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Roman Martonák

Publications and source records attributed to Roman Martonák.

6 recordsLinked to original sources
PubMed2006

Crystal structure transformations in SiO2 from classical and ab initio metadynamics.

Silica is the main component of the Earth's crust and is also of great relevance in many branches of materials science and technology. Its phase diagram is rather intricate and exhibits many different crystalline phases. The reported propensity to amorphization and the strong influence on the outcome of the initial structure and of the pressurization protocol indicate the presence of metastability and large kinetic barriers. As a consequence, theory is also faced with great difficulties and our understanding of the complex transformation mechanisms is still very sketchy despite a large number of simulations. Here, we introduce a substantial improvement of the metadynamics method, which finally brings simulations in close agreement with experiments. We unveil the subtle and non-intuitive stepwise mechanism of the pressure-induced transformation of fourfold-coordinated alpha-quartz into sixfold-coordinated stishovite at room temperature. We also predict that on compression fourfold-coordinated coesite will transform into the post-stishovite alpha-PbO2-type phase. The new method is far more efficient than previous methods, and for the first time the study of complex structural phase transitions with many intermediates is within the reach of molecular dynamics simulations. This insight will help in designing new experimental protocols capable of steering the system towards the desired transition.

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PubMed2005

Anisotropy of Earth's D'' layer and stacking faults in the MgSiO3 post-perovskite phase.

The post-perovskite phase of (Mg,Fe)SiO3 is believed to be the main mineral phase of the Earth's lowermost mantle (the D'' layer). Its properties explain numerous geophysical observations associated with this layer-for example, the D'' discontinuity, its topography and seismic anisotropy within the layer. Here we use a novel simulation technique, first-principles metadynamics, to identify a family of low-energy polytypic stacking-fault structures intermediate between the perovskite and post-perovskite phases. Metadynamics trajectories identify plane sliding involving the formation of stacking faults as the most favourable pathway for the phase transition, and as a likely mechanism for plastic deformation of perovskite and post-perovskite. In particular, the predicted slip planes are {010} for perovskite (consistent with experiment) and {110} for post-perovskite (in contrast to the previously expected {010} slip planes). Dominant slip planes define the lattice preferred orientation and elastic anisotropy of the texture. The {110} slip planes in post-perovskite require a much smaller degree of lattice preferred orientation to explain geophysical observations of shear-wave anisotropy in the D'' layer.

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PubMed2004

Quantum annealing of the traveling-salesman problem.

We propose a path-integral Monte Carlo quantum annealing scheme for the symmetric traveling-salesman problem, based on a highly constrained Ising-like representation, and we compare its performance against standard thermal simulated annealing. The Monte Carlo moves implemented are standard, and consist in restructuring a tour by exchanging two links (two-opt moves). The quantum annealing scheme, even with a drastically simple form of kinetic energy, appears definitely superior to the classical one, when tested on a 1002-city instance of the standard TSPLIB.

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PubMed2002

Theory of quantum annealing of an Ising spin glass.

Probing the lowest energy configuration of a complex system by quantum annealing was recently found to be more effective than its classical, thermal counterpart. By comparing classical and quantum Monte Carlo annealing protocols on the two-dimensional random Ising model (a prototype spin glass), we confirm the superiority of quantum annealing relative to classical annealing. We also propose a theory of quantum annealing based on a cascade of Landau-Zener tunneling events. For both classical and quantum annealing, the residual energy after annealing is inversely proportional to a power of the logarithm of the annealing time, but the quantum case has a larger power that makes it faster.

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