Stefan Schnabel

Microcanonical entropy inflection points: key to systematic understanding of transitions in finite systems.

We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends toward the thermodynamic limit, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. We demonstrate the power of this method through application to the long-standing problem of liquid-solid transitions in elastic, flexible homopolymers.

Elastic Lennard-Jones polymers meet clusters: Differences and similarities

We investigate solid-solid and solid-liquid transitions of elastic flexible off-lattice polymers with Lennard-Jones monomer-monomer interaction and anharmonic springs by means of sophisticated variants of multicanonical Monte Carlo methods. We find that the low-temperature behavior depends strongly and nonmonotonically on the system size and exhibits broad similarities to unbound atomic clusters. Particular emphasis is dedicated to the classification of icosahedral and nonicosahedral low-energy polymer morphologies.

Surface effects in the crystallization process of elastic flexible polymers

Investigating thermodynamic properties of liquid–solid transitions of flexible homopolymers with elastic bonds by means of multicanonical Monte Carlo simulations, we find crystalline conformations that resemble ground-state structures of Lennard-Jones clusters. This allows us to set up a structural classification scheme for finite-length flexible polymers and their freezing mechanism in analogy to atomic cluster formation. Crystals of polymers with ‘magic length’ turn out to be perfectly icosahedral.

Advanced multicanonical Monte Carlo methods for efficient simulations of nucleation processes of polymers

The investigation of freezing transitions of single polymers is computationally demanding, since surface effects dominate the nucleation process. In recent studies we have systematically shown that the freezing properties of flexible, elastic polymers depend on the precise chain length. Performing multicanonical Monte Carlo simulations, we faced several computational challenges in connection with liquid-solid and solid-solid transitions. For this reason, we developed novel methods and update strategies to overcome the arising problems. We introduce novel Monte Carlo moves and two extensions to the multicanonical method.

Two-state folding, folding through intermediates, and metastability in a minimalistic hydrophobic-polar model for proteins.

Within the frame of an effective, coarse-grained hydrophobic-polar protein model, we employ multicanonical Monte Carlo simulations to investigate free-energy landscapes and folding channels of exemplified heteropolymer sequences, which are permutations of each other. Despite the simplicity of the model, the knowledge of the free-energy landscape in dependence of a suitable system order parameter enables us to reveal complex folding characteristics known from real bioproteins and synthetic peptides, such as two-state folding, folding through weakly stable intermediates, and glassy metastability.

Best-case performance of quantum annealers on native spin-glass benchmarks: How chaos can affect success probabilities

Recent tests performed on the D-Wave Two quantum annealer have revealed no clear evidence of speedup over conventional silicon-based technologies. Here, we present results from classical parallel-tempering Monte Carlo simulations combined with isoenergetic cluster moves of the archetypal benchmark problem-an Ising spin glass-on the native chip topology. Using realistic uncorrelated noise models for the D-Wave Two quantum annealer, we study the best-case resilience, i.e., the probability that the ground-state configuration is not affected by random fields and random-bond fluctuations found on the chip. We thus compute classical upper-bound success probabilities for different types of disorder used in the benchmarks and predict that an increase in the number of qubits will require either error correction schemes or a drastic reduction of the intrinsic noise found in these devices. We outline strategies to develop robust, as well as hard benchmarks for quantum annealing devices, as well as any other computing paradigm affected by noise.

Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: a comparison for elastic flexible polymers.

For the estimation of transition points of finite elastic, flexible polymers with chain lengths from 13 to 309 monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification of transition points in finite systems, which is typically impossible in the conventional canonical analysis of thermodynamic quantities.

Identification of characteristic protein folding channels in a coarse-grained hydrophobic-polar peptide model

Folding channels and free-energy landscapes of hydrophobic-polar heteropolymers are discussed on the basis of a minimalistic off-lattice coarse-grained model. We investigate how rearrangements of hydrophobic and polar monomers in a heteropolymer sequence lead to completely different folding behaviors. Studying three exemplified sequences with the same content of hydrophobic and polar residues, we can reproduce within this simple model two-state folding, folding through intermediates, as well as metastability.

Effects Of Stiffness On Short, Semiflexible Homopolymer Chains

Conformational and transition behavior of finite, semiflexible homopolymers is studied using an extension of the Wang–Landau algorithm. Generation of a flat distribution in the sampling parameters energy and stiffness allows for efficient investigation of transitions between various conformational phases. Of particular importance is the ability to predict behavior for a given stiffness value, where three classes of minimum energy conformations are expected: Solid-globular, rod-like and toroidal. We present first results highlighting the behavior of a single N = 20 length chain.

Dynamic greedy algorithms for the Edwards–Anderson model

Abstract To provide a novel tool for the investigation of the energy landscape of the Edwards–Anderson spin-glass model we introduce an algorithm that allows an efficient execution of a greedy optimization based on data from a previously performed optimization for a similar configuration. As an application we show how the technique can be used to perform higher-order greedy optimizations and simulated annealing searches with improved performance.