On the spectrum of a bent chain graph

We study Schr\"odinger operators on an infinite quantum graph of a chain form which consists of identical rings connected at the touching points by $\delta$-couplings with a parameter $\alpha\in\R$. If the graph is "straight", i.e. periodic with respect to ring shifts, its Hamiltonian has a band spectrum with all the gaps open whenever $\alpha\ne 0$. We consider a "bending" deformation of the chain consisting of changing one position at a single ring and show that it gives rise to eigenvalues in the open spectral gaps. We analyze dependence of these eigenvalues on the coupling $\alpha$ and the "bending angle" as well as resonances of the system coming from the bending. We also discuss the behaviour of the eigenvalues and resonances at the edges of the spectral bands.Comment: LaTeX, 23 pages with 7 figures; minor changes, references added; to appear in J. Phys. A: Math. Theo

Persistent detwinning of iron pnictides by small magnetic fields

Our comprehensive study on EuFe$_2$As$_2$ reveals a dramatic reduction of magnetic detwinning fields compared to other AFe$_2$As$_2$ (A = Ba, Sr, Ca) iron pnictides by indirect magneto-elastic coupling of the Eu$^{2+}$ ions. We find that only 0.1T are sufficient for persistent detwinning below the local Eu$^{2+}$ ordering; above $T_\text{Eu}$ = 19K, higher fields are necessary. Even after the field is switched off, a significant imbalance of twin domains remains constant up to the structural and electronic phase transition (190K). This persistent detwinning provides the unique possibility to study the low temperature electronic in-plane anisotropy of iron pnictides without applying any symmetrybreaking external force.Comment: accepted by Physical Review Letter

Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT($\cdot$) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation $R$ such that SAT($R$) can be solved at least as fast as any other NP-hard SAT($\cdot$) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes($\Gamma$)) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP($\Delta$)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.Comment: This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201

Electronic Scattering Effects in Europium-Based Iron Pnictides

In a comprehensive study, we investigate the electronic scattering effects in EuFe$_{2}$(As$_{1-x}$P$_{x}$)$_{2}$ by using Fourier-transform infrared spectroscopy. In spite of the fact that Eu$^{2+}$ local moments order around $T_\text{Eu} \approx 20$\,K, the overall optical response is strikingly similar to the one of the well-known Ba-122 pnictides. The main difference lies within the suppression of the lower spin-density-wave gap feature. By analysing our spectra with a multi-component model, we find that the high-energy feature around 0.7\,eV -- often associated with Hund's rule coupling -- is highly sensitive to the spin-density-wave ordering, this further confirms its direct relationship to the dynamics of itinerant carriers. The same model is also used to investigate the in-plane anisotropy of magnetically detwinned EuFe$_{2}$As$_{2}$ in the antiferromagnetically ordered state, yielding a higher Drude weight and lower scattering rate along the crystallographic $a$-axis. Finally, we analyse the development of the room temperature spectra with isovalent phosphor substitution and highlight changes in the scattering rate of hole-like carriers induced by a Lifshitz transition

Families of superintegrable Hamiltonians constructed from exceptional polynomials

We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable

Economic Backwardness and Social Tension

We propose that relative economic backwardness contributes to the build-up of social tension and non-violent and violent conflict. We test our hypothesis using data on organized mass movements and armed civil conflict. The findings show that greater economic backwardness is consistently linked to a higher probability of onset of violent and especially non-violent forms of civil unrest. We provide evidence that the relationship is causal in instrumental variables estimations using new instruments, including mailing speeds and telegram charges around 1900. The magnitude of the effect of backwardness on social tension increases in the two-stage least-squares estimations

On sl(2)-equivariant quantizations

By computing certain cohomology of Vect(M) of smooth vector fields we prove that on 1-dimensional manifolds M there is no quantization map intertwining the action of non-projective embeddings of the Lie algebra sl(2) into the Lie algebra Vect(M). Contrariwise, for projective embeddings sl(2)-equivariant quantization exists.Comment: 09 pages, LaTeX2e, no figures; to appear in Journal of Nonlinear Mathematical Physic

Observation of Andreev Reflection Enhanced Shot Noise

We have experimentally investigated the quasiparticle shot noise in NbN/MgO/NbN superconductor - insulator - superconductor tunnel junctions. The observed shot noise is significantly larger than theoretically expected. We attribute this to the occurrence of multiple Andreev reflection processes in pinholes present in the MgO barrier. This mechanism causes the current to flow in large charge quanta (Andreev clusters), with a voltage dependent average value of m = 1+ 2 Delta/eV times the electron charge. Because of this charge enhancement effect, the shot noise is increased by the factor m.Comment: 4 pages, 5 figures include