Fluctuations in and out of equilibrium: Thermalization, quantum measurements and Coulomb disorder

This purely theoretical thesis covers aspects of two contemporary research fields: the non-equilibrium dynamics in quantum systems and the electronic properties of three-dimensional topological insulators. In the first part we investigate the non-equilibrium dynamics in closed quantum systems. Thanks to recent technologies, especially from the field of ultracold quantum gases, it is possible to realize such systems in the laboratory. The focus is on the influence of hydrodynamic slow modes on the thermalization process. Generic systems in equilibrium, either classical or quantum, in equilibrium are described by thermodynamics. This is characterized by an ensemble of maximal entropy, but constrained by macroscopically conserved quantities. We will show that these conservation laws slow down thermalization and the final equilibrium state can be approached only algebraically in time. When the conservation laws are violated thermalization takes place exponential in time. In a different study we calculate probability distributions of projective quantum measurements. Newly developed quantum microscopes provide the opportunity to realize new measurement protocols which go far beyond the conventional measurements of correlation functions. The second part of this thesis is dedicated to a new class of materials known as three-dimensional topological insulators. Also here new experimental techniques have made it possible to fabricate these materials to a high enough quality that their topological nature is revealed. However, their transport properties are not fully understood yet. Motivated by unusual experimental results in the optical conductivity we have investigated the formation and thermal destruction of spatially localized electron- and hole-doped regions. These are caused by charged impurities which are introduced into the material in order to make the bulk insulating. Our theoretical results are in agreement with the experiment and can explain the results semi-quantitatively. Furthermore, we study emergent lengthscales in the bulk as well as close to the conducting surface.

Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Computational modelling of non-equilibrium condensing steam flows in low-pressure steam turbines

The steam turbines play a significant role in global power generation. Especially, research on low pressure (LP) steam turbine stages is of special importance for steam turbine man- ufactures, vendors, power plant owners and the scientific community due to their lower efficiency than the high pressure steam turbine stages. Because of condensation, the last stages of LP turbine experience irreversible thermodynamic losses, aerodynamic losses and erosion in turbine blades. Additionally, an LP steam turbine requires maintenance due to moisture generation, and therefore, it is also affecting on the turbine reliability. Therefore, the design of energy efficient LP steam turbines requires a comprehensive analysis of condensation phenomena and corresponding losses occurring in the steam tur- bine either by experiments or with numerical simulations. The aim of the present work is to apply computational fluid dynamics (CFD) to enhance the existing knowledge and understanding of condensing steam flows and loss mechanisms that occur due to the irre- versible heat and mass transfer during the condensation process in an LP steam turbine. Throughout this work, two commercial CFD codes were used to model non-equilibrium condensing steam flows. The Eulerian-Eulerian approach was utilised in which the mix- ture of vapour and liquid phases was solved by Reynolds-averaged Navier-Stokes equa- tions. The nucleation process was modelled with the classical nucleation theory, and two different droplet growth models were used to predict the droplet growth rate. The flow turbulence was solved by employing the standard k-ε and the shear stress transport k-ω turbulence models. Further, both models were modified and implemented in the CFD codes. The thermodynamic properties of vapour and liquid phases were evaluated with real gas models. In this thesis, various topics, namely the influence of real gas properties, turbulence mod- elling, unsteadiness and the blade trailing edge shape on wet-steam flows, are studied with different convergent-divergent nozzles, turbine stator cascade and 3D turbine stator-rotor stage. The simulated results of this study were evaluated and discussed together with the available experimental data in the literature. The grid independence study revealed that an adequate grid size is required to capture correct trends of condensation phenomena in LP turbine flows. The study shows that accurate real gas properties are important for the precise modelling of non-equilibrium condensing steam flows. The turbulence modelling revealed that the flow expansion and subsequently the rate of formation of liquid droplet nuclei and its growth process were affected by the turbulence modelling. The losses were rather sensitive to turbulence modelling as well. Based on the presented results, it could be observed that the correct computational prediction of wet-steam flows in the LP turbine requires the turbulence to be modelled accurately. The trailing edge shape of the LP turbine blades influenced the liquid droplet formulation, distribution and sizes, and loss generation. The study shows that the semicircular trailing edge shape predicted the smallest droplet sizes. The square trailing edge shape estimated greater losses. The analysis of steady and unsteady calculations of wet-steam flow exhibited that in unsteady simulations, the interaction of wakes in the rotor blade row affected the flow field. The flow unsteadiness influenced the nucleation and droplet growth processes due to the fluctuation in the Wilson point.

Other-Regarding Preferences in General Equilibrium

We study competitive market outcomes in economies where agents have other-regarding preferences. We identify a separability condition on monotone preferences that is necessary and sufficient for one’s own demand to be independent of the allocations and characteristics of other agents in the economy. Given separability, it is impossible to identify other-regarding preferences from market behavior: agents be- have as if they had classical preferences that depend only on own consumption in competitive equilibrium. If preferences, in addition, depend only on the final allocation of consumption in society, the Sec- ond Welfare Theorem holds as long as an increase in resources can be distributed such that all agents are better off. Nevertheless, the First Welfare Theorem generally does not hold. Allowing agents to care about their own consumption and the distribution of consump- tion possibilities in the economy, we provide a condition under which agents have no incentive to make direct transfers, and show that this condition implies that competitive equilibria are efficient given prices.

Rare sex or out of reach equilibrium? The dynamics of F-IS in partially clonal organisms

Background: Partially clonal organisms are very common in nature, yet the influence of partial asexuality on the temporal dynamics of genetic diversity remains poorly understood. Mathematical models accounting for clonality predict deviations only for extremely rare sex and only towards mean inbreeding coefficient (F-IS) over bar < 0. Yet in partially clonal species, both F-IS < 0 and F-IS > 0 are frequently observed also in populations where there is evidence for a significant amount of sexual reproduction. Here, we studied the joint effects of partial clonality, mutation and genetic drift with a state-and-time discrete Markov chain model to describe the dynamics of F-IS over time under increasing rates of clonality. Results: Results of the mathematical model and simulations show that partial clonality slows down the asymptotic convergence to F-IS = 0. Thus, although clonality alone does not lead to departures from Hardy-Weinberg expectations once reached the final equilibrium state, both negative and positive F-IS values can arise transiently even at intermediate rates of clonality. More importantly, such "transient" departures from Hardy Weinberg proportions may last long as clonality tunes up the temporal variation of F-IS and reduces its rate of change over time, leading to a hyperbolic increase of the maximal time needed to reach the final mean (F-IS,F-infinity) over bar value expected at equilibrium. Conclusion: Our results argue for a dynamical interpretation of F-IS in clonal populations. Negative values cannot be interpreted as unequivocal evidence for extremely scarce sex but also as intermediate rates of clonality in finite populations. Complementary observations (e.g. frequency distribution of multiloci genotypes, population history) or time series data may help to discriminate between different possible conclusions on the extent of clonality when mean (F-IS) over bar values deviating from zero and/or a large variation of F-IS over loci are observed.

Equilibrium Sorption Studies of Hg (II) Ions from Aqueous Solution using Powdered Swamp Arum ( Lasimorpha senegalensis ) Seeds.

The potential of swamp arum ( Lasimorpha senegalensis ) seeds as a low-cost adsorbent for the removal of Hg (II) ions from aqueous solution was investigated in this study. The influence of initial metal concentration on the percent adsorption of Hg (II) ions onto powdered swamp arum seeds was studied in a batch system and the filtrate was analyzed using Atomic Absorption Spectrometry (AAS). The percent adsorbed for 10, 20, 40, 60 and 80 mg/L of the aqueous solution were 97.7, 98.9, 99.3, 99.7, and 96.5% respectively. Three isotherms; Langmuir, Freundlich, and BET were used to model the equilibrium sorption of Hg (II) ions onto powdered swamp arum seeds, with a correlation coefficient of 0.998, 0.784 and0.842 respectively. The Langmuir model fitted the equilibrium data best, with a correlation coefficient of 0.998 and a maximum adsorption capacity qm, of 5.917 mg/g. Thus, indicating monolayer coverage on the adsorbent. The results showed that swamp arum seed have the potential to be applied as alternative lowcost biosorbent in the remediation of heavy metal contamination in waste water.

Vapor–liquid equilibrium of binary mixtures containing isopropyl acetate and alkanols at 101.32 kPa

Isobaric vapor-liquid equilibria of binary mixtures of isopropyl acetate plus an alkanol (1-propanol, 2-propanol, 1-butanol, or 2-butanol) were measured at 101.32 kPa, using a dynamic recirculating still. An azeotropic behavior was observed only in the mixtures of isopropyl acetate + 2-propanol and isopropyl acetate + 1-propanol. The application of four thermodynamic consistency tests (the Herington test, the Van Ness test, the infinite dilution test, and the pure component test) showed the high quality of the experimental data. Finally, both NRTL and UNIQUAC activity coefficient models were successfully applied in the correlation of the measured data, with the average absolute deviations in vapor phase composition and temperature of 0.01 and 0.16 K, respectively.

Methane seep carbonates yield clumped isotope signatures out of equilibrium with formation temperatures

Methane cold seep systems typically exhibit extensive buildups of authigenic carbonate minerals, resulting from local increases in alkalinity driven by methane oxidation. Here, we demonstrate that modern seep authigenic carbonates exhibit anomalously low clumped isotope values (Delta(47)), as much as similar to 0.2 parts per thousand lower than expected values. In modern seeps, this range of disequilibrium translates into apparent temperatures that are always warmer than ambient temperatures, by up to 50 degrees C. We examine various mechanisms that may induce disequilibrium behaviour in modern seep carbonates, and suggest that the observed values result from several factors including kinetic isotopic effects during methane oxidation, mixing of inorganic carbon pools, pH effects and rapid precipitation. Ancient seep carbonates studied here also exhibit potential disequilibrium signals. Ultimately, these findings indicate the predominance of disequilibrium clumped isotope behaviour in modern cold seep carbonates that must be considered when characterizing environmental conditions in both modern and ancient cold seep settings.

Designing Efficient Subsidy Policies in a Regional Economy: A Multicriteria Decision-Making (MCDM)-Computable General Equilibrium (CGE) Approach

Since policy-makers usually pursue several conflicting objectives, policy-making can be understood as a multicriteria decision problem. Following the methodological proposal by André and Cardenete (2005) André, F. J. and Cardenete, M. A. 2005. Multicriteria Policy Making. Defining Efficient Policies in a General Equilibrium Model, Seville: Centro de Estudios Andaluces. Working Paper No. E2005/04, multi-objective programming is used in connection with a computable general equilibrium model to represent optimal policy-making and to obtain so-called efficient policies in an application to a regional economy (Andalusia, Spain). This approach is applied to the design of subsidy policies under two different scenarios. In the first scenario, it is assumed that the government is concerned just about two objectives: ensuring the profitability of a key strategic sector and increasing overall output. Finally, the scope of the exercise is enlarged by solving a problem with seven policy objectives, including both general and sectorial objectives. It is concluded that the observed policy could have been Pareto-improved in several directions.

Defining efficient policies in a general equilibrium model: a multi-objective approach

Macroeconomic policy makers are typically concerned with several indicators of economic performance. We thus propose to tackle the design of macroeconomic policy using Multicriteria Decision Making (MCDM) techniques. More specifically, we employ Multiobjective Programming (MP) to seek so-called efficient policies. The MP approach is combined with a computable general equilibrium (CGE) model. We chose use of a CGE model since they have the dual advantage of being consistent with standard economic theory while allowing one to measure the effect(s) of a specific policy with real data. Applying the proposed methodology to Spain (via the 1995 Social Accounting Matrix) we first quantified the trade-offs between two specific policy objectives: growth and inflation, when designing fiscal policy. We then constructed a frontier of efficient policies involving real growth and inflation. In doing so, we found that policy in 1995 Spain displayed some degree of inefficiency with respect to these two policy objectives. We then offer two sets of policy recommendations that, ostensibly, could have helped Spain at the time. The first deals with efficiency independent of the importance given to both growth and inflation by policy makers (we label this set: general policy recommendations). A second set depends on which policy objective is seen as more important by policy makers: increasing growth or controlling inflation (we label this one: objective-specific recommendations).

Equilibrium profiles of liquids in tilted Taylor-Hauksbee cells

In this work we study theoretically and experimentally the equilibrium profiles attained under spontaneous capillary rise of viscous liquids in the wedge-shaped narrow gap between two vertical plates intersecting at a tight angle α<<1. We contrast the differences among the case with vertical edge and those in which the arista is tilted to the vertical. Our theoretical description agrees well with experimental data for several analyzed inclinations.

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.