1,964 research outputs found
Notes on coherent backscattering from a random potential
We consider the quantum scattering from a random potential of strength
and with a support on the scale of the mean free path, which is
of order . 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 , in the case of a single, spinless
electron. As well known, if denotes the bare mass and \mass the mass
computed from the theory, to order 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 . If correct, in
order 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 . The result is as leading term, suggesting
a more complicated dependence of on
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 -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 Discoveryâclass mission will provide an important baseline to constrain the presentâday 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 3âD 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 presentâday surface heat flux pattern is dominated by the imposed crustal structure. The largest surface heat flux peakâto peak variations lie between 17.2 and 49.9 mW mâ2, 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 mâ2, while at the InSight location it lies between 18.8 and 24.2 mW mâ2. 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
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
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
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