2-Dimensional Polymers Confined in a Strip

Single two dimensional polymers confined to a strip are studied by Monte Carlo simulations. They are described by N-step self-avoiding random walks on a square lattice between two parallel hard walls with distance 1 << D << N^\nu (\nu = 3/4 is the Flory exponent). For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. We measure the densities of monomers and of end points as functions of the distance from the walls, the longitudinal extent of the chain, and the forces exerted on the walls. Their scaling with D and the universal ratio between force and monomer density at the wall are compared to theoretical predictions.Comment: 5 pages RevTex, 7 figures include

Spin-state crossover and hyperfine interactions of ferric iron in MgSiO3_3 perovskite

Using density functional theory plus Hubbard $U$ calculations, we show that the ground state of (Mg,Fe)(Si,Fe)O$_3$ perovskite, a major mineral phase in the Earth's lower mantle, has high-spin ferric iron ($S=5/2$) at both the dodecahedral (A) and octahedral (B) site. As the pressure increases, the B-site iron undergoes a spin-state crossover to the low-spin state ($S=1/2$), while the A-site iron remains in the high-spin state. Our calculation shows that the B-site spin-state crossover in the pressure range of 40-70 GPa is accompanied by a noticeable volume reduction and an increase in quadrupole splitting, consistent with recent X-ray diffraction and M\"ossbauer spectroscopy measurements. The volume reduction leads to a significant softening in the bulk modulus, which suggests a possible source of seismic velocity anomalies in the lower mantle.Comment: 11 pages, 4 figures, 1 tabl

Monte Carlo Protein Folding: Simulations of Met-Enkephalin with Solvent-Accessible Area Parameterizations

Treating realistically the ambient water is one of the main difficulties in applying Monte Carlo methods to protein folding. The solvent-accessible area method, a popular method for treating water implicitly, is investigated by means of Metropolis simulations of the brain peptide Met-Enkephalin. For the phenomenological energy function ECEPP/2 nine atomic solvation parameter (ASP) sets are studied that had been proposed by previous authors. The simulations are compared with each other, with simulations with a distance dependent electrostatic permittivity $\epsilon (r)$, and with vacuum simulations ($\epsilon =2$). Parallel tempering and a recently proposed biased Metropolis technique are employed and their performances are evaluated. The measured observables include energy and dihedral probability densities (pds), integrated autocorrelation times, and acceptance rates. Two of the ASP sets turn out to be unsuitable for these simulations. For all other sets, selected configurations are minimized in search of the global energy minima. Unique minima are found for the vacuum and the $\epsilon(r)$ system, but for none of the ASP models. Other observables show a remarkable dependence on the ASPs. In particular, autocorrelation times vary dramatically with the ASP parameters. Three ASP sets have much smaller autocorrelations at 300 K than the vacuum simulations, opening the possibility that simulations can be speeded up vastly by judiciously chosing details of the forceComment: 10 pages; published in "NIC Symposium 2004", eds. D. Wolf at el. (NIC, Juelich, 2004

Polymers Confined between Two Parallel Plane Walls

Single three dimensional polymers confined to a slab, i.e. to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by $N$-step walks on a simple cubic lattice confined to the region $1 \le z \le D$. The simulations cover both regions $D > R_F$ (where $R_F \sim N^\nu$ is the Flory radius, with $\nu \approx 0.587$), as well as the cross-over region in between. Chain lengths are up to $N=80,000$, slab widths up to D=120. In order to test the analysis program and to check for finite size corrections, we actually studied three different models: (a) Ordinary random walks (mimicking $\Theta$-polymers); (b) Self-avoiding walks (SAW); and (c) Domb-Joyce walks with the self-repulsion tuned to the point where finite size corrections for free (unrestricted) chains are minimal. For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. In addition to the partition sum (which gives us a direct estimate of the forces exerted onto the walls), we measure the density profiles of monomers and of end points transverse to the slab, and the radial extent of the chain parallel to the walls. All scaling laws and some of the universal amplitude ratios are compared to theoretical predictions.Comment: 8 pages, 14 figures include

Nuclear-spin-induced localization of the edge states in two-dimensional topological insulators

We investigate the influence of nuclear spins on the resistance of helical edge states of two-dimensional topological insulators (2DTIs). Via the hyperfine interaction, nuclear spins allow electron backscattering, otherwise forbidden by time reversal symmetry. We identify two backscattering mechanisms, depending on whether the nuclear spins are ordered or not. Their temperature dependence is distinct but both give resistance, which increases with the edge length, decreasing temperature, and increasing strength of the electron-electron interaction. Overall, we find that the nuclear spins will typically shut down the conductance of the 2DTI edges at zero temperature.Comment: 5 pages, 3 figures, revised version accepted for publication in Phys. Rev.

Effects of nuclear spins on the transport properties of the edge of two-dimensional topological insulators

The electrons in the edge channels of two-dimensional topological insulators can be described as a helical Tomonaga-Luttinger liquid. They couple to nuclear spins embedded in the host materials through the hyperfine interaction, and are therefore subject to elastic spin-flip backscattering on the nuclear spins. We investigate the nuclear-spin-induced edge resistance due to such backscattering by performing a renormalization-group analysis. Remarkably, the effect of this backscattering mechanism is stronger in a helical edge than in nonhelical channels, which are believed to be present in the trivial regime of InAs/GaSb quantum wells. In a system with sufficiently long edges, the disordered nuclear spins lead to an edge resistance which grows exponentially upon lowering the temperature. On the other hand, electrons from the edge states mediate an anisotropic Ruderman-Kittel-Kasuya-Yosida nuclear spin-spin interaction, which induces a spiral nuclear spin order below the transition temperature. We discuss the features of the spiral order, as well as its experimental signatures. In the ordered phase, we identify two backscattering mechanisms, due to charge impurities and magnons. The backscattering on charge impurities is allowed by the internally generated magnetic field, and leads to an Anderson-type localization of the edge states. The magnon-mediated backscattering results in a power-law resistance, which is suppressed at zero temperature. Overall, we find that in a sufficiently long edge the nuclear spins, whether ordered or not, suppress the edge conductance to zero as the temperature approaches zero.Comment: 20 pages, 11 figures; revised version accepted for publication in Phys. Rev.

Growth Algorithms for Lattice Heteropolymers at Low Temperatures

Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are proposed and tested on simple models of lattice heteropolymers. Both are found to outperform not only the previous version of PERM, but also all other stochastic algorithms which have been employed on this problem, except for the core directed chain growth method (CG) of Beutler & Dill. In nearly all test cases they are faster in finding low-energy states, and in many cases they found new lowest energy states missed in previous papers. The CG method is superior to our method in some cases, but less efficient in others. On the other hand, the CG method uses heavily heuristics based on presumptions about the hydrophobic core and does not give thermodynamic properties, while the present method is a fully blind general purpose algorithm giving correct Boltzmann-Gibbs weights, and can be applied in principle to any stochastic sampling problem.Comment: 9 pages, 9 figures. J. Chem. Phys., in pres