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

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

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 $m$

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

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

All (qubit) decoherences: Complete characterization and physical implementation

We investigate decoherence channels that are modelled as a sequence of collisions of a quantum system (e.g., a qubit) with particles (e.g., qubits) of the environment. We show that collisions induce decoherence when a bi-partite interaction between the system qubit and an environment (reservoir) qubit is described by the controlled-U unitary transformation (gate). We characterize decoherence channels and in the case of a qubit we specify the most general decoherence channel and derive a corresponding master equation. Finally, we analyze entanglement that is generated during the process of decoherence between the system and its environment.Comment: 10 pages, 3 figure

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