aluminum-rich inclusions (CAIs). A general effect of the porous nature of the starting material is that relatively small bodies (< few km) will also differentiate if they form within 2 Ma after CAIs. A particular interesting feature to be explored is the possibility that some chondrites may derive from the outer undifferentiated layers of asteroids that are differentiated in their interiors. This could explain the presence of remnant magnetization in some chondrites due to a planetary magnetic field.Comment: 24 pages, 9 figures, Accepted for publication as a chapter in Protostars and Planets VI, University of Arizona Press (2014), eds. H. Beuther, R. Klessen, C. Dullemond, Th. Hennin

Ground States in the Spin Boson Model

We prove that the Hamiltonian of the model describing a spin which is linearly coupled to a field of relativistic and massless bosons, also known as the spin-boson model, admits a ground state for small values of the coupling constant lambda. We show that the ground state energy is an analytic function of lambda and that the corresponding ground state can also be chosen to be an analytic function of lambda. No infrared regularization is imposed. Our proof is based on a modified version of the BFS operator theoretic renormalization analysis. Moreover, using a positivity argument we prove that the ground state of the spin-boson model is unique. We show that the expansion coefficients of the ground state and the ground state energy can be calculated using regular analytic perturbation theory

Phosphorus and nitrogen cycling in forest soils depending on long-term nitrogen inputs

Foliar phosphorus (P) contents have been decreasing in a range of temperate forests in Europe and North America during the last decades, and one reason for this might be atmospheric nitrogen (N) deposition (1,2,3). Therefore, we studied the effect of N inputs on P and N cycling in long-term N fertilization experiments in temperate forests. The aim of the study was to test how increased N inputs affect P and N cycling in forest soils. We sampled the organic layer of three N fertilization experiments in the USA (Harvard Forest, Cary Institute and Bear Brook), that are between 17 and 25 years old. Net N and P mineralization rates were determined along with microbial biomass, enzyme activities and soil C, N and P stoichiometry. Total C and N concentrations in the organic layer (Oe+Oa horizon) increased significantly due to long-term fertilization in Harvard Forest and the same trend was observed in the two other experiments that are based on lower N fertilization rates. Contrariwise, total P concentrations in the organic layer decreased on average by 15% due to N fertilization, while C:P ratios increased by 60%. Phosphatase activity was elevated in the N fertilized soils in all experiments by a factor of 2 to 5, and the ratio of chitinase:phosphatase activity was on average decreased by 30%, indicating that specifically phosphatase production was upregulated. The results imply that trees and/or microorganisms invested more N in the production of phosphatases in the N fertilized soils than in the non-fertilized controls. Net P mineralization did not change consistently with N inputs, indicating that mineralized P was quickly taken up by the plants in most of the N fertilized soils. In contrast, net N mineralization increased in all experiments in response to N fertilization, while microbial biomass C was only little affected by N fertilization In conclusion, the experiments indicate that high inputs of N in temperate forest ecosystems lead to increased P demand and hence to increased phosphatase activity. Moreover, the decreased P concentration and the elevated C:P ratio of the organic layer indicate that P is preferentially mineralized and taken up by plants. Our results support the hypothesis that increased atmospheric N inputs are the reason for an emerging P limitation in temperate forests