Fluctuation Analysis of the Atmospheric Energy Cycle

The atmosphere gains available potential energy by solar radiation and dissipates kinetic energy mainly in the atmospheric boundary layer. We analyze the fluctuations of the global mean energy cycle defined by Lorenz (1955) in a simulation with a simplified hydrostatic model. The energy current densities are well approximated by the generalized Gumbel distribution (Bramwell, Holdsworth and Pinton, 1998) and the Generalized Extreme Value (GEV) distribution. In an attempt to assess the fluctuation relation of Evans, Cohen, and Morriss (1993) we define entropy production by the injected power and use the GEV location parameter as a reference state. The fluctuation ratio reveals a linear behavior in a finite range.Comment: 17 pages, 5 figure

Dynamical and Topological Properties of the Kitaev Model in a [111] Magnetic Field

The Kitaev model exhibits a Quantum Spin Liquid hosting emergent fractionalized excitations. We study the Kitaev model on the honeycomb lattice coupled to a magnetic field along the [111] axis. Utilizing large scale matrix product based numerical models, we confirm three phases with transitions at different field strengths depending on the sign of the Kitaev exchange: a non-abelian topological phase at low fields, an enigmatic intermediate regime only present for antiferromagnetic Kitaev exchange, and a field-polarized phase. For the topological phase, we numerically observe the expected cubic scaling of the gap and extract the quantum dimension of the non-Abelian anyons. Furthermore, we investigate dynamical signatures of the topological and the field-polarized phase using a matrix product operator based time evolution method.Comment: Changed convention to be in accordance with published articl

Multi-scale modelling of macromolecular conformational changes

Modelling protein flexibility and plasticity is computationally challenging but important for understanding the function of biological systems. Furthermore, it has great implications for the prediction of (macro) molecular complex formation. Recently, coarse-grained normal mode approaches have emerged as efficient alternatives for investigating large-scale conformational changes for which more accurate methods like MD simulation are limited due to their computational burden. We have developed a Normal Mode based Simulation (NMSim) approach for efficient conformation generation of macromolecules. Combinations of low energy normal modes are used to guide a simulation pathway, whereas an efficient constraints correction approach is applied to generate stereochemically allowed conformations. Non-covalent bonds like hydrogen bonds and hydrophobic tethers and phi-psi favourable regions are also modelled as constraints. Conformations from our approach were compared with a 10 ns MD trajectory of lysozyme. A 2-D RMSD plot shows a good overlap of conformational space, and rms fluctuations of residues show a correlation coefficient of 0.78 between the two sets of conformations. Furthermore, a comparison of NMSim simulations starting from apo structures of different proteins show that ligand-bound conformations can be sampled for those cases where conformational changes are mainly correlated, e.g., domain-like motion in adenylate kinase. Efforts are currently being made to also model localized but functionally important motions for protein binding pockets and protein-protein interfaces using relevant normal mode selection criteria and implicit rotamer basin creation

Dynamics of the Kitaev-Heisenberg Model

We introduce a matrix-product state based method to efficiently obtain dynamical response functions for two-dimensional microscopic Hamiltonians, which we apply to different phases of the Kitaev-Heisenberg model. We find significant broad high energy features beyond spin-wave theory even in the ordered phases proximate to spin liquids. This includes the phase with zig-zag order of the type observed in $\alpha$-RuCl$_3$, where we find high energy features like those seen in inelastic neutron scattering experiments. Our results provide an example of a natural path for proximate spin liquid features to arise at high energies above a conventionally ordered state, as the diffuse remnants of spin-wave bands intersect to yield a broad peak at the Brillouin zone center.Comment: 7 pages, 8 figure

Inflation word entropy for semi-compatible random substitutions

Gohlke P. Inflation word entropy for semi-compatible random substitutions. Monatshefte für Mathematik. 2020;192:93-110.We introduce the concept of inflation word entropy for random substitutions with a constant and primitive substitution matrix. Previous calculations of the topological entropy of such systems implicitly used this concept and established equality of topological entropy and inflation word entropy, relying on ad hoc methods. We present a unified scheme, proving that inflation word entropy and topological entropy in fact coincide. The topological entropy is approximated by a converging series of upper and lower bounds which, in many cases, lead to an analytic expression

Quantum spin liquid signatures in Kitaev-like frustrated magnets

Motivated by recent experiments on $\alpha$-RuCl$_3$, we investigate a possible quantum spin liquid ground state of the honeycomb-lattice spin model with bond-dependent interactions. We consider the $K-\Gamma$ model, where $K$ and $\Gamma$ represent the Kitaev and symmetric-anisotropic interactions between spin-1/2 moments on the honeycomb lattice. Using the infinite density matrix renormalization group (iDMRG), we provide compelling evidence for the existence of quantum spin liquid phases in an extended region of the phase diagram. In particular, we use transfer matrix spectra to show the evolution of two-particle excitations with well-defined two-dimensional dispersion, which is a strong signature of quantum spin liquid. These results are compared with predictions from Majorana mean-field theory and used to infer the quasiparticle excitation spectra. Further, we compute the dynamical structure factor using finite size cluster computations and show that the results resemble the scattering continuum seen in neutron scattering experiments on $\alpha$-RuCl$_3$. We discuss these results in light of recent and future experiments.Comment: Modified manuscript: 17 pages, 21 figure