The number of magnetoelectric multiferroic materials reported to date is scarce, as magnetic structures that break inversion symmetry and induce an improper ferroelectric polarization typically arise through subtle competition between different magne
tic interactions. The (NH4)2[FeCl5(H2O)] compound is a rare case where such improper ferroelectricity has been observed in a molecular material. We have used single crystal and powder neutron diffraction to obtain detailed solutions for the crystal and magnetic structures of (NH4)2[FeCl5(H2O)], from which we determined the mechanism of multiferroicity. From the crystal structure analysis, we observed an order-disorder phase transition related to the ordering of the ammonium counterion. We have determined the magnetic structure below TN, at 2K and zero magnetic field, which corresponds to a cycloidal spin arrangement with magnetic moments contained in the ac-plane, propagating parallel to the c-axis. The observed ferroelectricity can be explained, from the obtained magnetic structure, via the inverse Dzyaloshinskii-Moriya mechanism.
We study the scattering of a matter-wave from an interacting system of bosons in an optical lattice, focusing on the strong-interaction regime. Analytical expressions for the many-body scattering cross section are derived from a strong-coupling expan
sion and a site-decoupling mean-field approximation, and compared to numerically obtained exact results. In the thermodynamic limit, we find a non-vanishing inelastic cross section throughout the Mott insulating regime, which decays quadratically as a function of the boson-boson interaction.
For an ordered subset $S = {s_1, s_2,dots s_k}$ of vertices and a vertex $u$ in a connected graph $G$, the metric representation of $u$ with respect to $S$ is the ordered $k$-tuple $ r(u|S)=(d_G(v,s_1), d_G(v,s_2),dots,$ $d_G(v,s_k))$, where $d_G(x,y
)$ represents the distance between the vertices $x$ and $y$. The set $S$ is a metric generator for $G$ if every two different vertices of $G$ have distinct metric representations. A minimum metric generator is called a metric basis for $G$ and its cardinality, $dim(G)$, the metric dimension of $G$. It is well known that the problem of finding the metric dimension of a graph is NP-Hard. In this paper we obtain closed formulae and tight bounds for the metric dimension of strong product graphs.
We describe how to engineer wavefunction delocalization in disordered systems modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together with suita
bly chosen hopping strengths, allows a resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate that these features persist in the thermodynamic limit for a continuous range of the system parameters. Numerical results support these findings and highlight the robustness of the extended regime with respect to deviations from the exact resonance condition for finite systems. The localization and transport properties of the system can be engineered almost at will and independently in each direction. This study gives rise to the possibility of designing disordered potentials that work as switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.
(Abridge) The relationship between coronal line (CL) emission and nuclear activity in active galactic nuclei (AGNs) is analyzed, for the first time, based on NIR spectra. The 8 CLs studied, of Si, S, Fe, Al and Ca elements and corresponding to ioniza
tion potentials (IP) in the range 125-450 eV, are detected in 67% (36 AGNs) of the sample. The four most frequent CLs - [SiVI] 19630AA, [SVIII] 9913AA, [SIX] 12520AA and [SiX] 14320AA, - display a narrow range in luminosity, with most lines located in the interval logL 39-40 erg/s. We found that the non-detection is largely associated with either a lost of spatial resolution or increasing object distance. Yet, there are AGNs where the lack of CLs may be genuine and reflect an AGN ionising continuum lacking photons below a few keV. The FWHM of the lines profiles increases with increasing IP up to energies around 300 eV, where a maximum in the FWHM is reached. For higher IP lines, the FWHM remains nearly constant or decreases with increasing IP. We ascribe this effect to an increasing density environment as we approach to the innermost regions of the AGN, where densities above the critical density of the CLs with IP larger than 300 eV are reached. This sets a strict range limit for the density in the boundary region between the narrow and the broad region of 10^8 - 10^9 cm^{-3}. A relationship between the luminosity of the coronal lines and that of the soft and hard X-ray emission and the soft X-ray photon index is observed: the coronal emission becomes stronger with both increasing x-ray emission (soft and hard) and steeper X-ray photon index. Thus, photoionization appears as the dominant excitation mechanism. These trends hold when considering Type 1 sources only; they get weaker or vanish when including Type 2 sources, very likely because the X-ray emission measured in the later is not the intrinsic ionising continuum.
We describe a new multifractal finite size scaling (MFSS) procedure and its application to the Anderson localization-delocalization transition. MFSS permits the simultaneous estimation of the critical parameters and the multifractal exponents. Simula
tions of system sizes up to L^3=120^3 and involving nearly 10^6 independent wavefunctions have yielded unprecedented precision for the critical disorder W_c=16.530 (16.524,16.536) and the critical exponent nu=1.590 (1.579,1.602). We find that the multifractal exponents Delta_q exhibit a previously predicted symmetry relation and we confirm the non-parabolic nature of their spectrum. We explain in detail the MFSS procedure first introduced in our Letter [Phys. Rev. Lett. 105, 046403 (2010)] and, in addition, we show how to take account of correlations in the simulation data. The MFSS procedure is applicable to any continuous phase transition exhibiting multifractal fluctuations in the vicinity of the critical point.
A defensive $k$-alliance in a graph is a set $S$ of vertices with the property that every vertex in $S$ has at least $k$ more neighbors in $S$ than it has outside of $S$. A defensive $k$-alliance $S$ is called global if it forms a dominating set. In
this paper we study the problem of partitioning the vertex set of a graph into (global) defensive $k$-alliances. The (global) defensive $k$-alliance partition number of a graph $Gamma=(V,E)$, ($psi_{k}^{gd}(Gamma)$) $psi_k^{d}(Gamma)$, is defined to be the maximum number of sets in a partition of $V$ such that each set is a (global) defensive $k$-alliance. We obtain tight bounds on $psi_k^{d}(Gamma)$ and $psi_{k}^{gd}(Gamma)$ in terms of several parameters of the graph including the order, size, maximum and minimum degree, the algebraic connectivity and the isoperimetric number. Moreover, we study the close relationships that exist among partitions of $Gamma_1times Gamma_2$ into (global) defensive $(k_1+k_2)$-alliances and partitions of $Gamma_i$ into (global) defensive $k_i$-alliances, $iin {1,2}$.
The probability density function (PDF) for critical wavefunction amplitudes is studied in the three-dimensional Anderson model. We present a formal expression between the PDF and the multifractal spectrum f(alpha) in which the role of finite-size cor
rections is properly analyzed. We show the non-gaussian nature and the existence of a symmetry relation in the PDF. From the PDF, we extract information about f(alpha) at criticality such as the presence of negative fractal dimensions and we comment on the possible existence of termination points. A PDF-based multifractal analysis is hence shown to be a valid alternative to the standard approach based on the scaling of general inverse participation ratios.
