Low-frequency expansion for probability amplitudes: An alternative approach to certain intramolecular dynamics problems

We present an algorithm to determine the averaged time evolution of the probability amplitude for a nonstationary state in a quantum mechanical system. The algorithm is based on a low‐frequency expansion of the probability amplitude and is related to the generalized moment expansion method which has been applied successfully to the description of dynamic correlation functions in stochastic systems. It is shown that the proposed algorithm gives excellent results for the description of quantum beats in the time evolution of the occupation probability for a nonstationary state in model systems. The relation of the algorithm to other theoretical approaches and the relevance for the description of intramolecular energy transfer processes is discussed

Side-chain and backbone ordering in Homopolymers

In order to study the relation between backbone and side chain ordering in proteins, we have performed multicanonical simulations of deka-peptide chains with various side groups. Glu10, Gln10, Asp10, Asn10, and Lys10 were selected to cover a wide variety of possible interactions between the side chains of the monomers. All homopolymers undergo helix-coil transitions. We found that peptides with long side chains that are capable of hydrogen bonding, i.e. Glu10, and Gln10, exhibit a second transition at lower temperatures connected with side chain ordering. This occurs in gas phase as well as in solvent, although the character of the side chain structure is different in each case. However, in polymers with short side chains capable of hydrogen bonding, i.e. Asp10 and Asn10, side chain ordering takes place over a wide temperature range and exhibits no phase transition like character. Moreover, non-backbone hydrogen bonds show enhanced formation and fluctuations already at the helix-coil transition temperature, indicating competition between side chain and backbone hydrogen bond formation. Again, these results are qualitatively independent of the environment. Side chain ordering in Lys10, whose side groups are long and polar, also takes place over a wide temperature range and exhibits no phase transition like character in both environments. Reasons for the observed chain length threshold and consequences from these results for protein folding are discussed.Comment: 12 pages,11 figure

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

Optimizing Replica Exchange Moves For Molecular Dynamics

In this short note we sketch the statistical physics framework of the replica exchange technique when applied to molecular dynamics simulations. In particular, we draw attention to generalized move sets that allow a variety of optimizations as well as new applications of the method.Comment: 4 pages, 3 figures; revised version (1 figure added), PRE in pres

Violating conformal invariance: Two-dimensional clusters grafted to wedges, cones, and branch points of Riemann surfaces

We present simulations of 2-d site animals on square and triangular lattices in non-trivial geomeLattice animals are one of the few critical models in statistical mechanics violating conformal invariance. We present here simulations of 2-d site animals on square and triangular lattices in non-trivial geometries. The simulations are done with the newly developed PERM algorithm which gives very precise estimates of the partition sum, yielding precise values for the entropic exponent $\theta$ ($Z_N \sim \mu^N N^{-\theta}$). In particular, we studied animals grafted to the tips of wedges with a wide range of angles $\alpha$, to the tips of cones (wedges with the sides glued together), and to branching points of Riemann surfaces. The latter can either have $k$ sheets and no boundary, generalizing in this way cones to angles $\alpha > 360$ degrees, or can have boundaries, generalizing wedges. We find conformal invariance behavior, $\theta \sim 1/\alpha$, only for small angles ($\alpha \ll 2\pi$), while $\theta \approx const -\alpha/2\pi$ for $\alpha \gg 2\pi$. These scalings hold both for wedges and cones. A heuristic (non-conformal) argument for the behavior at large $\alpha$ is given, and comparison is made with critical percolation.Comment: 4 pages, includes 3 figure

Backbone and Sidechain Ordering in a small Protein

We investigate the relation between backbone and side-chain ordering in a small protein. For this purpos e we have performed multicanonical simulations of the villin headpiece subdomain HP-36, an often used to y model in protein studies. Concepts of circular statistics are introduced to analyze side-chain fluctuations. In contrast to earlier studies on homopolypeptides (Wei et al., J. Phys. Chem. B, 111 (2007) 4244) we do not find collective effects leading to a separate transition. Rather, side-chain ordering is spread over a wide temperature range. Our results indicate a thermal hierarchy of ordering events, with side-chain ordering appearing at temperatures below the helix-coil transition but above the folding transition. We conjecture that this thermal hierarchy reflects an underlying temporal order, and that side-chain ordering facilitates the search for the correct backbone topology.Comment: accepted in J. Chem. Phy

Heat Conduction and Entropy Production in a One-Dimensional Hard-Particle Gas

We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses. We correct several claims in the recent literature based on much smaller simulations. Both for boundary conditions with two heat baths at different temperatures at both ends and from heat current autocorrelations in equilibrium we find heat conductivities kappa to diverge with the number N of particles. These depended very strongly on the mass ratios, and extrapolation to N -> infty resp. t -> infty is difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law kappa ~ N^alpha with alpha approx 0.33. This suggests a relation to the Kardar-Parisi-Zhang model. We finally show that the hard-point gas with periodic boundary conditions is not chaotic in the usual sense and discuss why the system, when kept out of equilibrium, leads nevertheless to energy dissipation and entropy production.Comment: 4 pages (incl. 5 figures), RevTe