Double Well Potential: Perturbation Theory, Tunneling, WKB (beyond instantons)

A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the potential, semi-classical approximation at large distances and a description of tunneling under the barrier. It provides 9-10 significant digits in energies and gives for wavefunctions the relative deviation in real $x$-space less than $\lesssim 10^{-3}$.Comment: 13 pages, invited talk at "Crossing the boundaries: Gauge dynamics at strong coupling (Shifmania)", Minneapolis, May 14-17, 200

Exotic composites: the decay of deficit angles in global-local monopoles

We study static, spherically symmetric, composite global-local monopoles with a direct interaction term between the two sectors in the regime where the interaction potential is large. At some critical coupling the global defect disappears and with it the deficit angle of the space-time. We find new solutions which represent local monopoles in an Anti-de-Sitter spacetime. In another parameter range the magnetic monopole, or even both, disappear. The decay of the magnetic monopole is accompanied by a dynamical transition from the higgsed phase to the gauge-symmetric phase. We comment on the applications to cosmology, topological inflation and braneworlds.Comment: 17 pages, 11 figures; Minor corrections, matches published versio

Colloquium : disclination loops, point defects, and all that in nematic liquid crystals

The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress was made in controlling and measuring colloidal inclusions in liquid crystalline phases. The topological structure of these systems is quite rich but, at the same time, subtle. Motivated by experiment and the power of topological reasoning, the classification of defects in uniaxial nematic liquid crystals was reviewed and expounded upon. Particular attention was paid to the ambiguities that arise in these systems, which have no counterpart in the much-storied XY model or the Heisenberg ferromagnet

More on core instabilities of magnetic monopoles

In this paper we present new results on the core instability of the 't Hooft Polyakov monopoles we reported on before. This instability, where the spherical core decays in a toroidal one, typically occurs in models in which charge conjugation is gauged. In this paper we also discuss a third conceivable configuration denoted as ``split core'', which brings us to some details of the numerical methods we employed. We argue that a core instability of 't Hooft Polyakov type monopoles is quite a generic feature of models with charged Higgs particles.Comment: Latex, 15 pages, 6 figures; published versio

Eco-friendly iron-humic nanofertilizers synthesis for the prevention of iron chlorosis in soybean (Glycine max) grown in calcareous soil

Iron deficiency is a frequent problem for many crops, particularly in calcareous soils and iron humates are commonly applied in the Mediterranean basin in spite of their lesser efficiency than iron synthetic chelates. Development and application of new fertilizers using nanotechnology are one of the potentially effective options of enhancing the iron humates, according to the sustainable agriculture. Particle size, pH, and kinetics constrain the iron humate efficiency. Thus, it is relevant to understand the iron humate mechanism in the plant–soil system linking their particle size, characterization and iron distribution in plant and soil using 57Fe as a tracer tool. Three hybrid nanomaterials (F, S, and M) were synthesized as iron-humic nanofertilizers (57Fe-NFs) from leonardite potassium humate and 57Fe used in the form of 57Fe(NO3)3 or 57Fe2(SO4)3. They were characterized using Mössbauer spectroscopy, X-ray diffraction (XRD), extended X-ray absorption fine structure spectroscopy (EXAFS), transmission electron microscopy (TEM) and tested for iron availability in a calcareous soil pot experiment carried out under growth chamber conditions. Three doses (35, 75, and 150 mmol pot-1) of each iron-humic material were applied to soybean iron deficient plants and their iron nutrition contributions were compared to 57FeEDDHA and leonardite potassium humate as control treatments. Ferrihydrite was detected as the main structure of all three 57Fe- NFs and the plants tested with iron-humic compounds exhibited continuous long-term statistically reproducible iron uptake and showed high shoot fresh weight. Moreover, the 57Fe from the humic nanofertilizers remained available in soil and was detected in soybean pods. The Fe-NFs offers a natural, low cost and environmental option to the traditional iron fertilization in calcareous soilsThe Russian Science Foundation (16-14-00167), the Russian Foundation for Basic Research (18-29-25065), and the Spanish Ministry of Science and Innovation (AGL2013-44474-R) have financially supported this research

Case study of ozone anomalies over northern Russia in the 2015/2016 winter: measurements and numerical modelling

Episodes of extremely low ozone columns were observed over the territory of Russia in the Arctic winter of 2015/2016 and the beginning of spring 2016. We compare total ozone columns (TOCs) from different remote sensing techniques (satellite and ground-based observations) with results of numerical modelling over the territory of the Urals and Siberia for this period. We demonstrate that the provided monitoring systems (including the new Russian Infrared Fourier Spectrometer IKFS-2) and modern three-dimensional atmospheric models can capture the observed TOC anomalies. However, the results of observations and modelling show differences of up to 20&thinsp;%–30&thinsp;% in TOC measurements. Analysis of the role of chemical and dynamical processes demonstrates that the observed short-term TOC variability is not a result of local photochemical loss initiated by heterogeneous halogen activation on particles of polar stratospheric clouds that formed under low temperatures in the mid-winter.</p

Many-body localization and delocalization in large quantum chains

We theoretically study the quench dynamics for an isolated Heisenberg spin chain with a random on-site magnetic field, which is one of the paradigmatic models of a many-body localization transition. We use the time-dependent variational principle as applied to matrix product states, which allows us to controllably study chains of a length up to $L=100$ spins, i.e., much larger than $L \simeq 20$ that can be treated via exact diagonalization. For the analysis of the data, three complementary approaches are used: (i) determination of the exponent $\beta$ which characterizes the power-law decay of the antiferromagnetic imbalance with time; (ii) similar determination of the exponent $\beta_\Lambda$ which characterizes the decay of a Schmidt gap in the entanglement spectrum, (iii) machine learning with the use, as an input, of the time dependence of the spin densities in the whole chain. We find that the consideration of the larger system sizes substantially increases the estimate for the critical disorder $W_c$ that separates the ergodic and many-body localized regimes, compared to the values of $W_c$ in the literature. On the ergodic side of the transition, there is a broad interval of the strength of disorder with slow subdiffusive transport. In this regime, the exponents $\beta$ and $\beta_\Lambda$ increase, with increasing $L$, for relatively small $L$ but saturate for $L \simeq 50$, indicating that these slow power laws survive in the thermodynamic limit. From a technical perspective, we develop an adaptation of the "learning by confusion" machine learning approach that can determine $W_c$.Comment: 14 pages, 11 figures. Title changed compared to earlier arXiv versions. Comments welcom

Static Black Hole Solutions without Rotational Symmetry

We construct static black hole solutions that have no rotational symmetry. These arise in theories, including the standard electroweak model, that include charged vector mesons with mass $m\ne 0$. In such theories, a magnetically charged Reissner-Nordstrom black hole with horizon radius less than a critical value of the order of $m^{-1}$ is classically unstable against the development of a nonzero vector meson field just outside the horizon, indicating the existence of static black hole solutions with vector meson hair. For the case of unit magnetic charge, spherically symmetric solutions of this type have previously been studied. For other values of the magnetic charge, general arguments show that any new solution with hair cannot be spherically symmetric. In this paper we develop and apply a perturbative scheme (which may have applicability in other contexts) for constructing such solutions in the case where the Reissner-Nordstrom solution is just barely unstable. For a few low values of the magnetic charge the black holes retain a rotational symmetry about a single axis, but this axial symmetry disappears for higher charges. While the vector meson fields vanish exponentially fast at distances greater than $O(m^{-1})$, the magnetic field and the metric have higher multipole components that decrease only as powers of the distance from the black hole.Comment: 42 pages, phyzzx. 4 figures (PostScript, 1.7 MB when uncompressed) available by email from the Authors on reques

Extended multiplet structure in Logarithmic Conformal Field Theories

We use the process of quantum hamiltonian reduction of SU(2)_k, at rational level k, to study explicitly the correlators of the h_{1,s} fields in the c_{p,q} models. We find from direct calculation of the correlators that we have the possibility of extra, chiral and non-chiral, multiplet structure in the h_{1,s} operators beyond the `minimal' sector. At the level of the vacuum null vector h_{1,2p-1}=(p-1)(q-1) we find that there can be two extra non-chiral fermionic fields. The extra indicial structure present here permeates throughout the entire theory. In particular we find we have a chiral triplet of fields at h_{1,4p-1}=(2p-1)(2q-1). We conjecture that this triplet algebra may produce a rational extended c_{p,q} model. We also find a doublet of fields at h_{1,3p-1}=(\f{3p}{2}-1)(\f{3q}{2}-1). These are chiral fermionic operators if p and q are not both odd and otherwise parafermionic.Comment: 24 pages LATEX. Minor corrections and extra reference