Strongly nonlinear thermovoltage and heat dissipation in interacting quantum dots

We investigate the nonlinear regime of charge and energy transport through Coulomb-blockaded quantum dots. We discuss crossed effects that arise when electrons move in response to thermal gradients (Seebeck effect) or energy flows in reaction to voltage differences (Peltier effect). We find that the differential thermoelectric conductance shows a characteristic Coulomb butterfly structure due to charging effects. Importantly, we show that experimentally observed thermovoltage zeros are caused by the activation of Coulomb resonances at large thermal shifts. Furthermore, the power dissipation asymmetry between the two attached electrodes can be manipulated with the applied voltage, which has implications for the efficient design of nanoscale coolers.Comment: 6 pages, 4 figure

Heat current through an artificial Kondo impurity beyond linear response

We investigate the heat current of a strongly interacting quantum dot in the presence of a voltage bias in the Kondo regime. Using the slave- boson mean-field theory, we discuss the behavior of the energy flow and the Joule heating. We find that both contributions to the heat current dis- play interesting symmetry properties under reversal of the applied dc bias. We show that the symmetries arise from the behavior of the dot trans- mission function. Importantly, the transmission probability is a function of both energy and voltage. This allows us to analyze the heat current in the nonlinear regime of transport. We observe that nonlinearities ap- pear already for voltages smaller than the Kondo temperature. Finally, we suggest to use the contact and electric symmetry coefficients as a way to measure pure energy currents.Comment: 9 pages, 2 figures, proceeding of the Low Temperature Physics Conferenc

Fate of the spin-\frac{1}{2} Kondo effect in the presence of temperature gradients

We consider a strongly interacting quantum dot connected to two leads held at quite different temperatures. Our aim is to study the behavior of the Kondo effect in the presence of large thermal biases. We use three different approaches, namely, a perturbation formalism based on the Kondo Hamiltonian, a slave-boson mean-field theory for the Anderson model at large charging energies and a truncated equation-of-motion approach beyond the Hartree-Fock approximation. The two former formalisms yield a suppression of the Kondo peak for thermal gradients above the Kondo temperature, showing a remarkably good agreement despite their different ranges of validity. The third technique allows us to analyze the full density of states within a wide range of energies. Additionally, we have investigated the quantum transport properties (electric current and thermocurrent) beyond linear response. In the voltage-driven case, we reproduce the split differential conductance due to the presence of different electrochemical potentials. In the temperature-driven case, we observe a strongly nonlinear thermocurrent as a function of the applied thermal gradient. Depending on the parameters, we can find nontrivial zeros in the electric current for finite values of the temperature bias. Importantly, these thermocurrent zeros yield direct access to the system's characteristic energy scales (Kondo temperature and charging energy).Comment: 14 pages, 11 figures, revised versio

Interactions and thermoelectric effects in a parallel-coupled double quantum dot

We investigate the nonequilibrium transport properties of a double quantum dot system connected in parallel to two leads, including intradot electron-electron interaction. In the absence of interactions the system supports a bound state in the continuum. This state is revealed as a Fano antiresonance in the transmission when the energy levels of the dots are detuned. Using the Keldysh nonequilibrium Green's function formalism, we find that the occurrence of the Fano antiresonance survives in the presence of Coulomb repulsion. We give precise predictions for the experimental detection of bound states in the continuum. First, we calculate the differential conductance as a function of the applied voltage and the dot level detuning and find that crossing points in the diamond structure are revealed as minima due to the transmission antiresonances. Second, we determine the thermoelectric current in response to an applied temperature bias. In the linear regime, quantum interference gives rise to sharp peaks in the thermoelectric conductance. Remarkably, we find interaction induced strong current nonlinearities for large thermal gradients that may lead to several nontrivial zeros in the thermocurrent. The latter property is especially attractive for thermoelectric applications.Comment: 9 pages, 8 figure

Essays on the Economics of Statelessness and State Formation

This dissertation empirically examines economic exchange in the absence of the state. While economic analysis focuses traditionally on economic exchange within a state able to enforce property rights, functioning states are an anomalous environment in the development process. However, a fundamental problem is that in the absence of a functioning state, there is no data collection capacity. In order to observe economic exchange in the absence of a state, I focus on a collapsed state in the current period: the Democratic Republic of the Congo (DRC). As a foundation for this dissertation, I conducted fieldwork in areas of the Eastern provinces of the Democratic Republic of the Congo that are removed from the central state. I managed a team of 12 surveyors, as well as a team of 20 traders, in order to observe economic exchange in such areas. The DRC is a well suited location to study the rules that govern economic exchange in the absence of the state. The central state is considered a failed state", the second weakest state in the world. Lacking a state to protect property rights and provide a judicial system, the economy has organized informally. Actors independent of the state regularly use coercion to define property rights. Contracts are enforced under the threat of social sanctions, or the threat of village armed men who administer disputes. To analyze economic exchange without a state, I use standard economic analysis and standard econometrics but I am constrained to introduce different notions than the ones on which traditional economic analysis usually relies (Acemoglu and Wolitzky, 2011, Grossman, 1999, Hirshleifer, 1995). Instead of assuming that property rights are stable, I allow some agents to use coercion in order to dene property rights over goods and labor services. In anarchy, coercion can lead to large efficiency losses, since uncoordinated coercive actors do not internalize the distortions they generate on the incentives of those who produce (Grossman, 1999). This leads me to the question of Chapter 1: when will individuals with a comparative advantage in coercion organize violence in a particular location, and hold a "monopoly of violence"? Since a dominant view across disciplines views a "monopoly of violence" as a sufficient characterization of the state and traces back state origins to coercion and organized crime in medieval Europe (Tilly, 1985), my exercise uncovers the economic forces that lead to the formation of states - whether these monopolies of violence are recognized as states by the international community or not. However, in this exercise, I take the notion of the state as a "monopoly of violence" as given. But is this a useful view of the state? Why should any monopoly of violence, even those with purely criminal motives, act as states? Olson (1993) endows this view of the state with theoretical foundations: since criminals who hold a monopoly of violence are partial residual claimants through the taxes they collect, it is in their interest to protect economic activity, promote growth. Indeed, by doing so they can increase the tax revenues they collect. Therefore, in Chapter 2, I confront these theoretical foundations to the data. I examine in detail the behavior of village monopolies of violence held by armed men in Eastern Congo, and introduce economic analysis to predict state-like behavior: optimal taxation, public goods provision, and popular support. I go a step further to refine this view of the state, and show that the view of the state as a "monopoly of violence" is useful only if the time horizon is long and the monopoly of violence is uncontested. Once I have established the economic causes of state formation and the links between organized crime and states, I turn to the impact of the state on economic organization. In Chapter 3, I implement a field experiment that allows me to observe the impact of the penetration of the state legal system. I find that the state legal system allows for an increase in trade, and does not crowd-out pre-existing social mechanisms generating trust and trade. However, there are limits to the effectiveness of the formal system of contract enforcement. Indeed, I nd that only the groups which have captured the state benefit from the leverage provided by the legal system. This confirms the view of the state, as an organization that holds a monopoly of violence but which can be captured by a subset of the population. In what follows, I describe each chapter in more detail. In Chapter 1, I focus on the following question: why do states arise, and when do they fail to arise? A dominant view across disciplines is that states arise when violent actors impose a "monopoly of violence" in order to extract taxes (Tilly, 1985). One key fact underlies all existing studies: statistics exist only after the state is formed. In this chapter, I provide the first econometric evidence on the determinants of state formation at their early stages. As a foundation for this chapter, I conducted fieldwork in areas of Eastern Congo removed from control by the central state, managing a team that collected village-level panel data on current armed groups. I develop a model that introduces optimal taxation theory to the decision of armed groups to form local "monopolies of violence", and argue that the returns to such decision hinge on their ability to tax the local population. A sharp, exogenous rise in the price of a bulky commodity used in the electronics industry, coltan, leads armed groups to impose a "monopoly of violence" in coltan villages. A later increase in the price of gold, easier to conceal and hence more dicult to tax, does not. Results from auxiliary tests provide additional support to the theory. The findings support the hypothesis that the expected Revenue from taxation, in particular tax base elasticity, is a determinant of state formation. In Chapter 2, I go a step further, and challenge the theory associating monopolies of violence to state-like behavior. A dominant view across disciplines defines states as a monopoly of violence" and argues that states are a developed form of successful organized crime. But, is this a useful definition of the state? If current states are monopolies of violence and also engage in state-like behavior, this may be the result of a long historical process unrelated to the fact that they are a "monopoly of violence". In this chapter, I examine this view of the state empirically, and provide one of the first studies with econometric evidence linking criminal "monopolies of violence" before they develop into the states as most of us know them, to state-like behavior. To observe the behavior of criminal "monopolies of violence", I draw on the same data collection exercise as in Chapter 1. I apply optimal taxation theory to armed groups, and show that armed groups will tax and promote growth like states whenever their "monopoly of violence" is uncontested. Based on this data, I find that criminal "monopolies of violence" consistently provide public goods, develop popular support, and elaborate taxation schemes consistent with optimal taxation and European medieval states. In addition, using the timing of a peace agreement as an instrument for the presence of armed men in the village, I establish that the village "monopolies of violence" have a positive impact on economic activity. In 2003, a peace agreement (Sun-city agreement) led a large number of village "monopolies of violence" to relocate, in order to integrate the national government. This led to a security vacuum. I find that the vacuum caused by this peace agreement led to reductions in economic activity. I then use the timing of a large scale military operation in order to instrument for changes in the time horizon of existing village "monopolies of violence", which came under threat as a result of the military operation. I find that when their "monopoly of violence" comes under threat, armed groups turn from partial expropriation through stable taxation with full commitment, to full-scale violent expropriations. These findings support the view that the origins and workings of states can be obtained from criminal "monopolies of violence", but only if they have a stable time horizon. In Chapter 3, I turn to the experimental component of the dissertation. Having established the causes that lead to the emergence of states - taxation and coercion - I investigate how to take advantage of the state in order to increase trade in contexts where distrust prevents trade to occur. Absent states to enforce contracts, societies may develop group-based mechanisms to generate trade when commitment problems prevail (Greif, 1993). However, groups are often fragmented. Can expanding access to the state legal system complement social mechanisms of contract enforcement sustained by groups? Or does legal intermediation by the state crowd them out? In this chapter, I provide evidence on the impact of state contracts on trade. As a foundation for this chapter, I created a home delivery business in East Congo. Traders sell a domestic good in households of different ethnic groups, and commit to deliver the good in the future. Shared ethnicity and formal contracts are equally effective at increasing trade by sustaining trust. Furthermore, contracts do not crowd-out ethnic group based mechanisms of trust production. Why do contracts increase trust? Results from a last experiment suggest that contracts are enforceable. However, they only protect claimants of ethnic groups that have captured the state administration. These findings suggest that even the state apparatus is embedded in the social structure, and expanding the reach of the state may have positive welfare effects, only for the groups that have vested control in the state institutions. Each of the three chapters is self-contained, so a reader interested in only one of these parts can focus on only one chapter. Each chapter contains an overview of the context relevant for that chapter. There are overlaps in the descriptions of the context. Chapters one and two are based on the same data collection exercise, but are the focus of different questions and different variables. Chapter 3 draws on a different field experiment

Editorial. Relações Internacionais e Redes Sociais

O presente dossier temático sistematiza as grandes linhas de reflexão apresentadas no painel das Relações Internacionais do II Congresso Internacional de Comunicação e Redes Sociais na Sociedade da Informação, que decorreu na Universidade Autónoma de Lisboa entre os dias 31 de Março e 1 de Abril de 2021

Stochastic Differential Mean-Field Games in a Weak Formulation

We study a Mean Field Game system in a weak formulation through its associated McKean-Vlasov Forward-Backward Stochastic Differential Equation (FBSDE). Our main goal is to obtain existence and regularity results of this FBSDE using the techniques of Malliavin calculus, in particular, classical and Malliavin differentiability. Using these results, we characterize the decoupling (master) field.Comment: 21 page

A Poisson basis theorem for symmetric algebras of infinite-dimensional Lie algebras

We consider when the symmetric algebra of an infinite-dimensional Lie algebra, equipped with the natural Poisson bracket, satisfies the ascending chain condition (ACC) on Poisson ideals. We define a combinatorial condition on a graded Lie algebra which we call Dicksonian because it is related to Dickson's lemma on finite subsets of $\mathbb N^k$. Our main result is: Theorem. If $\mathfrak g$ is a Dicksonian graded Lie algebra over a field of characteristic zero, then the symmetric algebra $S(\mathfrak g)$ satisfies the ACC on radical Poisson ideals. As an application, we establish this ACC for the symmetric algebra of any graded simple Lie algebra of polynomial growth, and for the symmetric algebra of the Virasoro algebra. We also derive some consequences connected to the Poisson primitive spectrum of finitely Poisson-generated algebras.Comment: 29 pages; comments welcome; v2 minor changes to introduction, submitte

Instituciones, orden jurídico y representaciones políticas en Colombia

Latin American Studie