Improved numerical methods for infinite spin chains with long-range interactions

We present several improvements of the infinite matrix product state (iMPS) algorithm for finding ground states of one-dimensional quantum systems with long-range interactions. As a main new ingredient we introduce the superposed multi-optimization (SMO) method, which allows an efficient optimization of exponentially many MPS of different length at different sites all in one step. Hereby the algorithm becomes protected against position dependent effects as caused by spontaneously broken translational invariance. So far, these have been a major obstacle to convergence for the iMPS algorithm if no prior knowledge of the systems translational symmetry was accessible. Further, we investigate some more general methods to speed up calculations and improve convergence, which might be partially interesting in a much broader context, too. As a more special problem, we also look into translational invariant states close to an invariance braking phase transition and show how to avoid convergence into wrong local minima for such systems. Finally, we apply the new methods to polar bosons with long-range interactions. We calculate several detailed Devil's Staircases with the corresponding phase diagrams and investigate some supersolid properties.Comment: Main text: 17 pages plus references, 8 figures. Supplementary info: 6 pages. v2: improved presentation and more results adde

Collective vibrational states with fast iterative QRPA method

An iterative method we previously proposed to compute nuclear strength functions is developed to allow it to accurately calculate properties of individual nuclear states. The approach is based on the quasi-particle-random-phase approximation (QRPA) and uses an iterative non-hermitian Arnoldi diagonalization method where the QRPA matrix does not have to be explicitly calculated and stored. The method gives substantial advantages over conventional QRPA calculations with regards to the computational cost. The method is used to calculate excitation energies and decay rates of the lowest lying 2+ and 3- states in Pb, Sn, Ni and Ca isotopes using three different Skyrme interactions and a separable gaussian pairing force.Comment: 10 pages, 11 figure

A discrete time-dependent method for metastable atoms in intense fields

The full-dimensional time-dependent Schrodinger equation for the electronic dynamics of single-electron systems in intense external fields is solved directly using a discrete method. Our approach combines the finite-difference and Lagrange mesh methods. The method is applied to calculate the quasienergies and ionization probabilities of atomic and molecular systems in intense static and dynamic electric fields. The gauge invariance and accuracy of the method is established. Applications to multiphoton ionization of positronium and hydrogen atoms and molecules are presented. At very high intensity above saturation threshold, we extend the method using a scaling technique to estimate the quasienergies of metastable states of the hydrogen molecular ion. The results are in good agreement with recent experiments.Comment: 10 pages, 9 figure, 4 table

Kinematic dynamo action in a sphere. I. Effects of differential rotation and meridional circulation on solutions with axial dipole symmetry

A sphere containing electrically conducting fluid can generate a magnetic field by dynamo action, provided the flow is sufficiently complicated and vigorous. The dynamo mechanism is thought to sustain magnetic fields in planets and stars. The kinematic dynamo problem tests steady flows for magnetic instability, but rather few dynamos have been found so far because of severe numerical difficulties. Dynamo action might, therefore, be quite unusual, at least for large-scale steady flows. We address this question by testing a two-parameter class of flows for dynamo generation of magnetic fields containing an axial dipole. The class of flows includes two completely different types of known dynamos, one dominated by differential rotation (D) and one with none. We find that 36% of the flows in seven distinct zones in parameter space act as dynamos, while the remaining 64% either fail to generate this type of magnetic field or generate fields that are too small in scale to be resolved by our numerical method. The two previously known dynamo types lie in the same zone, and it is therefore possible to change the flow continuously from one to the other without losing dynamo action. Differential rotation is found to promote large-scale axisymmetric toroidal magnetic fields, while meridional circulation (M) promotes large-scale axisymmetric poloidal fields concentrated at high latitudes near the axis. Magnetic fields resembling that of the Earth are generated by D > 0, corresponding to westward flow at the surface, and M of either sign but not zero. Very few oscillatory solutions are found

Spatial and spectral properties of the pulsed second-harmonic generation in a PP-KTP waveguide

Spatial and spectral properties of the pulsed second harmonic generation in a periodically-poled KTP waveguide exploiting simultaneously the first, second, and third harmonics of periodic nonlinear modulation are analyzed. Experimental results are interpreted using a model based on finite elements method. Correlations between spatial and spectral properties of the fundamental and second-harmonic fields are revealed. Individual nonlinear processes can be exploited combining spatial and spectral filtering. Also the influence of waveguide parameters to the second-harmonic spectra is addressed.Comment: 13 pages, 8 figure

Bogoliubov modes of a dipolar condensate in a cylindrical trap

The calculation of properties of Bose-Einstein condensates with dipolar interactions has proven a computationally intensive problem due to the long range nature of the interactions, limiting the scope of applications. In particular, the lowest lying Bogoliubov excitations in three dimensional harmonic trap with cylindrical symmetry were so far computed in an indirect way, by Fourier analysis of time dependent perturbations, or by approximate variational methods. We have developed a very fast and accurate numerical algorithm based on the Hankel transform for calculating properties of dipolar Bose-Einstein condensates in cylindrically symmetric traps. As an application, we are able to compute many excitation modes by directly solving the Bogoliubov-De Gennes equations. We explore the behavior of the excited modes in different trap geometries. We use these results to calculate the quantum depletion of the condensate by a combination of a computation of the exact modes and the use of a local density approximation

Stability and Complexity of Minimising Probabilistic Automata

We consider the state-minimisation problem for weighted and probabilistic automata. We provide a numerically stable polynomial-time minimisation algorithm for weighted automata, with guaranteed bounds on the numerical error when run with floating-point arithmetic. Our algorithm can also be used for "lossy" minimisation with bounded error. We show an application in image compression. In the second part of the paper we study the complexity of the minimisation problem for probabilistic automata. We prove that the problem is NP-hard and in PSPACE, improving a recent EXPTIME-result.Comment: This is the full version of an ICALP'14 pape

Dynamic and Static Magnetic Resonance Angiography of the Supra-aortic Vessels at 3.0 T Intraindividual Comparison of Gadobutrol, Gadobenate Dimeglumine, and Gadoterate Meglumine at Equimolar Dose

Purpose: The purpose of this study was the intraindividual comparison of a 1.0 M and two 0.5 M gadolinium-based contrast agents (GBCA) using equimolar dosing in dynamic and static magnetic resonance angiography (MRA) of the supra-aortic vessels. Materials and Methods: In this institutional review board-approved study, a total of 20 healthy volunteers (mean +/- SD age, 29 +/- 6 years) underwent 3 consecutive supra-aortic MRA examinations on a 3.0 T magnetic resonance system. The order of GBCA (Gadobutrol, Gadobenate dimeglumine, and Gadoterate meglumine) was randomized with a minimum interval of 48 hours between the examinations. Before each examination and 45 minutes after each examination, circulatory parameters were recorded. Total GBCA dose per MRA examination was 0.1 mmol/kg with a 0.03 mmol/kg and 0.07 mmol/kg split for dynamic and static MRA, respectively, injected at a rate of 2 mL/s. Two blinded readers qualitatively assessed static MRA data sets independently using pairwise rankings (superior, inferior, and equal). In addition, quantitative analysis was performed with signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) evaluation as well as vessel sharpness analysis of static MRA using an in-house-developed semiautomated tool. Dynamic MRA was evaluated for maximal SNR. Statistical analysis was performed using the Cohen kappa, the Wilcoxon rank sum tests, and mixed effects models. Results: No significant differences of hemodynamic parameters were observed. In static MRA, Gadobutrol was rated superior to Gadoterate meglumine (P 0.05). Maximal SNR in dynamic MRA using Gadobutrol was significantly higher than both comparators at the level of the proximal and distal internal carotid artery (P < 0.05 and P < 0.05; P < 0.05 and P < 0.05). Conclusions: At equimolar doses, 1.0 M Gadobutrol demonstrates higher SNR/CNR than do Gadobenate dimeglumine and Gadoterate meglumine, with superior image quality as compared with Gadoterate meglumine for dynamic and static carotid MRA. Despite the shortened bolus with Gadobutrol, no blurring of vessel edges was observed

Markov chain analysis of random walks on disordered medium

We study the dynamical exponents $d_{w}$ and $d_{s}$ for a particle diffusing in a disordered medium (modeled by a percolation cluster), from the regime of extreme disorder (i.e., when the percolation cluster is a fractal at $p=p_{c}$) to the Lorentz gas regime when the cluster has weak disorder at $p>p_{c}$ and the leading behavior is standard diffusion. A new technique of relating the velocity autocorrelation function and the return to the starting point probability to the asymptotic spectral properties of the hopping transition probability matrix of the diffusing particle is used, and the latter is numerically analyzed using the Arnoldi-Saad algorithm. We also present evidence for a new scaling relation for the second largest eigenvalue in terms of the size of the cluster, $|\ln{\lambda}_{max}|\sim S^{-d_w/d_f}$, which provides a very efficient and accurate method of extracting the spectral dimension $d_s$ where $d_s=2d_f/d_w$.Comment: 34 pages, REVTEX 3.

Biological Characterization of Computationally Designed Analogs of peptide TVFTSWEEYLDWV (Pep2-8) with Increased PCSK9 Antagonistic Activity

The inhibition of the PCSK9/LDLR protein-protein interaction (PPI) is a promising strategy for developing new hypocholesterolemic agents. Recently, new antibodies have been approved for therapy, but the high cost and low patients\u2019 compliance stimulate the development of alternatives. Starting from the structural information available for the complex between PCSK9 and TVFTSWEEYLDWV (Pep2-8) peptide inhibitor and using computational methods, in this work we identified two Pep2-8 analogs as potential inhibitors of the PCSK9/LDLR PPI. Their biological characterization confirmed the theoretical outcomes. Remarkably, the treatment of HepG2 cells with these peptides increased the LDLR protein level on the cellular membrane, with activities that were 100 and 50 times better than the one of Pep2-8 tested at a 50 \u3bcM concentration. Moreover, they were 50 and 5 times more active than Pep2-8 in improving the functional ability of HepG2 cells to uptake extracellular LDL