Disorder driven transitions in non-equilibrium quantum systems

This thesis presents studies of the role of disorder in non-equilibrium quantum systems. The quantum states relevant to dynamics in these systems are very different from the ground state of the Hamiltonian. Two distinct systems are studied, (i) periodically driven Hamiltonians in two dimensions, and (ii) electrons in a one-dimensional lattice with power-law decaying hopping amplitudes. In the first system, the novel phases that are induced from the interplay of periodic driving, topology and disorder are studied. In the second system, the Anderson transition in all the eigenstates of the Hamiltonian are studied, as a function of the power-law exponent of the hopping amplitude.

In periodically driven systems the study focuses on the effect of disorder in the nature of the topology of the steady states. First, we investigate the robustness to disorder of Floquet topological insulators (FTIs) occurring in semiconductor quantum wells. Such FTIs are generated by resonantly driving a transition between the valence and conduction band. We show that when disorder is added, the topological nature of such FTIs persists as long as there is a gap at the resonant quasienergy. For strong enough disorder, this gap closes and all the states become localized as the system undergoes a transition to a trivial insulator.

Interestingly, the effects of disorder are not necessarily adverse, disorder can also induce a transition from a trivial to a topological system, thereby establishing a Floquet Topological Anderson Insulator (FTAI). Such a state would be a dynamical realization of the topological Anderson insulator. We identify the conditions on the driving field necessary for observing such a transition. We realize such a disorder induced topological Floquet spectrum in the driven honeycomb lattice and quantum well models.

Finally, we show that two-dimensional periodically driven quantum systems with spatial disorder admit a unique topological phase, which we call the anomalous Floquet-Anderson insulator (AFAI). The AFAI is characterized by a quasienergy spectrum featuring chiral edge modes coexisting with a fully localized bulk. Such a spectrum is impossible for a time-independent, local Hamiltonian. These unique characteristics of the AFAI give rise to a new topologically protected nonequilibrium transport phenomenon: quantized, yet nonadiabatic, charge pumping. We identify the topological invariants that distinguish the AFAI from a trivial, fully localized phase, and show that the two phases are separated by a phase transition.

The thesis also present the study of disordered systems using Wegner's Flow equations. The Flow Equation Method was proposed as a technique for studying excited states in an interacting system in one dimension. We apply this method to a one-dimensional tight binding problem with power-law decaying hoppings. This model presents a transition as a function of the exponent of the decay. It is shown that the the entire phase diagram, i.e. the delocalized, critical and localized phases in these systems can be studied using this technique. Based on this technique, we develop a strong-bond renormalization group that procedure where we solve the Flow Equations iteratively. This renormalization group approach provides a new framework to study the transition in this system.

Equilibrium existence in the circle model with linear quadratic transport cost

We treat the problem of existence of a location-then-price equilibrium in the circle model with a linear quadratic type of transportation cost function which can be either convex or concave. We show the existence of a unique perfect equilibrium for the concave case when the linear and quadratic terms are equal and of a unique perfect equilibrium for the convex case when the linear term is equal to zero. Aside from these two cases, there are feasible locations by the firms for which no equilibrium in the price subgame exists. Finally, we provide a full taxonomy of the price equilibrium regions in terms of weights of the linear and quadratic terms in the cost function.

Diversity and Stability in Food Webs : Impacts of Non-Equilibrium Dynamics, Topology and Variation

With progressive climate change, the preservation of biodiversity is becoming increasingly important. Only if the gene pool is large enough and requirements of species are diverse, there will be species that can adapt to the changing circumstances. To maintain biodiversity, we must understand the consequences of the various strategies. Mathematical models of population dynamics could provide prognoses. However, a model that would reproduce and explain the mechanisms behind the diversity of species that we observe experimentally and in nature is still needed. A combination of theoretical models with detailed experiments is needed to test biological processes in models and compare predictions with outcomes in reality. In this thesis, several food webs are modeled and analyzed. Among others, models are formulated of laboratory experiments performed in the Zoological Institute of the University of Cologne. Numerical data of the simulations is in good agreement with the real experimental results. Via numerical simulations it can be demonstrated that few assumptions are necessary to reproduce in a model the sustained oscillations of the population size that experiments show. However, analysis indicates that species "thrown together by chance" are not very likely to survive together over long periods. Even larger food nets do not show significantly different outcomes and prove how extraordinary and complicated natural diversity is. In order to produce such a coexistence of randomly selected species—as the experiment does—models require additional information about biological processes or restrictions on the assumptions. Another explanation for the observed coexistence is a slow extinction that takes longer than the observation time. Simulated species survive a comparable period of time before they die out eventually. Interestingly, it can be stated that the same models allow the survival of several species in equilibrium and thus do not follow the so-called competitive exclusion principle. This state of equilibrium is more fragile, however, to changes in nutrient supply than the oscillating coexistence. Overall, the studies show, that having a diverse system means that population numbers are probably oscillating, and on the other hand oscillating population numbers stabilize a food web both against demographic noise as well as against changes of the habitat. Model predictions can certainly not be converted at their face value into policies for real ecosystems. But the stabilizing character of fluctuations should be considered in the regulations of animal populations.

New measures for assessing model equilibrium and prediction mismatch in species distribution models

Models based on species distributions are widely used and serve important purposes in ecology, biogeography and conservation. Their continuous predictions of environmental suitability are commonly converted into a binary classification of predicted (or potential) presences and absences, whose accuracy is then evaluated through a number of measures that have been the subject of recent reviews. We propose four additional measures that analyse observation-prediction mismatch from a different angle – namely, from the perspective of the predicted rather than the observed area – and add to the existing toolset of model evaluation methods. We explain how these measures can complete the view provided by the existing measures, allowing further insights into distribution model predictions. We also describe how they can be particularly useful when using models to forecast the spread of diseases or of invasive species and to predict modifications in species’ distributions under climate and land-use change

Convergence time to equilibrium distributions of autonomous and periodic non-autonomous graphs

We present some estimates of the time of convergence to the equilibrium distribution in autonomous and periodic non-autonomous graphs, with ergodic stochastic adjacency matrices, using the eigenvalues of these matrices. On this way we generalize previous results from several authors, that only considered reversible matrices.

Deposition of thin films by a non-equilibrium atmospheric pressure Plasma Jet: a poly-diagnostic study

The use of atmospheric pressure plasmas for thin film deposition on thermo-sensitive materials is currently one of the main challenges of the plasma scientific community. Despite the growing interest in this field, the existing knowledge gap between gas-phase reaction mechanisms and thin film properties is still one of the most important barriers to overcome for a complete understanding of the process. In this work, thin films surface characterization techniques, combined with passive and active gas-phase diagnostic methods, were used to provide a comprehensive study of the Ar/TEOS deposition process assisted by an atmospheric pressure plasma jet. SiO2-based thin films exhibiting a well-defined chemistry, a good morphological structure and high uniformity were studied in detail by FTIR, XPS, AFM and SEM analysis. Furthermore, non-intrusive spectroscopy techniques (OES, filter imaging) and laser spectroscopic methods (Rayleigh scattering, LIF and TALIF) were employed to shed light on the complexity of gas-phase mechanisms involved in the deposition process and discuss the influence of TEOS admixture on gas temperature, electron density and spatial-temporal behaviours of active species. The poly-diagnostic approach proposed in this work opens interesting perspectives both in terms of process control and optimization of thin film performances.

Non-Equilibrium Atmospheric Plasma As A Novel Route To Nanomaterial Synthesis And Processing For Biomedical Applications

Since last century, the rising interest of value-added and advanced functional materials has spurred a ceaseless development in terms of industrial processes and applications. Among the emerging technologies, thanks to their unique features and versatility in terms of supported processes, non-equilibrium plasma discharges appear as a key solvent-free, high-throughput and cost-efficient technique. Nevertheless, applied research studies are needed with the aim of addressing plasma potentialities optimizing devices and processes for future industrial applications. In this framework, the aim of this dissertation is to report on the activities carried out and the results achieved concerning the development and optimization of plasma techniques for nanomaterial synthesis and processing to be applied in the biomedical field. In the first section, the design and investigation of a plasma assisted process for the production of silver (Ag) nanostructured multilayer coatings exhibiting anti-biofilm and anti-clot properties is described. With the aim on enabling in-situ and on-demand deposition of Ag nanoparticles (NPs), the optimization of a continuous in-flight aerosol process for particle synthesis is reported. The stability and promising biological performances of deposited coatings spurred further investigation through in-vitro and in-vivo tests which results are reported and discussed. With the aim of addressing the unanswered questions and tuning NPs functionalities, the second section concerns the study of silver containing droplet conversion in a flow-through plasma reactor. The presented results, obtained combining different analysis techniques, support a formation mechanism based on droplet to particle conversion driven by plasma induced precursor reduction. Finally, the third section deals with the development of a simulative and experimental approach used to investigate the in-situ droplet evaporation inside the plasma discharge addressing the main contributions to liquid evaporation in the perspective of process industrial scale up.

Non perturbative aspects of non equilibrium physics in two dimensional models

The present manuscript focuses on out of equilibrium physics in two dimensional models. It has the purpose of presenting some results obtained as part of out of equilibrium dynamics in its non perturbative aspects. This can be understood in two different ways: the former is related to integrability, which is non perturbative by nature; the latter is related to emergence of phenomena in the out of equilibirum dynamics of non integrable models that are not accessible by standard perturbative techniques. In the study of out of equilibirum dynamics, two different protocols are used througout this work: the bipartitioning protocol, within the Generalised Hydrodynamics (GHD) framework, and the quantum quench protocol. With GHD machinery we study the Staircase Model, highlighting how the hydrodynamic picture sheds new light into the physics of Integrable Quantum Field Theories; with quench protocols we analyse different setups where a non-perturbative description is needed and various dynamical phenomena emerge, such as the manifistation of a dynamical Gibbs effect, confinement and the emergence of Bloch oscillations preventing thermalisation.

Characterization Of Microsatellite Markers Developed From Prosopis Rubriflora And Prosopis Ruscifolia (leguminosae - Mimosoideae), Legume Species That Are Used As Models For Genetic Diversity Studies In Chaquenian Areas Under Anthropization In South America.

Prosopis rubriflora and Prosopis ruscifolia are important species in the Chaquenian regions of Brazil. Because of the restriction and frequency of their physiognomy, they are excellent models for conservation genetics studies. The use of microsatellite markers (Simple Sequence Repeats, SSRs) has become increasingly important in recent years and has proven to be a powerful tool for both ecological and molecular studies. In this study, we present the development and characterization of 10 new markers for P. rubriflora and 13 new markers for P. ruscifolia. The genotyping was performed using 40 P. rubriflora samples and 48 P. ruscifolia samples from the Chaquenian remnants in Brazil. The polymorphism information content (PIC) of the P. rubriflora markers ranged from 0.073 to 0.791, and no null alleles or deviation from Hardy-Weinberg equilibrium (HW) were detected. The PIC values for the P. ruscifolia markers ranged from 0.289 to 0.883, but a departure from HW and null alleles were detected for certain loci; however, this departure may have resulted from anthropic activities, such as the presence of livestock, which is very common in the remnant areas. In this study, we describe novel SSR polymorphic markers that may be helpful in future genetic studies of P. rubriflora and P. ruscifolia.

The Crystal-t Algorithm: A New Approach To Calculate The Sle Of Lipidic Mixtures Presenting Solid Solutions.

Lipidic mixtures present a particular phase change profile highly affected by their unique crystalline structure. However, classical solid-liquid equilibrium (SLE) thermodynamic modeling approaches, which assume the solid phase to be a pure component, sometimes fail in the correct description of the phase behavior. In addition, their inability increases with the complexity of the system. To overcome some of these problems, this study describes a new procedure to depict the SLE of fatty binary mixtures presenting solid solutions, namely the Crystal-T algorithm. Considering the non-ideality of both liquid and solid phases, this algorithm is aimed at the determination of the temperature in which the first and last crystal of the mixture melts. The evaluation is focused on experimental data measured and reported in this work for systems composed of triacylglycerols and fatty alcohols. The liquidus and solidus lines of the SLE phase diagrams were described by using excess Gibbs energy based equations, and the group contribution UNIFAC model for the calculation of the activity coefficients of both liquid and solid phases. Very low deviations of theoretical and experimental data evidenced the strength of the algorithm, contributing to the enlargement of the scope of the SLE modeling.

Atomic Charge Transfer-counter Polarization Effects Determine Infrared Ch Intensities Of Hydrocarbons: A Quantum Theory Of Atoms In Molecules Model.

Atomic charge transfer-counter polarization effects determine most of the infrared fundamental CH intensities of simple hydrocarbons, methane, ethylene, ethane, propyne, cyclopropane and allene. The quantum theory of atoms in molecules/charge-charge flux-dipole flux model predicted the values of 30 CH intensities ranging from 0 to 123 km mol(-1) with a root mean square (rms) error of only 4.2 km mol(-1) without including a specific equilibrium atomic charge term. Sums of the contributions from terms involving charge flux and/or dipole flux averaged 20.3 km mol(-1), about ten times larger than the average charge contribution of 2.0 km mol(-1). The only notable exceptions are the CH stretching and bending intensities of acetylene and two of the propyne vibrations for hydrogens bound to sp hybridized carbon atoms. Calculations were carried out at four quantum levels, MP2/6-311++G(3d,3p), MP2/cc-pVTZ, QCISD/6-311++G(3d,3p) and QCISD/cc-pVTZ. The results calculated at the QCISD level are the most accurate among the four with root mean square errors of 4.7 and 5.0 km mol(-1) for the 6-311++G(3d,3p) and cc-pVTZ basis sets. These values are close to the estimated aggregate experimental error of the hydrocarbon intensities, 4.0 km mol(-1). The atomic charge transfer-counter polarization effect is much larger than the charge effect for the results of all four quantum levels. Charge transfer-counter polarization effects are expected to also be important in vibrations of more polar molecules for which equilibrium charge contributions can be large.

Improved Selective Cholesterol Adsorption By Molecularly Imprinted Poly(methacrylic Acid)/silica (pmaa-sio₂) Hybrid Material Synthesized With Different Molar Ratios.

The present paper describes the synthesis of molecularly imprinted polymer - poly(methacrylic acid)/silica and reports its performance feasibility with desired adsorption capacity and selectivity for cholesterol extraction. Two imprinted hybrid materials were synthesized at different methacrylic acid (MAA)/tetraethoxysilane (TEOS) molar ratios (6:1 and 1:5) and characterized by FT-IR, TGA, SEM and textural data. Cholesterol adsorption on hybrid materials took place preferably in apolar solvent medium, especially in chloroform. From the kinetic data, the equilibrium time was reached quickly, being 12 and 20 min for the polymers synthesized at MAA/TEOS molar ratio of 6:1 and 1:5, respectively. The pseudo-second-order model provided the best fit for cholesterol adsorption on polymers, confirming the chemical nature of the adsorption process, while the dual-site Langmuir-Freundlich equation presented the best fit to the experimental data, suggesting the existence of two kinds of adsorption sites on both polymers. The maximum adsorption capacities obtained for the polymers synthesized at MAA/TEOS molar ratios of 6:1 and 1:5 were found to be 214.8 and 166.4 mg g(-1), respectively. The results from isotherm data also indicated higher adsorption capacity for both imprinted polymers regarding to corresponding non-imprinted polymers. Nevertheless, taking into account the retention parameters and selectivity of cholesterol in the presence of structurally analogue compounds (5-α-cholestane and 7-dehydrocholesterol), it was observed that the polymer synthesized at the MAA/TEOS molar ratio of 6:1 was much more selective for cholesterol than the one prepared at the ratio of 1:5, thus suggesting that selective binding sites ascribed to the carboxyl group from MAA play a central role in the imprinting effect created on MIP.

Species Fractionation In Atomic Chains From Mechanically Stretched Alloys.

Bettini et al (2006 Nat. Nanotechnol. 1 182-5) reported the first experimental realization of linear atomic chains (LACs) composed of different atoms (Au and Ag). The different contents of Au and Ag were observed in the chains from what was found in the bulk alloys, which raises the question of what the wire composition is, if it is in equilibrium with a bulk alloy. In this work we address the thermodynamic driving force for species fractionation in LACs under tension, and we present the density-functional theory results for Ag-Au chain alloys. A pronounced stabilization of the wires with an alternating Ag-Au sequence is observed, which could be behind the experimentally observed Au enrichment in LACs from alloys with high Ag content.

The Basic Reproduction Number Obtained From Jacobian And Next Generation Matrices - A Case Study Of Dengue Transmission Modelling.

The basic reproduction number is a key parameter in mathematical modelling of transmissible diseases. From the stability analysis of the disease free equilibrium, by applying Routh-Hurwitz criteria, a threshold is obtained, which is called the basic reproduction number. However, the application of spectral radius theory on the next generation matrix provides a different expression for the basic reproduction number, that is, the square root of the previously found formula. If the spectral radius of the next generation matrix is defined as the geometric mean of partial reproduction numbers, however the product of these partial numbers is the basic reproduction number, then both methods provide the same expression. In order to show this statement, dengue transmission modelling incorporating or not the transovarian transmission is considered as a case study. Also tuberculosis transmission and sexually transmitted infection modellings are taken as further examples.