Non-Abelian statistics as a Berry phase in exactly solvable models

We demonstrate how to directly study non-Abelian statistics for a wide class of exactly solvable many-body quantum systems. By employing exact eigenstates to simulate the adiabatic transport of a model's quasiparticles, the resulting Berry phase provides a direct demonstration of their non-Abelian statistics. We apply this technique to Kitaev's honeycomb lattice model and explicitly demonstrate the existence of non-Abelian Ising anyons confirming the previous conjectures. Finally, we present the manipulations needed to transport and detect the statistics of these quasiparticles in the laboratory. Various physically realistic system sizes are considered and exact predictions for such experiments are provided.Comment: 10 pages, 3 figures. To appear in New Journal of Physic

Topological Degeneracy and Vortex Manipulation in Kitaev's Honeycomb Model

The classification of loop symmetries in Kitaev's honeycomb lattice model provides a natural framework to study the Abelian topological degeneracy. We derive a perturbative low-energy effective Hamiltonian that is valid to all orders of the expansion and for all possible toroidal configurations. Using this form we demonstrate at what order the system's topological degeneracy is lifted by finite size effects and note that in the thermodynamic limit it is robust to all orders. Further, we demonstrate that the loop symmetries themselves correspond to the creation, propagation, and annihilation of fermions. We note that these fermions, made from pairs of vortices, can be moved with no additional energy cost

Sedimentation dynamics of spherical particles in confined geometries

We study the steady-state dynamics of sedimenting non-Brownian particles in confined geometries with full hydrodynamic interactions at small but finite Reynolds numbers. We employ extensive computer simulations using a method where a continuum liquid phase is coupled through Stokesian friction to a discrete particle phase. In particular, we consider a sedimentation box which is otherwise periodic except that it is confined by two parallel walls parallel to gravity with a spacing Lx. By systematically varying Lx we explore the change in dynamics from a quasi-two-dimensional (2D) case to a three-dimensional case. We find that in such confined geometries there is a depletion of particle number density at the walls for small volume fractions, while for large volume fractions there is an excess number of particles at the walls. For the average sedimentation velocity, we find that the Richardson-Zaki law is well obeyed but the decrease of the velocity for dilute systems is slower for smaller values of Lx. We study the anisotropy of the velocity fluctuations and find that in the direction of gravity there is excellent agreement with the predicted scaling with respect to Lx. We also find that the behavior of the corresponding diffusion coefficients as a function of Lx is qualitatively different in the direction parallel to gravity and perpendicular to it. In the quasi-2D limit where particles block each other, the velocity fluctuations behave differently from the other confined systems.Peer reviewe

Collective Effects in Settling of Spheroids under Steady-State Sedimentation

We study the settling dynamics of non-Brownian prolate spheroids under steady-state sedimentation. We consider the case of moderate particle Reynolds numbers properly taking into account the hydrodynamic effects. For small volume fractions, we find an orientational transition of the spheroids, characterized by enhanced density fluctuations. Around the transition, the average settling velocity has a maximum which may even exceed the terminal velocity of a single spheroid, in accordance with experiments.Peer reviewe

Diffusion of hard disks and rodlike molecules on surfaces

We study the submonolayer diffusion of hard disks and rodlike molecules on smooth surfaces through numerical simulations and theoretical arguments. We concentrate on the behavior of the various diffusion coefficients as a function of the two-dimensional (2D) number density ρ in the case where there are no explicit surface-particle interactions. For the hard disk case, we find that while the tracer diffusion coefficient DT(ρ) decreases monotonically up to the freezing transition, the collective diffusion coefficient DC(ρ) is wholly determined by the inverse compressibility which increases rapidly on approaching freezing. We also study memory effects associated with tracer diffusion, and present theoretical estimates of DT(ρ) from the mode-mode coupling approximation. In the case of rigid rods with short-range repulsion and no orientational ordering, we find behavior very similar to the case of disks with the same repulsive interaction. Both DT(ρ) and the angular diffusion coefficient DR(ρ) decrease with ρ. Also in this case DC(ρ) is determined by inverse compressibility and increases rapidly close to freezing. This is in contrast to the case of flexible chainlike molecules in the lattice-gas limit, where DC(ρ) first increases and then decreases as a function of the density due to the interplay between compressibility and mobility.Peer reviewe

Teolliset symbioosit Laanilan teollisuusalueella

Industrial symbioses in the Laanila industrial area. Abstract. Teolliset symbioosit ovat yksi tapa edistää teollisten yrityksien resurssitehokkuutta. Symbiooseissa yritykset hyödyntävät toistensa materiaali- tai energiavirtoja omassa toiminnassaan. Työn kirjallisuuskatsauksessa tutkittiin teollisia symbiooseja, ekoteollisuuspuistoja, niiden onnistumisen edellytyksiä, sekä biovoimalaitoksen sivuvirtojen (energiapuu, höyry ja hiilidioksidi) hyötykäyttötapoja. Näiden pohjalta tarkasteltiin, millaisia symbiooseja sivuvirroille voisi rakentua Laanilan alueella ja millainen toteutustapa niille sopisi. Tavoitteena Laanilassa on kasvattaa alueen sivuvirtojen hyötykäyttöä sekä saada alueelle uusi teollinen toimija. Tarkasteltua energiapuuta voi hyödyntää esim. pyrolyysi- ja/tai uuteainelaitoksessa. Symbioosi muodostuu, kun tuotantolaitos hyödyntää biovoimalaitoksen höyryä ja biovoimalaitos hyödyntää tuotantolaitoksen biopohjaisia sivuvirtoja polttoaineenaan. Höyryn symbiooseja on jo alueen kemianlaitosten kanssa, mutta potentiaalia on tuottaa höyryä myös uusille toimijoille. Hiilidioksidin hyödyntämisen symbioosit syntyvät, jos hiilidioksidi jalostettaan tai käytetään suoraan alueen teollisuudessa. Jotta symbioosit kehittyisivät tehokkaasti, alueella olisi hyvä olla hallinto. Potentiaalisin hallintomalli tässä tapauksessa on julkishallinnon/koordinoijan ja yritysten yhteishallintomalli. Uusien yrityksien löytämiseksi voidaan hyödyntää verkostoja tai suoraa kontaktointia. Työtä tehdessä havaittiin, että Laanilan teollisuusalueella on jo ennestään ekoteollisuuspuiston kriteerit täyttävää toimintaa. Työn tuloksia voidaan hyödyntää jatkossa Laanilan symbioosien kehityksessä. Käytetty symbioosien suunnittelutapa on hyödynnettävissä myös muilla teollisuusalueilla.Industrial symbioses in the Laanila industrial area. Abstract. Industrial symbioses are one way to promote the resource efficiency of industrial companies. In symbioses, companies utilize each other’s material or energy flows in their own operations. The literature examination reviews industrial symbioses, eco-industrial parks, the conditions for their success, and the utilization of the by-products of the biopower plant (energy wood, steam and carbon dioxide). On the basis of these, it was examined what kind of symbiosis for side streams could be built in the Laanila area and what kind of implementation would be suitable for them. The goal in Laanila is to increase the utilization of the area’s by-products and to get a new industrial player in the area. The examined energy wood is utilized, for example, in a pyrolysis and/or extractant plant. The symbiosis is formed when a production plant utilizes the steam of a biopower plant and the biopower plant utilizes the bio-based by-products of the production plant as its fuel. There are already symbioses of steam with chemical plants in the area, but there is potential to generate steam for new entrants as well. Symbiosis of carbon recovery arises if CO₂ is refined or used directly in the region’s industry. For symbioses to develop effectively, it would be good to have governance in the region. The most potential governance model in this case is the public administration/coordinator and corporate governance model. Networks or direct contact can be used to find new companies. It was found that the Laanila industrial area already has activities that meet the criteria of the eco-industrial park. The results of the thesis can be utilized in the future in the development of the park’s symbioses. The symbiosis design method used can also be utilized in other industrial areas

Diffusive dynamics of interacting particles in equilibrium and under hydrodynamic sedimentation

Diffusive motion of particles plays an important role in many phenomena in surface physics, for example in chemical reactions, surface growth, and spreading. Diffusive motion can be observed in many different systems. In this thesis we study diffusion and dynamics in two fundamentally different kinds of systems: (i) in Brownian surface systems, and (ii) in a non-Brownian system of sedimenting particles with full hydrodynamic interactions. The quantities of central importance are the diffusion coefficients and the related correlation functions. In the sedimentation system we also discuss the behavior of the velocity fluctuations which has attracted a lot of attention recently. First we study the system of spherical Brownian particles on a smooth surface. We find that while the tracer diffusion coefficient is a decreasing function of density, as expected, the collective diffusion coefficient strongly increases with increasing density. This behavior is completely dictated by the isothermal compressibility, since the center of mass mobility is independent of density in this system. Then we consider the influence of a periodic surface potential and the relation of the continuum model to the lattice gas model. It turns out that the lattice gas model approximates well the dynamics of the continuum model except at the limit when coverage approaches unity. Next we present the corresponding results in a system of rodlike molecules. For the rodlike molecules the normalized tracer diffusion coefficient is found to behave exactly as the tracer diffusion coefficient of the single spheres, while the collective diffusion coefficient is strongly enhanced. In the system of sedimenting non-Brownian particles we find that the average sedimentation velocity of spherical particles decreases monotonically as a function of density but deviates from the phenomenological Richardson-Zaki law at the lowest densities. However, the average sedimentation velocity of spheroids displays non-monotonic behavior as a function of density. The maximum at the intermediate densities is attributed to a change in the orientational distribution of the spheroids. Finally, we study velocity fluctuations and diffusion coefficients in a system of sedimenting spherical particles confined between two parallel vertical walls. We find that the velocity fluctuations in the direction parallel to gravity grow linearly with system size, while the velocity fluctuations in the horizontal directions saturate. Also the tracer diffusion coefficient, which is closely related to the velocity fluctuations, demonstrates similar behavior.reviewe

Scaling Properties of Random Walks on Small-World Networks

Using both numerical simulations and scaling arguments, we study the behavior of a random walker on a one-dimensional small-world network. For the properties we study, we find that the random walk obeys a characteristic scaling form. These properties include the average number of distinct sites visited by the random walker, the mean-square displacement of the walker, and the distribution of first-return times. The scaling form has three characteristic time regimes. At short times, the walker does not see the small-world shortcuts and effectively probes an ordinary Euclidean network in $d$-dimensions. At intermediate times, the properties of the walker shows scaling behavior characteristic of an infinite small-world network. Finally, at long times, the finite size of the network becomes important, and many of the properties of the walker saturate. We propose general analytical forms for the scaling properties in all three regimes, and show that these analytical forms are consistent with our numerical simulations.Comment: 7 pages, 8 figures, two-column format. Submitted to PR