Bound States in n Dimensions (Especially n = 1 and n = 2)

We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two dimensions, examples of weak potentials with one or infinitely many bound states. We derive bounds for one and two dimensions which have the "right" coupling constant behaviour for large coupling.Comment: Talk given by A. Martin at Les Houches, October 2001, to appear in "Few-Body Problems

The period-luminosity and period-radius relations of Type II and anomalous Cepheids

Method: In an accompanying paper (arXiv: 1705.00886) we determined luminosity and effective temperature for the 335 T2Cs and ACs in the LMC and SMC discovered in the OGLE-III survey, by constructing the spectral energy distribution (SED) and fitting this with model atmospheres and a dust radiative transfer model (in the case of dust excess). Building on these results we study the PL and PR relations. Using existing pulsation models for RR Lyrae and classical Cepheids we derive the period-luminosity-mass-temperature-metallicity relations, and then estimate the pulsation mass. Results: The PL relation for the T2Cs does not appear to depend on metallicity, and, excluding the dusty RV Tau stars, is $M_{\rm bol}= +0.12 -1.78 \log P$ (for $P < 50$ days). Relations for fundamental and first overtone LMC ACs are also presented. The PR relation for T2C also shows little or no dependence on metallicity or period. Our preferred relation combines SMC and LMC stars and all T2C subclasses, and is $\log R = 0.846 + 0.521 \log P$. Relations for fundamental and first overtone LMC ACs are also presented. The pulsation masses from the RR Lyrae and classical Cepheid pulsation models agree well for the short period T2Cs, the BL Her subtype, and ACs, and are consistent with estimates in the literature, i.e. $M_{\rm BLH} \sim 0.49$ \msol\ and $M_{\rm AC} ~\sim 1.3$ \msol, respectively. The masses of the W Vir appear similar to the BL Her. The situation for the pWVir and RV Tau stars is less clear. For many RV Tau the masses are in conflict with the standard picture of (single-star) post-AGB evolution, the masses being either too large ($\gtrsim$ 1 \msol) or too small ($\lesssim$ 0.4 \msol).Comment: A&A accepte

Nanomechanical effects in an Andreev quantum dot

We consider a quantum dot with mechanical degrees of freedom which is coupled to superconducting electrodes. A Josephson current is generated by applying a phase difference. In the absence of coupling to vibrations, this setup was previously proposed as a detector of magnetic flux and we wish here to address the effect of the phonon coupling to this detection scheme. We compute the charge on the quantum dot and determine its dependence on the phase difference in the presence of phonon coupling and Coulomb interaction. This allows to identify regions in parameter space with the highest charge to phase sensitivity, which are relevant for flux detection. Further insight about the interplay of such couplings and subsequent entanglement properties between electron and phonon degrees of freedom are gained by computing the von Neuman entropy.Comment: 9 pages, 7 figures; minor corretion

Cooper pair splitting in a nanoSQUID geometry at high transparency

We describe a Josephson device composed of two superconductors separated by two interacting quantum dots in parallel, as a probe for Cooper pair splitting. In addition to sequential tunneling of electrons through each dot, an additional transport channel exists in this system: crossed Andreev reflection, where a Cooper pair from the source is split between the two dots and recombined in the drain superconductor. Unlike non-equilibrium scenarios for Cooper pair splitting which involves superconducting/normal metal "forks", our proposal relies on an Aharonov-Bohm measurement of the DC Josephson current when a flux is inserted between the two dots. We provide a path integral approach to treat arbitrary transparencies, and we explore all contributions for the individual phases ($0$ or $\pi$) of the quantum dots. We propose a definition of the Cooper pair splitting efficiency for arbitrary transparencies, which allows us to find the phase associations which favor the crossed Andreev process. Possible applications to experiments using nanowires as quantum dots are discussed.Comment: 12 pages, 13 figure

Giant shot noise from Majorana zero modes in topological trijunctions

The clear-cut experimental identification of Majorana bound states in transport measurements still poses experimental challenges. We here show that the zero-energy Majorana state formed at a junction of three topological superconductor wires is directly responsible for giant shot noise amplitudes, in particular at low voltages and for small contact transparency. The only intrinsic noise limitation comes from the current-induced dephasing rate due to multiple Andreev reflection processes