The one-dimensional Hubbard model with open ends: Universal divergent contributions to the magnetic susceptibility

The magnetic susceptibility of the one-dimensional Hubbard model with open boundary conditions at arbitrary filling is obtained from field theory at low temperatures and small magnetic fields, including leading and next-leading orders. Logarithmic contributions to the bulk part are identified as well as algebraic-logarithmic divergences in the boundary contribution. As a manifestation of spin-charge separation, the result for the boundary part at low energies turns out to be independent of filling and interaction strength and identical to the result for the Heisenberg model. For the bulk part at zero temperature, the scale in the logarithms is determined exactly from the Bethe ansatz. At finite temperature, the susceptibility profile as well as the Friedel oscillations in the magnetisation are obtained numerically from the density-matrix renormalisation group applied to transfer matrices. Agreement is found with an exact asymptotic expansion of the relevant correlation function.Comment: 30 pages, 8 figures, reference adde

Lattice vs. continuum theory of the periodic Heisenberg chain

We consider the detailed structure of low energy excitations in the periodic spin-1/2 XXZ Heisenberg chain. By performing a perturbative calculation of the non-linear corrections to the Gaussian model, we determine the exact coefficients of asymptotic expansions in inverse powers of the system length N for a large number of low-lying excited energy levels. This allows us to calculate eigenenergies of the lattice model up to order order N^-4, without having to solve the Bethe Ansatz equations. At the same time, it is possible to express the exact eigenstates of the lattice model in terms of bosonic modes.Comment: 17 pages, 8 Figures. The latest version can be found at http://www.physik.uni-kl.de/eggert/papers/index.htm

Bethe Ansatz study of one-dimensional Bose and Fermi gases with periodic and hard wall boundary conditions

We extend the exact periodic Bethe Ansatz solution for one-dimensional bosons and fermions with delta-interaction and arbitrary internal degrees of freedom to the case of hard wall boundary conditions. We give an analysis of the ground state properties of fermionic systems with two internal degrees of freedom, including expansions of the ground state energy in the weak and strong coupling limits in the repulsive and attractive regimes.Comment: 27 pages, 6 figures, key reference added, typos correcte

Study of the island morphology at the early stages of Fe/Mo(110) MBE growth

We present theoretical study of morphology of Fe islands grown at Mo(110) surface in sub-monolayer MBE mode. We utilize atomistic SOS model with bond counting, and interactions of Fe adatom up to third nearest neighbors. We performed KMC simulations for different values of adatom interactions and varying temperatures. We have found that, while for the low temperature islands are fat fractals, for the temperature 500K islands have faceted rhombic-like shape. For the higher temperature, islands acquire a rounded shape. In order to evaluated qualitatively morphological changes, we measured averaged aspect ration of islands. We calculated dependence of the average aspect ratio on the temperature, and on the strength of interactions of an adatom with neighbors.Comment: 6 pages, 6 figures. Proceedings of 11-th Symposium on Surface Physics, Prague 200

Biological age estimation using circulating blood biomarkers

Biological age captures physiological deterioration better than chronological age and is amenable to interventions. Blood-based biomarkers have been identified as suitable candidates for biological age estimation. This study aims to improve biological age estimation using machine learning models and a feature-set of 60 circulating biomarkers available from the UK Biobank (n = 306,116). We implement an Elastic-Net derived Cox model with 25 selected biomarkers to predict mortality risk (C-Index = 0.778; 95% CI [0.767–0.788]), which outperforms the well-known blood-biomarker based PhenoAge model (C-Index = 0.750; 95% CI [0.739–0.761]), providing a C-Index lift of 0.028 representing an 11% relative increase in predictive value. Importantly, we then show that using common clinical assay panels, with few biomarkers, alongside imputation and the model derived on the full set of biomarkers, does not substantially degrade predictive accuracy from the theoretical maximum achievable for the available biomarkers. Biological age is estimated as the equivalent age within the same-sex population which corresponds to an individual’s mortality risk. Values ranged between 20-years younger and 20-years older than individuals’ chronological age, exposing the magnitude of ageing signals contained in blood markers. Thus, we demonstrate a practical and cost-efficient method of estimating an improved measure of Biological Age, available to the general population

Soft versus Hard Dynamics for Field-driven Solid-on-Solid Interfaces

Analytical arguments and dynamic Monte Carlo simulations show that the microstructure of field-driven Solid-on-Solid interfaces depends strongly on the dynamics. For nonconservative dynamics with transition rates that factorize into parts dependent only on the changes in interaction energy and field energy, respectively (soft dynamics), the intrinsic interface width is field-independent. For non-factorizing rates, such as the standard Glauber and Metropolis algorithms (hard dynamics), it increases with the field. Consequences for the interface velocity and its anisotropy are discussed.Comment: 9 pages LaTex with imbedded .eps figs. Minor revision

Ground-state properties of the attractive one-dimensional Bose-Hubbard model

We study the ground state of the attractive one-dimensional Bose-Hubbard model, and in particular the nature of the crossover between the weak interaction and strong interaction regimes for finite system sizes. Indicator properties like the gap between the ground and first excited energy levels, and the incremental ground-state wavefunction overlaps are used to locate different regimes. Using mean-field theory we predict that there are two distinct crossovers connected to spontaneous symmetry breaking of the ground state. The first crossover arises in an analysis valid for large L with finite N, where L is the number of lattice sites and N is the total particle number. An alternative approach valid for large N with finite L yields a second crossover. For small system sizes we numerically investigate the model and observe that there are signatures of both crossovers. We compare with exact results from Bethe ansatz methods in several limiting cases to explore the validity for these numerical and mean-field schemes. The results indicate that for finite attractive systems there are generically three ground-state phases of the model.Comment: 17 pages, 12 figures, Phys.Rev.B(accepted), minor changes and updated reference

Effects of Lateral Diffusion on the Dynamics of Desorption

The adsorbate dynamics during simultaneous action of desorption and lateral adsorbate diffusion is studied in a simple lattice-gas model by kinetic Monte Carlo simulations. It is found that the action of the coverage-conserving diffusion process during the course of the desorption has two distinct, competing effects: a general acceleration of the desorption process, and a coarsening of the adsorbate configuration through Ostwald ripening. The balance between these two effects is governed by the structure of the adsorbate layer at the beginning of the desorption process

Local Inhomogeneity in Asymmetric Simple Exclusion Processes with Extended Objects

Totally asymmetric simple exclusion processes (TASEP) with particles which occupy more than one lattice site and with a local inhomogeneity far away from the boundaries are investigated. These non-equilibrium processes are relevant for the understanding of many biological and chemical phenomena. The steady-state phase diagrams, currents, and bulk densities are calculated using a simple approximate theory and extensive Monte Carlo computer simulations. It is found that the phase diagram for TASEP with a local inhomogeneity is qualitatively similar to homogeneous models, although the phase boundaries are significantly shifted. The complex dynamics is discussed in terms of domain-wall theory for driven lattice systems.Comment: 11 pages, 5 figure

Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids

By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation, we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former, and the other in a fragile glass former. At low temperatures, both models exhibit violation of the Stokes-Einstein relation, $D\sim\tau^{-1}$, where $D$ is the self diffusion constant and $\tau$ is the structural relaxation time. In the strong case, the violation is sensitive to dimensionality $d$, going as $D\sim\tau^{-2/3}$ for $d=1$, and as $D\sim \tau^{-0.95}$ for $d=3$. In the fragile case, however, we argue that dimensionality dependence is weak, and show that for $d=1$, $D \sim \tau^{-0.73}$. This scaling for the fragile case compares favorably with the results of a recent experimental study for a three-dimensional fragile glass former.Comment: 7 pages, 7 figures, submitted to Phys. Rev.