Higher-order Floquet topological phases with corner and bulk bound states

We report the theoretical discovery and characterization of higher-order Floquet topological phases dynamically generated in a periodically driven system with mirror symmetries. We demonstrate numerically and analytically that these phases support lower-dimensional Floquet bound states, such as corner Floquet bound states at the intersection of edges of a two-dimensional system, protected by the nonequilibrium higher-order topology induced by the periodic drive. We characterize higher-order Floquet topologies of the bulk Floquet Hamiltonian using mirror-graded Floquet topological invariants. This allows for the characterization of a new class of higher-order "anomalous" Floquet topological phase, where the corners of the open system host Floquet bound states with the same as well as with double the period of the drive. Moreover, we show that bulk vortex structures can be dynamically generated by a drive that is spatially inhomogeneous. We show these bulk vortices can host multiple Floquet bound states. This "stirring drive protocol" leverages a connection between higher-order topologies and previously studied fractionally charged, bulk topological defects. Our work establishes Floquet engineering of higher-order topological phases and bulk defects beyond equilibrium classification and offers a versatile tool for dynamical generation and control of topologically protected Floquet corner and bulk bound states.Comment: v2: 13 pages, 8 figures, 3 appendices; new references, and new analytical and numerical work showing the robustness of Z invariant without diagonal mirror symmetrie

Mothers and Daughters at Imperial Crossroads: Expressions of Status, Economy and Nurture in 16th Century Mexico.

My dissertation, Mothers and Daughters at Imperial Crossroads: Expressions of Status, Economy, and Nurture in 16th Century Mexico considers an often overlooked but foundational aspect of colonization in the New World: the transfer of status and wealth through indigenous women in a confluence of political economy and ritual ceremony. Chapter 1 sets up this analysis through the Nahua historian Chimalpahin Quautlehuanitzin’s exposé on the crisis of government in Chalco, a formerly powerful Nahua state at the southern edge of the valley of Mexico. Chimalpahin’s insistence that colonial authorities recognize women’s nobility prompts an investigation, in Chapter 2, of the gendered dimensions of nobility between Spanish and Nahua societies. To this end, these first two chapters advance a triangular reading of Chimalpahin’s representation of nobility alongside the Florentine Codex, a 16th century encyclopedia of life in pre-Conquest Mesoamerica, and the legal codes propagated by Alfonso X in the Siete Partidas. While Chapters 1 and 2 focus on the stakes of nobility within the colonial regime, Chapter 3 explores the chameleon-like status of the tribute women given to the conquistador Hernán Cortés during his march to Tenochtitlan in 1519. The transformation of young common women into noble brides through body paints, feathers and fine clothing enacts a deliberate dissolution of hierarchies that prefigures the crisis of government in Chalco. Alongside Spanish and Nahuatl accounts of the Conquest, the Lienzo de Tlaxcala’s visual representation of indigenous tribute gifts to Cortés anchors this exploration of Mexico’s tribute women. In Chapter 4, the maguey plant in its deified form, as the goddess Mayahuel, becomes an avatar for a transfer of wealth that flows from women’s bodies to the imperial capital. The insistence of women, however, to harvest maguey and sell its products on their own terms challenges the limitations to their mobility and appropriation of their income—an intrusion into the masculinist historiographies and imperial spaces of 16th century Mexico.PhDRomance Languages and Literatures: SpanishUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133456/1/martinv_1.pd

Anticoncentration theorems for schemes showing a quantum speedup

One of the main milestones in quantum information science is to realise quantum devices that exhibit an exponential computational advantage over classical ones without being universal quantum computers, a state of affairs dubbed quantum speedup, or sometimes "quantum computational supremacy". The known schemes heavily rely on mathematical assumptions that are plausible but unproven, prominently results on anticoncentration of random prescriptions. In this work, we aim at closing the gap by proving two anticoncentration theorems and accompanying hardness results, one for circuit-based schemes, the other for quantum quench-type schemes for quantum simulations. Compared to the few other known such results, these results give rise to a number of comparably simple, physically meaningful and resource-economical schemes showing a quantum speedup in one and two spatial dimensions. At the heart of the analysis are tools of unitary designs and random circuits that allow us to conclude that universal random circuits anticoncentrate as well as an embedding of known circuit-based schemes in a 2D translation-invariant architecture.Comment: 12+2 pages, added applications sectio

Impurity in a granular gas under nonlinear Couette flow

We study in this work the transport properties of an impurity immersed in a granular gas under stationary nonlinear Couette flow. The starting point is a kinetic model for low-density granular mixtures recently proposed by the authors [Vega Reyes F et al. 2007 Phys. Rev. E 75 061306]. Two routes have been considered. First, a hydrodynamic or normal solution is found by exploiting a formal mapping between the kinetic equations for the gas particles and for the impurity. We show that the transport properties of the impurity are characterized by the ratio between the temperatures of the impurity and gas particles and by five generalized transport coefficients: three related to the momentum flux (a nonlinear shear viscosity and two normal stress differences) and two related to the heat flux (a nonlinear thermal conductivity and a cross coefficient measuring a component of the heat flux orthogonal to the thermal gradient). Second, by means of a Monte Carlo simulation method we numerically solve the kinetic equations and show that our hydrodynamic solution is valid in the bulk of the fluid when realistic boundary conditions are used. Furthermore, the hydrodynamic solution applies to arbitrarily (inside the continuum regime) large values of the shear rate, of the inelasticity, and of the rest of parameters of the system. Preliminary simulation results of the true Boltzmann description show the reliability of the nonlinear hydrodynamic solution of the kinetic model. This shows again the validity of a hydrodynamic description for granular flows, even under extreme conditions, beyond the Navier-Stokes domain.Comment: 23 pages, 11 figures; v2: Preliminary DSMC results from the Boltzmann equation included, Fig. 11 is ne

Free zones in Brazil: analysis of existing legislation

Este trabajo, en su primera parte, hace una introducción general a la institución llamada zona franca, aportando algunos conceptos tanto doctrinarios como legislativos. Trata a su vez cómo ha evolucionado a lo largo de la historia y cuáles son los tipos que han ido surgiendo, siempre conservando algunas características comunes. La segunda parte se refiere a la legislación específica de Brasil, pasando por la zona franca de Manaos y por las normas que regulan las Zonas de Procesamiento de Exportación. Aquí encontraremos los distintos beneficios que se otorgan, las similitudes y diferencias existentes entre ambos modelos.The first part of this paper gives a general introduction of the institution named free zone, providing some doctrinal and legislative concepts. We will also see how it has evolved throughout history and the types of these that have been emerging, but always preserving common characteristics. The second part refers to specific legislation in Brazil, passing for the free zone of Manaus and the Export Processing Zone´s rules. Here we will find the different benefits, the similarities and differences between both models.Fil: Vega Correa, Martin Lautaro. Universidad Nacional de Córdoba; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Disorder Effects in Dirac Heterostructures

In this dissertation, we study theoretically heterostructures based on Dirac mate- rials, i.e. materials, such as graphene in which the electrons behave as massless Dirac fermions at low energies. We first examine how the presence of long-range disorder affects the electronic ground state of a double layer graphene heterostruc- ture formed by two graphene layers separated by a thin dielectric film. We then identify the necessary conditions for the formation of an interlayer exciton conden- sate in such a system. We also comment on the effect of long-range disorder on the broken symmetry ground state induced by electron-electron interactions in bilayer graphene. Then, we study the transport properties of heterostructures obtained by stacking a graphene layer on the surface of a strong three-dimensional topological insulator (TI). In particular, we determine the non-equilibrium current-induced spin density accumulation for these systems using linear response theory and taking into account the effects of long- and short-range disorder both in the limit of strong and weak tunneling between the graphene layer and the TI. Finally, using some of the theoretical approaches developed to characterize the effect of long-range disorder in Dirac materials, we study the effect of long-range inhomogeneities in first-order phase transitions. In particular, we present a theoretical model to describe the ef- fect of inhomogeneities on the relaxation dynamics of vanadium dioxide films after a photo-induced metal-insulator transition

Mathematical Modelling and Analysis of Spatially Correlated Heterogeneous and Vehicular Networks - A Stochastic Geometry Approach

Heterogeneous Cellular Networks (HCNs) and vehicular communications are two key ingredients of future 5G communication networks, which aim at providing high data rates on the one former case and high reliability on the latter one. Nevertheless, in these two scenarios, interference is the main limiting factor, which makes achieving the required performance, i.e., data rate or reliability, a challenging task. Hence, in order to cope with such issue, concepts like uplink/downlink (UL/DL) decoupling, Interference-Aware (IA) strategies or cooperative communications with Cloud Radio Access Networks (CRANs) has been introduced for new releases of 4G and future 5G networks. Additionally, for the sake of increasing the data rates, new multiple access schemes like Non-Orthogonal Multiple Access (NOMA) has been proposed for 5G networks. All these techniques and concepts require accurate and tractable mathematical modelling for performance analysis. This analysis allows us to obtain theoretical insights about key performance indicators leading to a deep understanding about the considered techniques. Due to the random and irregular nature that exhibits HCNs, as well as vehicular networks, stochastic geometry has appeared recently as a promising tool for system-level modelling and analysis. Nevertheless, some features of HCNs and vehicular networks, like power control, scheduling or frequency planning, impose spatial correlations over the underlying point process that complicates significantly the mathematical analysis. In this thesis, it has been used stochastic geometry and point process theories to investigate the performance of these aforementioned techniques. Firstly, it is derived a mathematical framework for the analysis of an Interference-Aware Fractional Power Control (IAFPC) for interference mitigation in the UL of HCNs. The analysis reveals that IAFPC outperforms the classical FPC in terms of Spectral Efficiency (SE), average transmitted power, and mean and variance of the interference. Then, it is investigated the performance of a scheduling algorithm where the Mobile Terminals (MTs) may be turned off if they cause a level of interference greater than a given threshold. Secondly, a multi-user UL model to assess the coverage probability of different MTs in each cell is proposed. Then, the coverage probability of cellular systems under Hoyt fading (Nakagami-q) is studied. This fading model, allows us to consider more severe fading conditions than Rayleigh, which is normally the considered fading model for the sake of tractability. Thirdly, a novel NOMA-based scheme for CRANs is proposed, modelled and analyzed. In this scheme, two users are scheduled in the same resources according to NOMA; however the performance of cell-edge users is enhanced by means of coordinated beamforming. Finally, the performance of a decentralized Medium Access Control (MAC) algorithm for vehicular communications is investigated. With this strategy, the cellular network provides frequency and time synchronization for direct Vehicle to Vehicle (V2V) communication, which is based on its geographical information. The analysis demonstrates that there exists an operation regime where the performance is noise-limited. Then, the optimal transmit power that maximizes the Energy Efficiency (EE) of the system subject to a minimum capture probability constraint is derived