The bipolaron in the strong coupling limit

The bipolaron are two electrons coupled to the elastic deformations of an ionic crystal. We study this system in the Fr\"{o}hlich approximation. If the Coulomb repulsion dominates, the lowest energy states are two well separated polarons. Otherwise the electrons form a bound pair. We prove the validity of the Pekar-Tomasevich energy functional in the strong coupling limit, yielding estimates on the coupling parameters for which the binding energy is strictly positive. Under the condition of a strictly positive binding energy we prove the existence of a ground state at fixed total momentum $P$, provided $P$ is not too large.Comment: 31 page

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

On the convergence to statistical equilibrium for harmonic crystals

We consider the dynamics of a harmonic crystal in $d$ dimensions with $n$ components, $d,n$ arbitrary, $d,n\ge 1$, and study the distribution $\mu_t$ of the solution at time $t\in\R$. The initial measure $\mu_0$ has a translation-invariant correlation matrix, zero mean, and finite mean energy density. It also satisfies a Rosenblatt- resp. Ibragimov-Linnik type mixing condition. The main result is the convergence of $\mu_t$ to a Gaussian measure as $t\to\infty$. The proof is based on the long time asymptotics of the Green's function and on Bernstein's ``room-corridors'' method

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

Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in 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 the $N$-particle quantum boson system with attractive interactions. We find the full set of eigenfunctions and eigenvalues of this many-body system and perform the summation over the entire spectrum of excited states. It is shown that in the thermodynamic limit the problem is reduced to the Fredholm determinant with the Airy kernel yielding the universal Tracy-Widom distribution, which is known to describe the statistical properties of the Gaussian unitary ensemble as well as many other statistical systems.Comment: 23 page