Class of invariants for the 2D time-dependent Landau problem and harmonic oscillator in a magnetic field

We consider an isotropic two dimensional harmonic oscillator with arbitrarily time-dependent mass $M(t)$ and frequency $\Omega(t)$ in an arbitrarily time-dependent magnetic field $B(t)$. We determine two commuting invariant observables (in the sense of Lewis and Riesenfeld) $L,I$ in terms of some solution of an auxiliary ordinary differential equation and an orthonormal basis of the Hilbert space consisting of joint eigenvectors $\phi_\lambda$ of $L,I$. We then determine time-dependent phases $\alpha_\lambda(t)$ such that the $\psi_\lambda(t)=e^{i\alpha_\lambda}\phi_\lambda$ are solutions of the time-dependent Schr\"odinger equation and make up an orthonormal basis of the Hilbert space. These results apply, in particular to a two dimensional Landau problem with time-dependent $M,B$, which is obtained from the above just by setting $\Omega(t) \equiv 0$. By a mere redefinition of the parameters, these results can be applied also to the analogous models on the canonical non-commutative plane.Comment: 13 pages, 3 references adde

Coronal Loop Expansion Properties Explained Using Separators

One puzzling observed property of coronal loops is that they are of roughly constant thickness along their length. Various studies have found no consistent pattern of width variation along the length of loops observed by TRACE and SOHO. This is at odds with expectations of magnetic flux tube expansion properties, which suggests that loops are widest at their tops, and significantly narrower at their footpoints. Coronal loops correspond to areas of the solar corona which have been preferentially heated by some process, so this observed property might be connected to the mechanisms that heat the corona. One means of energy deposition is magnetic reconnection, which occurs along field lines called separators. These field lines begin and end on magnetic null points, and loops forming near them can therefore be relatively wide at their bases. Thus, coronal energization by magnetic reconnection may replicate the puzzling expansion properties observed in coronal loops. We present results of a Monte Carlo survey of separator field line expansion properties, comparing them to the observed properties of coronal loops.Comment: 16 pages, 9 figures, to be submitted to Ap

A variant transfer matrix method suitable for transport through multi-probe systems

We have developed a variant transfer matrix method that is suitable for transport through multi-probe systems. Using this method, we have numerically studied the quantum spin Hall effect (QSHE) on 2D graphene with both intrinsic (Vso) and Rashba (Vr) spin-orbit (SO) couplings. The integer QSHE arises in the presence of intrinsic SO interaction and is gradually destroyed by the Rashba SO interaction and disorder fluctuation. We have numerically determined the phase boundaries separating integer QSHE and spin Hall liquid. We have found that when Vso> 0.2t with t the hopping constant the energy gap needed for the integer QSHE is the largest satisfying |E|<t. For smaller Vso the energy gap decreases linearly. In the presence of Rashba SO interaction or disorders, the energy gap diminishes. With Rashba SO interaction the integer QSHE is robust at the largest energy within the energy gap while at the smallest energy within the energy gap the integer QSHE is insensitive to the disorder

Non-conformal coarse-grained potentials for water

Water is a notoriously difficult substance to model both accurately and efficiently. Here, we focus on descriptions with a single coarse-grained particle per molecule using the so-called Approximate Non-Conformal (ANC) and generalized Stockmayer potentials as the starting points. They are fitted using the radial density function and the density of the atomistic SPC/E model by downhill simplex optimization. We compare the results with monatomic water (mW), ELBA, as well as with direct Iterative Boltzmann Inversion (IBI) of SPC/E. The results show that symmetrical potentials result in non-transferable models, that is, they need to be reparametrized for new state-points. This indicates that transferability may require more complex models. Furthermore, the results also show that the addition of a point dipole is not sufficient to make the potentials accurate and transferable to different temperatures (300 K-500 K) and pressures without an appropriate choice of properties as targets during model optimization

Revealing the large nuclear dust structures in NGC 1068 with MIDI/VLTI

To understand the relation between the small "obscuring torus" and dusty structures at larger scales (5-10 pc) in NGC 1068, we use ESO's Mid-Infrared Interferometer (MIDI) with the 1.8 m Auxiliary Telescopes to achieve the necessary spatial resolution (~ 20-100 millarcsec). We use the chromatic phases in the data to improve the spatial fidelity of the analysis. We present interferometric data for NGC 1068 obtained in 2007 and 2012. We find no evidence of source variability. Many (u,v) points show non-zero chromatic phases indicating significant asymmetries. Gaussian model fitting of the correlated fluxes and chromatic phases provides a 3-component best fit with estimates of sizes, temperatures and positions of the components. A large, warm, off-center component is required at a distance approximately 90 mas to the north-west at a PA ~ -18 deg. The dust at 5-10 pc in the polar region contributes 4 times more to the mid-infrared flux at 12 um than the dust located at the center. This dust may represent the inner wall of a dusty cone. If similar regions are heated by the direct radiation from the nucleus, then they will contribute substantially to the classification of many Seyfert galaxies as Type 2. Such a region is also consistent in other Seyfert galaxies (the Circinus galaxy, NGC 3783 and NGC 424).Comment: 21 pages, 10 figures; Accepted for publication on A&

Depletion potential in the infinite dilution limit

The depletion force and depletion potential between two in principle unequal "big" hard spheres embedded in a multicomponent mixture of "small" hard spheres are computed using the Rational Function Approximation method for the structural properties of hard-sphere mixtures [S. B. Yuste, A. Santos, and M. L\'opez de Haro, J. Chem. Phys. {\bf 108}, 3683 (1998)]. The cases of equal solute particles and of one big particle and a hard planar wall in a background monodisperse hard-sphere fluid are explicitly analyzed. An improvement over the performance of the Percus-Yevick theory and good agreement with available simulation results are foundComment: 10 pages, 5 figures; v2: few minor additions and reduction in the number of figures; v3: Fig. 2 corrected (see http://dx.doi.org/10.1063/1.4874639

Morpho-kinematic analysis of the point-symmetric, bipolar planetary nebulae Hb 5 and K 3-17, a pathway to poly-polarity

The kinematics of the bipolar planetary nebulae Hb~5 and K 3-17 are investigated in detail by means of a comprehensive set of spatially resolved high spectral resolution, long-slit spectra. Both objects share particularly interesting characteristics, such as a complex filamentary, rosette-type nucleus, axial point-symmetry and very fast bipolar outflows. The kinematic information of Hb~5 is combined with {\it HST} imagery to construct a detailed 3D model of the nebula using the code SHAPE. The model shows that the large scale lobes are growing in a non-homologous way. The filamentary loops in the core are proven to actually be secondary lobes emerging from what appears to be a randomly punctured, dense, gaseous core and the material that forms the point symmetric structure flows within the lobes with a distinct kinematic pattern and its interaction with the lobes has had a shaping effect on them. Hb~5 and K~3-17 may represent a class of fast evolving planetary nebulae that will develop poly-polar characteristics once the nebular core evolves and expands.Comment: 19 pages, 8 figures. To appear in The Astrophysical Journa

Quantum effects on Higgs-strahlung events at Linear Colliders within the general 2HDM

The associated production of neutral Higgs bosons with the Z gauge boson is investigated in the context of the future linear colliders, such as the ILC and CLIC, within the general two-Higgs-doublet model (2HDM). We compute the corresponding production cross-sections at one-loop, in full consistency with the available theoretical and phenomenological constraints. We find that the wave-function renormalization corrections to the external Higgs fields are the dominant source of the quantum effects, which turn out to be large and negative, and located predominantly in the region around \tan\beta=1 and moderate values of the parameter \lambda_5 (being \lambda_5 < 0). This behavior can be ultimately traced back to the enhancement potential of the triple Higgs boson self-couplings, a trademark feature of the 2HDM with no counterpart in the Higgs sector of the Minimal Supersymmetric Standard Model. The predicted Higgs-strahlung rates comfortably reach a few tens of femtobarn, which means barely 10^3 - 10^4 events per 500 inverse femtobarn of integrated luminosity. Due to their great complementarity, we argue that the combined analysis of the Higgs-strahlung events and the previously computed one-loop Higgs-pair production processes could be instrumental to probe the structure of the Higgs sector at future linac facilities.Comment: LaTeX, 16 pages, 9 Figures, 2 Tables. Extended discussion, references added, matches published version in Phys. Rev.