The critical manifold of the Lorentz-Dirac equation

We investigate the solutions to the Lorentz-Dirac equation and show that its solution flow has a structure identical to the one of renormalization group flows in critical phenomena. The physical solutions of the Lorentz-Dirac equation lie on the critical surface. The critical surface is repelling, i.e. any slight deviation from it is amplified and as a result the solution runs away to infinity. On the other hand, Dirac's asymptotic condition (acceleration vanishes for long times) forces the solution to be on the critical manifold. The critical surface can be determined perturbatively. Thereby one obtains an effective second order equation, which we apply to various cases, in particular to the motion of an electron in a Penning trap

Adiabatic Decoupling and Time-Dependent Born-Oppenheimer Theory

We reconsider the time-dependent Born-Oppenheimer theory with the goal to carefully separate between the adiabatic decoupling of a given group of energy bands from their orthogonal subspace and the semiclassics within the energy bands. Band crossings are allowed and our results are local in the sense that they hold up to the first time when a band crossing is encountered. The adiabatic decoupling leads to an effective Schroedinger equation for the nuclei, including contributions from the Berry connection.Comment: Revised version. 19 pages, 2 figure

Collision rate ansatz for quantum integrable systems

For quantum integrable systems the currents averaged with respect to a generalized Gibbs ensemble are revisited. An exact formula is known, which we call "collision rate ansatz". While there is considerable work to confirm this ansatz in various models, our approach uses the symmetry of the current-charge susceptibility matrix, which holds in great generality. Besides some technical assumptions, the main input is the availability of a self-conserved current, i.e. some current which is itself conserved. The collision rate ansatz is then derived. The argument is carried out in detail for the Lieb-Liniger model and the Heisenberg XXZ chain. The Fermi-Hubbard model is not covered, since no self-conserved current seems to exist. It is also explained how from the existence of a boost operator a self-conserved current can be deduced.Comment: v1: 14 pages, v2: 15 pages, references added, typos corrected, v3: 17 pages, references added, explanations improved, an appendix on the collision rate ansatz for generalized currents is supplemente

The one-dimensional KPZ equation and its universality class

Our understanding of the one-dimensional KPZ equation, \textit{alias} noisy Burgers equation, has advanced substantially over the past five years. We provide a non-technical review, where we limit ourselves to the stochastic PDE and lattice type models approximating it.Comment: 24 pages, 2 figure