Diffusion Monte Carlo: Exponential scaling of computational cost for large systems

The computational cost of a Monte Carlo algorithm can only be meaningfully discussed when taking into account the magnitude of the resulting statistical error. Aiming for a fixed error per particle, we study the scaling behavior of the diffusion Monte Carlo method for large quantum systems. We identify the correlation within the population of walkers as the dominant scaling factor for large systems. While this factor is negligible for small and medium sized systems that are typically studied, it ultimately shows exponential scaling. The scaling factor can be estimated straightforwardly for each specific system and we find that is typically only becomes relevant for systems containing more than several hundred atoms.Comment: 6 pages, 3 figures, published by Phys. Rev. B (further changes following referee's reports

Benchmark all-electron ab initio quantum Monte Carlo calculations for small molecules

We study the efficiency, precision and accuracy of all-electron variational and diffusion quantum Monte Carlo calculations using Slater basis sets. Starting from wave functions generated by Hartree-Fock and density functional theory, we describe an algorithm to enforce the electron-nucleus cusp condition by linear projection. For the 55 molecules in the G2 set, the diffusion quantum Monte Carlo calculations recovers an average of 95% of the correlation energy and reproduces bond energies to a mean absolute deviation of 3.2 kcal/mol. Comparing the individual total energies with essentially exact values, we investigate the error cancellation in atomization and chemical reaction path energies, giving additional insight into the sizes of nodal surface errors.Comment: 7 pages, 7 figures, published by J. Chem. Phys (substantial changes after first submission

Contact Dependence of Carrier Injection in Carbon Nanotubes: An Ab Initio Study

We combine ab initio density functional theory with transport calculations to provide a microscopic basis for distinguishing between good and poor metal contacts to nanotubes. Comparing Ti and Pd as examples of different contact metals, we trace back the observed superiority of Pd to the nature of the metal-nanotube hybridization. Based on large scale Landauer transport calculations, we suggest that the `optimum' metal-nanotube contact combines a weak hybridization with a large contact length between the metal and the nanotube.Comment: final version, including minor corrections by edito

Hofstadter butterflies of bilayer graphene

We calculate the electronic spectrum of bilayer graphene in perpendicular magnetic fields nonperturbatively. To accommodate arbitrary displacements between the two layers, we apply a periodic gauge based on singular flux vortices of phase $2\pi$. The resulting Hofstadter-like butterfly plots show a reduced symmetry, depending on the relative position of the two layers against each other. The split of the zero-energy relativistic Landau level differs by one order of magnitude between Bernal and non-Bernal stacking.Comment: updated to refereed and edited versio

Hofstadter butterflies of carbon nanotubes: Pseudofractality of the magnetoelectronic spectrum

The electronic spectrum of a two-dimensional square lattice in a perpendicular magnetic field has become known as the Hofstadter butterfly [Hofstadter, Phys. Rev. B 14, 2239 (1976).]. We have calculated quasi-one-dimensional analogs of the Hofstadter butterfly for carbon nanotubes (CNTs). For the case of single-wall CNTs, it is straightforward to implement magnetic fields parallel to the tube axis by means of zone folding in the graphene reciprocal lattice. We have also studied perpendicular magnetic fields which, in contrast to the parallel case, lead to a much richer, pseudofractal spectrum. Moreover, we have investigated magnetic fields piercing double-wall CNTs and found strong signatures of interwall interaction in the resulting Hofstadter butterfly spectrum, which can be understood with the help of a minimal model. Ubiquitous to all perpendicular magnetic field spectra is the presence of cusp catastrophes at specific values of energy and magnetic field. Resolving the density of states along the tube circumference allows recognition of the snake states already predicted for nonuniform magnetic fields in the two-dimensional electron gas. An analytic model of the magnetic spectrum of electrons on a cylindrical surface is used to explain some of the results.Comment: 14 pages, 12 figures update to published versio

Diffusion and localization in carbon nanotubes and graphene nanoribbons

We study transport length scales in carbon nanotubes and graphene ribbons under the influence of Anderson disorder. We present generalized analytical expressions for the density of states, the elastic mean free path and the localization length in arbitrarily structured quantum wires. These allow us to analyze the electrical response over the full energy range, including the regions around van Hove singularies, traditionally difficult to access by alternative approaches. Comparing with the results of numerical simulations, we demonstrate that both the diffusive and the localized regime are well represented by the analytical approximations over a wide range of the energy spectrum. The approach works well for both metallic and semiconducting nanotubes and nanoribbons but breaks down near the edge states of zigzag ribbons

Modeling extended contacts to nanotube and graphene devices

Carrier injection into carbon nanotubes and graphene nanoribbons, contacted by a metal coating over an arbitrary length, is studied by various means: Minimal models allow for exact analytic solutions which can be transferred to the original system with high precision. Microscopic ab initio calculations of the electronic structure at the carbon-metal interface allow us to extract -- for Ti and Pd as contacting materials -- realistic parameters, which are then used in large scale tight-binding models for transport calculations. The results are shown to be robust against nonepitaxially grown electrodes and general disorder at the interface, as well as various refinements of the model.Comment: 13 pages, 13 figure

Structural Bootstrapping - A Novel, Generative Mechanism for Faster and More Efficient Acquisition of Action-Knowledge

eISSN: 1943-0612Humans, but also robots, learn to improve their behavior. Without existing knowledge, learning either needs to be explorative and, thus, slow or-to be more efficient-it needs to rely on supervision, which may not always be available. However, once some knowledge base exists an agent can make use of it to improve learning efficiency and speed. This happens for our children at the age of around three when they very quickly begin to assimilate new information by making guided guesses how this fits to their prior knowledge. This is a very efficient generative learning mechanism in the sense that the existing knowledge is generalized into as-yet unexplored, novel domains. So far generative learning has not been employed for robots and robot learning remains to be a slow and tedious process. The goal of the current study is to devise for the first time a general framework for a generative process that will improve learning and which can be applied at all different levels of the robot's cognitive architecture. To this end, we introduce the concept of structural bootstrapping-borrowed and modified from child language acquisition-to define a probabilistic process that uses existing knowledge together with new observations to supplement our robot's data-base with missing information about planning-, object-, as well as, action-relevant entities. In a kitchen scenario, we use the example of making batter by pouring and mixing two components and show that the agent can efficiently acquire new knowledge about planning operators, objects as well as required motor pattern for stirring by structural bootstrapping. Some benchmarks are shown, too, that demonstrate how structural bootstrapping improves performanceTaikomosios informatikos katedraVytauto Didžiojo universiteta

Quantum transport in carbon-based nanostructures

The electronic structure and the quantum transport properties of graphene, carbon nanotubes and graphene nanoribbons are studied using analytical and numerical tools. Special care is taken in considering fundamental questions of high experimental relevance and in relating the results to experiments. The main focus of the work is on numerical calculations based on the tight-binding description of electrons, also integrating the results of microscopic ab initio calculations and including several minimal models at various degrees of detail. Transport calculations are done based on the Landauer formalism of linear conductance, using Green function decimation algorithms for the efficient handling of large systems of up to thousands of atoms. Following three detailed theoretical introductory chapters, the work is organized in four parts: One chapter on the effects of realistically modelled metallic contacts on the transport properties of nanotubes and -ribbons, including a section dealing with ballistic magnetoresistance effects. Another chapter about the mesoscopic length scales in disordered and defective carbon systems. A chapter on multilayer carbon systems that deals with issues of approximate momentum conservation in incommensurate systems. Finally, a chapter on the effects of external magnetic fields on the electronic structure of carbon systems. The appendices give a precise derivation of the theoretical tools used in the work and include fully documented source code implementations of the relevant algorithms used throughout the project