Quench dynamics and defect production in the Kitaev and extended Kitaev models

We study quench dynamics and defect production in the Kitaev and the extended Kitaev models. For the Kitaev model in one dimension, we show that in the limit of slow quench rate, the defect density n∼1/√τ, where 1/τ is the quench rate. We also compute the defect correlation function by providing an exact calculation of all independent nonzero spin correlation functions of the model. In two dimensions, where the quench dynamics takes the system across a critical line, we elaborate on the results of earlier work [K. Sengupta, D. Sen, and S. Mondal, Phys. Rev. Lett. 100, 077204 (2008)] to discuss the unconventional scaling of the defect density with the quench rate. In this context, we outline a general proof that for a d-dimensional quantum model, where the quench takes the system through a d−m dimensional gapless (critical) surface characterized by correlation length exponent ν and dynamical critical exponent z, the defect density n∼1/τmν/(zν+1). We also discuss the variation of the shape and spatial extent of the defect correlation function with both the rate of quench and the model parameters and compute the entropy generated during such a quenching process. Finally, we study the defect scaling law, entropy generation and defect correlation function of the two-dimensional extended Kitaev model.

Structures and molecular-dynamics studies of three active-site mutants of bovine pancreatic phospholipase A(2)

Phospholipase A(2) hydrolyzes phospholipids at the sn-2 position to cleave the fatty-acid ester bond of L-glycerophospholipids. The catalytic dyad (Asp99 and His48) along with a nucleophilic water molecule is responsible for enzyme hydrolysis. Furthermore, the residue Asp49 in the calcium-binding loop is essential for controlling the binding of the calcium ion and the catalytic action of phospholipase A2. To elucidate the structural role of His48 and Asp49, the crystal structures of three active-site single mutants H48N, D49N and D49K have been determined at 1.9 angstrom resolution. Although the catalytically important calcium ion is present in the H48N mutant, the crystal structure shows that proton transfer is not possible from the catalytic water to the mutated residue. In the case of the Asp49 mutants, no calcium ion was found in the active site. However, the tertiary structures of the three active-site mutants are similar to that of the trigonal recombinant enzyme. Molecular-dynamics simulation studies provide a good explanation for the crystallographic results.

Studies of Earth Dynamics with the Superconducting Gravimeter

The superconducting (or cryogenic) gravimeter (SG) is based on the levitation of a super­conducting sphere in a stable magnetic field created by current in superconducting coils. Depending on frequency, it is capable of detecting gravity variations as small as 10-11ms-2. For a single event, the detection threshold is higher, conservatively about 10-9 ms-2. Due to its high sensitivity and low drift rate, the SG is eminently suitable for the study of geodynamical phenomena through their gravity signatures. I present investigations of Earth dynamics with the superconducting gravimeter GWR T020 at Metsähovi from 1994 to 2005. The history and key technical details of the installation are given. The data processing methods and the development of the local tidal model at Metsähovi are presented. The T020 is a part of the worldwide GGP (Global Geodynamics Project) network, which consist of 20 working station. The data of the T020 and of other participating SGs are available to the scientific community. The SG T020 have used as a long-period seismometer to study microseismicity and the Earth s free oscillation. The annual variation, spectral distribution, amplitude and the sources of microseism at Metsähovi were presented. Free oscillations excited by three large earthquakes were analyzed: the spectra, attenuation and rotational splitting of the modes. The lowest modes of all different oscillation types are studied, i.e. the radial mode 0S0, the "football mode" 0S2, and the toroidal mode 0T2. The very low level (0.01 nms-1) incessant excitation of the Earth s free oscillation was detected with the T020. The recovery of global and regional variations in gravity with the SG requires the modelling of local gravity effects. The most important of them is hydrology. The variation in the groundwater level at Metsähovi as measured in a borehole in the fractured bedrock correlates significantly (0.79) with gravity. The influence of local precipitation, soil moisture and snow cover are detectable in the gravity record. The gravity effect of the variation in atmospheric mass and that of the non-tidal loading by the Baltic Sea were investigated together, as sea level and air pressure are correlated. Using Green s functions it was calculated that a 1 metre uniform layer of water in the Baltic Sea increases the gravity at Metsähovi by 31 nms-2 and the vertical deformation is -11 mm. The regression coefficient for sea level is 27 nms-2m-1, which is 87% of the uniform model. These studies are associated with temporal height variations using the GPS data of Metsähovi permanent station. Results of long time series at Metsähovi demonstrated high quality of data and correctly carried out offsets and drift corrections. The superconducting gravimeter T020 has been proved to be an eminent and versatile tool in studies of the Earth dynamics.

Computational fluid dynamics simulations in aerosol and nucleation studies

Nucleation is the first step in the formation of a new phase inside a mother phase. Two main forms of nucleation can be distinguished. In homogeneous nucleation, the new phase is formed in a uniform substance. In heterogeneous nucleation, on the other hand, the new phase emerges on a pre-existing surface (nucleation site). Nucleation is the source of about 30% of all atmospheric aerosol which in turn has noticeable health effects and a significant impact on climate. Nucleation can be observed in the atmosphere, studied experimentally in the laboratory and is the subject of ongoing theoretical research. This thesis attempts to be a link between experiment and theory. By comparing simulation results to experimental data, the aim is to (i) better understand the experiments and (ii) determine where the theory needs improvement. Computational fluid dynamics (CFD) tools were used to simulate homogeneous onecomponent nucleation of n-alcohols in argon and helium as carrier gases, homogeneous nucleation in the water-sulfuric acid-system, and heterogeneous nucleation of water vapor on silver particles. In the nucleation of n-alcohols, vapor depletion, carrier gas effect and carrier gas pressure effect were evaluated, with a special focus on the pressure effect whose dependence on vapor and carrier gas properties could be specified. The investigation of nucleation in the water-sulfuric acid-system included a thorough analysis of the experimental setup, determining flow conditions, vapor losses, and nucleation zone. Experimental nucleation rates were compared to various theoretical approaches. We found that none of the considered theoretical descriptions of nucleation captured the role of water in the process at all relative humidities. Heterogeneous nucleation was studied in the activation of silver particles in a TSI 3785 particle counter which uses water as its working fluid. The role of the contact angle was investigated and the influence of incoming particle concentrations and homogeneous nucleation on counting efficiency determined.

Trap-State Dynamics in Visible-Light-Emitting ZnO:MgO Nanocrystals

Oleate-capped ZnO:MgO nanocrystals have been synthesized that are soluble in nonpolar solvents and which emit strongly in the visible region (450−600 nm) on excitation by UV radiation. The visible emission involves recombination of trap states of the nanocrystalline ZnO core and has a higher quantum yield than the band gap UV exciton emission. The spectrally resolved dynamics of the trap states have been investigated by time-resolved emission spectroscopy. The time-evolution of the photoluminescence spectra show that there are, in fact, two features in the visible emission whose relative importance and efficiencies vary with time. These features originate from recombination involving trapped electrons and holes, respectively, and with efficiencies that depend on the occupancy of the trap density of states.

Diffusion of Pure CH4 and Its Binary Mixture with CO2 in Faujasite NaY: A Combination of Neutron Scattering Experiments and Molecular Dynamics Simulations

The self-diffusion properties of pure CH4 and its binary mixture with CO2 within MY zeolite have been investigated by combining an experimental quasi-elastic neutron scattering (QENS) technique and classical Molecular dynamics simulations. The QENS measurements carried out at 200 K led to an unexpected self-diffusivity profile for Pure CH4 with the presence of a maximum for a loading of 32 CH4/unit cell, which was never observed before for the diffusion of apolar species in azeolite system With large windows. Molecular dynamics simulations were performed using two distinct microscopic models for representing the CH4/NaY interactions. Depending on the model, we are able to fairly reproduce either the magnitude or the profile of the self-diffusivity.Further analysis allowed LIS to provide some molecular insight into the diffusion mechanism in play. The QENS measurements report only a slight decrease of the self-diffusivity of CH4 in the presence of CO2 when the CO2 loading increases. Molecular dynamics simulations successfully capture this experimental trend and suggest a plausible microscopic diffusion mechanism in the case of this binary mixture.

Molecular dynamics studies of nanoparticle impacts

This thesis concerns the dynamics of nanoparticle impacts on solid surfaces. These impacts occur, for instance, in space, where micro- and nanometeoroids hit surfaces of planets, moons, and spacecraft. On Earth, materials are bombarded with nanoparticles in cluster ion beam devices, in order to clean or smooth their surfaces, or to analyse their elemental composition. In both cases, the result depends on the combined effects of countless single impacts. However, the dynamics of single impacts must be understood before the overall effects of nanoparticle radiation can be modelled. In addition to applications, nanoparticle impacts are also important to basic research in the nanoscience field, because the impacts provide an excellent case to test the applicability of atomic-level interaction models to very dynamic conditions. In this thesis, the stopping of nanoparticles in matter is explored using classical molecular dynamics computer simulations. The materials investigated are gold, silicon, and silica. Impacts on silicon through a native oxide layer and formation of complex craters are also simulated. Nanoparticles up to a diameter of 20 nm (315000 atoms) were used as projectiles. The molecular dynamics method and interatomic potentials for silicon and gold are examined in this thesis. It is shown that the displacement cascade expansionmechanism and crater crown formation are very sensitive to the choice of atomic interaction model. However, the best of the current interatomic models can be utilized in nanoparticle impact simulation, if caution is exercised. The stopping of monatomic ions in matter is understood very well nowadays. However, interactions become very complex when several atoms impact on a surface simultaneously and within a short distance, as happens in a nanoparticle impact. A high energy density is deposited in a relatively small volume, which induces ejection of material and formation of a crater. Very high yields of excavated material are observed experimentally. In addition, the yields scale nonlinearly with the cluster size and impact energy at small cluster sizes, whereas in macroscopic hypervelocity impacts, the scaling 2 is linear. The aim of this thesis is to explore the atomistic mechanisms behind the nonlinear scaling at small cluster sizes. It is shown here that the nonlinear scaling of ejected material yield disappears at large impactor sizes because the stopping mechanism of nanoparticles gradually changes to the same mechanism as in macroscopic hypervelocity impacts. The high yields at small impactor size are due to the early escape of energetic atoms from the hot region. In addition, the sputtering yield is shown to depend very much on the spatial initial energy and momentum distributions that the nanoparticle induces in the material in the first phase of the impact. At the later phases, the ejection of material occurs by several mechanisms. The most important mechanism at high energies or at large cluster sizes is atomic cluster ejection from the transient liquid crown that surrounds the crater. The cluster impact dynamics detected in the simulations are in agreement with several recent experimental results. In addition, it is shown that relatively weak impacts can induce modifications on the surface of an amorphous target over a larger area than was previously expected. This is a probable explanation for the formation of the complex crater shapes observed on these surfaces with atomic force microscopy. Clusters that consist of hundreds of thousands of atoms induce long-range modifications in crystalline gold.

Vibrational dynamics and boson peak in a supercooled polydisperse liquid

Vibrational density of states (VDOS) in a supercooled polydisperse liquid is computed by diagonalizing the Hessian matrix evaluated at the potential energy minima for systems with different values of polydispersity. An increase in polydispersity leads to an increase in the relative population of localized high-frequency modes. At low frequencies, the density of states shows an excess compared to the Debye squared-frequency law, which has been identified with the boson peak. The height of the boson peak increases with polydispersity and shows a rather narrow sensitivity to changes in temperature. While the modes comprising the boson peak appear to be largely delocalized, there is a sharp drop in the participation ratio of the modes that exist just below the boson peak indicative of the quasilocalized nature of the low-frequency vibrations. Study of the difference spectrum at two different polydispersity reveals that the increase in the height of boson peak is due to a population shift from modes with frequencies above the maximum in the VDOS to that below the maximum, indicating an increase in the fraction of the unstable modes in the system. The latter is further supported by the facilitation of the observed dynamics by polydispersity. Since the strength of the liquid increases with polydispersity, the present result provides an evidence that the intensity of boson peak correlates positively with the strength of the liquid, as observed earlier in many experimental systems.

An asymptotic analysis of a simple model for the structure and dynamics of the Ramdas layer

This paper presents a complete asymptotic analysis of a simple model for the evolution of the nocturnal temperature distribution on bare soil in calm clear conditions. The model is based on a simplified flux emissivity scheme that provides a nondiffusive local approximation for estimating longwave radiative cooling near ground. An examination of the various parameters involved shows that the ratio of the characteristic radiative to the diffusive timescale in the problem is of order 10(-3), and can therefore be treated as a small parameter (mu). Certain other plausible approximations and linearization lead to a new equation whose asymptotic solution as mu --> 0 can be written in closed form. Four regimes, consishttp://eprints.iisc.ernet.in/cgi/users/home?screen=EPrint::Edit&eprintid=27192&stage=core#tting of a transient at nominal sunset, a radiative-diffusive boundary ('Ramdas') layer on ground, a boundary layer transient and a radiative outer solution, are identified. The asymptotic solution reproduces all the qualitative features of more exact numerical simulations, including the occurrence of a lifted temperature minimum and its evolution during night, ranging from continuing growth to relatively sudden collapse of the Ramdas layer.