Efimov states near a Feshbach resonance and the limits of van der Waals universality at finite background scattering length

We calculate the spectrum of three-body Efimov bound states near a Feshbach resonance within a model which accounts both for the finite range of interactions and the presence of background scattering. The latter may be due to direct interactions in an open channel or a second overlapping Feshbach resonance. It is found that background scattering gives rise to substantial changes in the trimer spectrum as a function of the detuning away from a Feshbach resonance, in particular in the regime where the background channel supports Efimov states on its own. Compared to the situation with negligible background scattering, the regime where van der Waals universality applies is shifted to larger values of the resonance strength if the background scattering length is positive. For negative background scattering lengths, in turn, van der Waals universality extends to even small values of the resonance strength parameter, consistent with experimental results on Efimov states in $^{39}$K. Within a simple model, we show that short-range three-body forces do not affect van der Waals universality significantly. Repulsive three-body forces may, however, explain the observed variation between around $-8$ and $-10$ of the ratio between the scattering length where the first Efimov trimer appears and the van der Waals length.Comment: 17 pages, 13 figures; final version as publishe

The Avalanche Mechanism for Atom Loss near an Atom-Dimer Efimov Resonance

An Efimov trimer near the atom-dimer threshold can increase the atom loss rate in ultracold trapped atoms through the {\it avalanche mechanism} proposed by Zaccanti et al. A 3-body recombination event creates an energetic atom and dimer, whose subsequent elastic collisions produce additional atoms with sufficient energy to escape from the trapping potential. We use Monte Carlo methods to calculate the average number of atoms lost and the average heat generated by recombination events in both a Bose-Einstein condensate and a thermal gas. We take into account the energy-dependence of the cross sections and the spatial structure of the atom cloud. We confirm that the number of atoms lost can be much larger than the naive value 3 if there is an Efimov trimer near the atom-dimer threshold. This does not produce a narrow loss feature, but it can significantly affect the determination of Efimov parameters.Comment: 5 pages, 3 figure

Clock shift in a strongly interacting two-dimensional Fermi gas

We derive universal relations for the radio-frequency (rf) spectroscopy of a two-dimensional Fermi gas consisting of two spin states with a resonant S-wave interaction. The rf transition rate has a high-frequency tail that is proportional to the contact and displays logarithmic scaling violations, decreasing asymptotically like $1/(\omega^2 \ln^2 \omega)$. Its coefficient is proportional to $\ln^2(a_{2D}'/a_{2D})$, where $a_{2D}$ and $a_{2D}'$ are the 2-dimensional scattering lengths associated with initial-state and final-state interactions. The clock shift is proportional to the contact and to $\ln(a_{2D}'/a_{2D})$. If $|\ln(a_{2D}'/a_{2D})| \gg 1$, the clock shift arises as a cancellation between much larger contributions proportional to $\ln^2(a_{2D}'/a_{2D})$ from bound-bound and bound-free rf transitions.Comment: 4 pages, 1 figur

Reparation for Victims of Armed Conflict: Impulses from the Max Planck Trialogues

The international law on reparation for victims of armed conflict is complex. Numerous subfields of international law are involved, among them international human rights law, international criminal law, international humanitarian law, and the law on State responsibility. In addition to this complexity, reparation-related questions are often highly politically charged. They are focal points of contestation about moral values, different conceptions of justice, and approaches to international law, including the status of the individual human being in this order. Against this backdrop, the collection of short essays explores whether and under which circumstances individuals have a right to reparation under international law. The introduction unpacks the legal dimensions and identifies the currently most controversial issues. One set of essays then analyses, from different angles, whether a right to reparation for individuals exists as a matter of law. Another set recounts experiences with the implementation of reparation mechanisms and discusses the challenges. A third group of essays addresses the role of domestic courts. The essays (‘impulses’) are one outcome of the Max Planck Trialogue workshop on reparation for victims of armed conflict, held in November 2017 in Berlin