On the Influence of Spatial Dispersion on the Performance of Graphene-Based Plasmonic Devices

We investigate the effect of spatial dispersion phenomenon on the performance of graphene-based plasmonic devices at THz. For this purpose, two different components, namely a phase shifter and a low-pass filter, are taken from the literature, implemented in different graphene-based host waveguides, and analyzed as a function of the surrounding media. In the analysis, graphene conductivity is modeled first using the Kubo formalism and then employing a full-$k_\rho$ model which accurately takes into account spatial dispersion. Our study demonstrates that spatial dispersion up-shifts the frequency response of the devices, limits their maximum tunable range, and degrades their frequency response. Importantly, the influence of this phenomenon significantly increases with higher permittivity values of the surrounding media, which is related to the large impact of spatial dispersion in very slow waves. These results confirm the necessity of accurately assessing non-local effects in the development of practical plasmonic THz devices.Comment: 5 pages, 18 figures, 2 table

Hard-core bosons in phase diagrams of 2D Lattice Gauge Theories and Bosonization of Dirac Fermions

Hard-core bosons are versatile and useful in describing several physical systems due to their one-to-one mapping with spin-1/2 operators. We propose two frameworks where hard-core boson mapping not only reduces the complexity of the original problem, but also captures important features of the physics of the original system that would have implied high-computational procedures with not much profound insight in the mechanisms behind its behavior. The first case study comprising part i is an approach to the description of the phases 2D Lattice Gauge Theories, the Quantum 6-Vertex Model and the Quantum Dimer Model using one fluctuating electric string as an 1D precursor of the whole 2D systems[HAMS19]. Both models and consequently the string are described by the Rokhsar-Kivelson Hamiltonian with parameter v measuring the competition of potential versus kinetic terms. The string can be mapped one-to-one onto a 1D system of hard-core bosons that can be solved exactly for the Quantum 6-Vertex Model, and offers footprints of the phase diagram of the Quantum Dimer Model in the region close to the Rokhsar-Kivelson point v = 1, especially when |v| ≤ 1. The second case study we have discussed in part ii is an extension of higher-dimensional bosonization techniques in Landau Fermi liquids to the case of nodal semimetals where the Fermi surface shrinks to a point, so the description of particle-hole interactions as fluctuations of the Fermi surface is not available [MS20]. Additionaly, we focus our analysis on the Q = 0 sector where the electron and the hole have opposite momenta ±k, so they are mapped into a hard-core boson located at a site k in the reciprocal lattice. To test our extension we calculate nonperturbative corrections to the optical conductivity of 2D Dirac fermions with electron-electron interactins described as a Coulomb potential, obtaining results consistent to the literature and the experimental reports where corrections are small even in strong coupling regimes. Part iii discusses further ideas derived from parts i and ii, including a brief discussion on addressing the weak coupling instability in bilayer graphene using the bosonization extension that offers a picture of hard-core bosons describing Q = 0 excitons that undergo a Bose-Einstein condensation resulting in a ground state adiabatically disconnected from the noninteracting case.:1 Introduction 1 1.1 Quantum link models and fluctuating electric strings 2 1.2 Bosonization of Particle-hole excitations in 2D Dirac fermions 7 1.3 Structure of the document 11 i. Quantum link models and fluctuating electric strings 2. A Brief Introduction to Lattice Gauge Theories 15 2.1 Continuous formulation of U(1) gauge theories 15 2.1.1 Gauge field equations 16 2.1.2 Gauss’ law as generator of the gauge transformations 18 2.2 U(1) gauge theories on a lattice 19 2.2.1 Gauge field Hamiltonian 20 2.2.2 Cylindrical algebra from LGT 20 2.2.3 Generator of gauge transformations 21 2.3 Abelian Quantum Link Model 22 2.3.1 Quantum Link Models (QLMs) with S = 1 / 2 23 2.3.2 ’t Hooft operators and winding number sectors 24 2.3.3 Construction of the QLM Hamiltonian 26 2.4 Conclusions 28 3. Electric string in Q6VM as a XXZ chain 29 3.1 Realization of the Q6VM in the S = 1 / 2 QLM 31 3.2 Mapping the electric string to the XXZ chain 32 3.3 Phases of the electric string from the XXZ chain 33 3.3.1 v > 1: FM insulator 34 3.3.2 v = 1: RK point 36 3.3.3 −1 < v < 1: Gapless phase 36 3.3.4 v ≤ −1: KT transition and AFM insulator 37 3.4 Numerical approach: Drude Weight and system size effects 38 3.5 Summary and Discussion 40 4. Electric line in the QDM as a hard-core boson two-leg ladder 41 4.1 Realization of the QDM in the S = 1/ 2 QLM 42 4.2 Construction of an electric string in the QDM 43 4.3 Mapping the electric string in QDM to a two-leg ladder 45 4.3.1 QLM in a triangular lattice 45 4.3.2 From the triangular lattice to the two-leg ladder 45 4.3.3 Construction of the 1D bosonic Hamiltonian 46 4.4 Phases of the electric string from the bosonic two-leg ladder 48 4.4.1 Left Hand Side (LHS) of the Rokhsar-Kivelson (RK) point: Charge Density Wave (CDW) states 48 4.4.2 Right Hand Side (RHS) of the RK point: phase-separated states 50 4.5 Numerical approach: Drude Weight and system size effects 51 4.6 Summary and Discussion 52 ii Bosonization of particle-hole excitations in 2D Dirac fermions 5 Graphene in a nutshell 57 5.1 Origin of the hexagonal structure 57 5.1.1 Hybrid orbitals in C 58 5.1.2 Honeycomb lattice 60 5.2 Tight-binding approach 61 5.2.1 Hopping and overlapping matrices in Nearest Neighbor (NN) approximation 62 5.2.2 Dispersion relation for π electrons 62 5.3 Effective 2D Dirac Fermion Hamiltonian 64 5.4 Electron-electron interactions 65 6 Bosonization of the Q = 0 continuum of Dirac Fermions 67 6.1 Effective Hamiltonian and Hilbert space 69 6.2 Effective Heisenberg Hamiltonian 70 6.3 Quadratic Bosonic Hamiltonian 71 6.4 Connection to diagramatic perturbation theory 73 6.5 Parametrization of the reciprocal space 74 6.5.1 Coordinate transformation 74 6.5.2 Polar parametrization 75 6.5.3 Angular momentum channels 75 6.6 Discussion and Summary 76 7 Non-perturbative corrections to the Optical Conductivity of 2D Dirac Fermions 77 7.1 Optical Conductivity 79 7.1.1 Bosonized current operator and susceptibility 79 7.1.2 Susceptibility in terms of the eigenstates 80 7.1.3 Regularization of the Lehman representation 81 7.2 Numerical approach: IR regularization and system size effects 82 7.2.1 Discretization size dependence 82 7.2.2 Dependence on the IR cutoff 83 7.2.3 Comparison of numerical results with corrections from first order perturbation theory 84 7.2.4 Optical conductivity for several coupling constants 85 7.3 Discussion and Summary 86 iii Weak coupling instability, New Perspectives & Conclusions 8 Weak coupling instability in bilayer graphene from a bosonization picture 91 8.1 Band structure of Bernal-stacked bilayer graphene 92 8.2 Generalization of the effective Hamiltonian of graphene 93 8.2.1 Density of states in monolayer and bilayer graphene 94 8.2.2 Projection onto Q = 0 sector and effective Heisenberg pseudospin Hamiltonian 95 8.2.3 Zeeman vortex coordinates and HCB operators 95 8.2.4 Bogoliubov-Valatin basis 97 8.3 Interaction potentials 97 8.4 BCS instability in pseudospin picture 99 8.5 Numerical procedure 101 8.5.1 Numerical BCS instability 101 8.5.2 Functional form of the instability 101 8.5.3 Comparison to the instability from BCS theory 105 8.6 Conclusions 105 9 Conclusions 107 iv Appendices A. Yang & Yang’s expressions of ground state energy of XXZ Chain using Bethe Ansatz 115 A.1 Bethe Ansatz 115 A.2 Explicit formulas for f ( ∆, 0 ) 116 B. Kadanoff-Baym (KB) self-consistent Hartree-Fock (SCHF) approximation 119 B.1 Details of connection to perturbation theory 119 B.1.1 Bare and dressed fermion propagators 119 B.1.2 Bethe-Salpeter ladder 120 B.1.3 Particle-hole propagator and comparison to HP boson propagator 121 C, Optical Conductivity from Pseudospin precession 123 C.1 Minimal coupling and band (electron-hole) basis 123 C.2 Equations of motion of charge and pseudospin densities 124 C.3 Optical Conductivity from Fermi-Dirac distributions at finite temperature 124 D. Momentum space reparametrization 127 D.1 General coordinate transformations on the continuum limit 127 D.2 Polar re-discretization 129 D.3 Angular momentum channels 130 D.4 Selection of the radial parametrization 130 Bibliography 13

Emergent Time and Time Travel in Quantum Physics

Entertaining the possibility of time travel will invariably challenge dearly-held concepts in fundamental physics. It becomes relatively easy to construct multiple logical contradictions using differing starting points from various well-established fields of physics. Sometimes, the interpretation is that only a full theory of quantum gravity will be able to settle these logical contradictions. Even then, it remains unclear if the multitude of problems could be overcome. Yet as definitive as this seems to the notion of time travel in physics, such recourse to quantum gravity comes with its own, long-standing challenge to most of these counter-arguments to time travel: These arguments rely on time, while quantum gravity is (in)famously stuck with the problem of time. One attempt to answer this problem within the canonical framework resulted in the Page–Wootters formalism, and its recent gauge-theoretic reinterpretation as an emergent notion of time. Herein, we will begin a program to study toy models implementing the Hamiltonian constraint in quantum theory, with an aim toward understanding what an emergent notion of time can tell us about the (im)possibility of time travel.Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)Spanish ProjectCzech Science FoundationMarsden FundPeer Reviewe

Logistic Q-Learning

We propose a new reinforcement learning algorithm derived from a regularized linear-programming formulation of optimal control in MDPs. The method is closely related to the classic Relative Entropy Policy Search (REPS) algorithm of Peters et al. (2010), with the key difference that our method introduces a Q-function that enables efficient exact model-free implementation. The main feature of our algorithm (called QREPS) is a convex loss function for policy evaluation that serves as a theoretically sound alternative to the widely used squared Bellman error. We provide a practical saddle-point optimization method for minimizing this loss function and provide an error-propagation analysis that relates the quality of the individual updates to the performance of the output policy. Finally, we demonstrate the effectiveness of our method on a range of benchmark problems

An Analysis of Lazy and Eager Limited Preemption Approaches under DAG-Based Global Fixed Priority Scheduling

DAG-based scheduling models have been shown to effectively express the parallel execution of current many-core heterogeneous architectures. However, their applicability to real-time settings is limited by the difficulties to find tight estimations of the worst-case timing parameters of tasks that may arbitrarily be preempted/migrated at any instruction. An efficient approach to increase the system predictability is to limit task preemptions to a set of pre-defined points. This limited preemption model supports two different preemption approaches, eager and lazy, which have been analyzed only for sequential task-sets. This paper proposes a new response time analysis that computes an upper bound on the lower priority blocking that each task may incur with eager and lazy preemptions. We evaluate our analysis with both, synthetic DAG-based task-sets and a real case-study from the automotive domain. Results from the analysis demonstrate that, despite the eager approach generates a higher number of priority inversions, the blocking impact is generally smaller than in the lazy approach, leading to a better schedulability performance.This work was funded by the EU projects P-SOCRATES (FP7-ICT-2013-10) and HERCULES (H2020/ICT/2015/688860), and the Spanish Ministry of Science and Innovation under contract TIN2015-65316-P.Peer ReviewedPostprint (author's final draft

Effect of Coir Fiber Content and Compatibilizer on the Properties of Unidirectional Coir Fiber/Polypropylene Composites

The main objective of this research was to study the effect of fiber content variation and stearic acid (SA) treatment on the fundamental properties of unidirectional coir fiber (CF) reinforced polypropylene (PP) composites. Several percentages of filler contents were used (10–40 wt %) in order to gain insights into the effect of filler content on the properties of the composites. Coir/PP composites were fabricated by compression molding, and the properties of composites were studied by physico-mechanical and thermal properties. The results from mechanical properties such as tensile strength (TS), tensile modulus (TM) and impact strength (IS) of the CF/PP composites were found to be increased with increasing fiber content, reached an optimum and thereafter decreased with further increase in fiber content. Treatment of the coir with SA as the coupling agent enhanced the mechanical properties, crystallization temperature and crystallinity of virgin PP and water desorption of the resulting composites, resulting from the improved adhesion between the CF and PP matrix. Scanning electron micrographs (SEM) of the tensile fractured samples showed improved adhesion between fiber and matrix upon treatment with SA. Interfacial shear strength (IFSS) of the composites was measured by single fiber fragmentation test (SFFT)

Fermion mass hierarchy from nonuniversal abelian extensions of the Standard Model

The fermion mass hierarchy is addresed from the framework of an abelian extension of the Standard Model U(1)X. By taking into account the cancellation of chiral anomalies, a set of U(1)X charges is presented with extended scalar and fermionic sectors. The scalar potential is shown, together with the scalar spectrum of the model which includes the respective Goldstone bosons, new physical neutral and charged scalars at TeV scale and the 125 GeV Higgs boson. Then, the mass acquisition in the fermionic sector is studied in detail. The mass matrices present an specific texture called suppresion square texture (SST) which suggests the mass hierarchy when they are diagonalized by algebraic and numerical methods. The model turns out to be consistent is consistent at 5sigma and 3sigma in the quark and lepton sectors, respectively, without unpleasant fine-tuning procedures.Resumen: La jerarquía de masas de fermiones es abordada desde el marco de una extensión abeliana del Modelo Estándar U(1)X. Teniendo en cuenta la cancelación de anomalías quirales, un conjunto de cargas de U(1) es presentada con sectores escalares y fermiónicos extendidos. Se muestra el potencial escalar junto con el espectro escalar del modelo, el cual incluye los respectivos bosones de Goldstone, escalares físicos cargados y neutros a escala de TeV y el bosón de Higgs de 125 GeV. Después, la adquisición de masas en el sector de fermiones es estudiado en detalle. Las matrices de masa presentan una textura específica llamada textura de cuadros de supresión, la cual sugiere la jerarquía de masas cuando son diagonalizadas por métodos tanto algebraicos como numéricos. El modelo resulta ser consistente a 5sigma y 3sigma en los sectores de quarks y leptones, respectivamente, sin necesidad de usar ajustes finos indeseados.Maestrí

Hemp yields and its rotation effects on wheat under rainfed mediterranean conditions

Hemp (Cannabis sativa L.) has a low impact on the environment requiring few added resources, and has multiple downstream applications. Th ere is little information on hemp biomass, seed yields, and response to NPK fertilization under humid rainfed Mediterranean conditions. Moreover, the eff ects of hemp on subsequent wheat (Triticum aestivum L.) crops have not been determined. To address these issues, we performed a fi eld study for 6 yr in Catalonia (northeastern Spain). Hemp treatments included: hemp monoculture, unfertilized hemp succeeding wheat, and NPK-fertilized hemp succeeding wheat. In turn, wheat treatments included: wheat monoculture, fi rst-, second-, and third-year wheat succeeding unfertilized hemp, and fi rst-, second-, and third-year wheat succeeding NPK-fertilized hemp. Th e hemp biomass yields (5340–10,090 kg ha–1) were similar to or lower than those achieved in other European regions whereas the hemp seed yields were relatively high (604–1434 kg ha–1). Both the biomass yield and seed yield greatly increased with NPK fertilization. Th e rotation eff ects of hemp on the sub-sequent wheat crops increased the wheat yield by 1368 and 155 kg ha–1 in the fi rst and second years, respectively, but in the third year the yield was similar to the wheat monoculture. Th e benefi cial eff ects of hemp on wheat therefore appear to last for 2 yr. We conclude that dual-purpose hemp (harvested for fi ber and seed) is an excellent predecessor for wheat, improving the sustainability of cereal-based cropping systems under humid rainfed Mediterranean conditions

PKMζ Differentially Utilized between Sexes for Remote Long-Term Spatial Memory

It is well established that male rats have an advantage in acquiring place-learning strategies, allowing them to learn spatial tasks more readily than female rats. However many of these differences have been examined solely during acquisition or in 24h memory retention. Here, we investigated whether sex differences exist in remote long-term memory, lasting 30d after training, and whether there are differences in the expression pattern of molecular markers associated with long-term memory maintenance. Specifically, we analyzed the expression of protein kinase M zeta (PKMζ) and the α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor subunit GluA2. To adequately evaluate memory retention, we used a robust training protocol to attenuate sex differences in acquisition and found differential effects in memory retention 1d and 30d after training. Female cohorts tested for memory retention 1d after 60 training trials outperformed males by making significantly fewer reference memory errors at test. In contrast, male cohorts tested 30d after 60 training trials outperformed females of the same condition, making fewer reference memory errors and achieving significantly higher retention test scores. Furthermore, given 60 training trials, females tested 30d later showed significantly worse memory compared to females tested 1d later, while males tested 30d later did not differ from males tested 1d later. Together these data suggest that with robust training males do no retain spatial information as well as females do 24h post-training but maintain this spatial information for longer. Males also showed a significant increase in synaptic PKMζ expression and a positive correlation with retention test scores, while females did not. Interestingly, both sexes showed a positive correlation between retention test scores and synaptic GluA2 expression. Furthermore, the increased expression of synaptic PKMζ, associated with male memory but not with female memory, identifies another potential sex-mediated difference in memory processing

Acute Physiological Stress Promotes Clustering of Synaptic Markers and Alters Spine Morphology in the Hippocampus

GluA2-containing AMPA receptors and their association with protein kinase M zeta (PKMζ) and post-synaptic density-95 (PSD-95) are important for learning, memory and synaptic plasticity processes. Here we investigated these synaptic markers in the context of an acute 1h platform stress, which can disrupt spatial memory retrieval for a short-term memory on the object placement task and long-term memory retrieval on a well-learned radial arm maze task. Acute stress increased serum corticosterone and elevated the expression of synaptic PKMζ while decreasing synaptic GluA2. Using co-immunoprecipitation, we found that this stressor promotes the clustering of GluA2, PKMζ and PSD-95, which is consistent with effects reported from overexpression of PKMζ in cell culture. Because PKMζ overexpression has also been shown to induce spine maturation in culture, we examined how stress impacts synaptic markers within changing spines across various hippocampal subfields. To achieve this, we employed a new technique combining Golgi staining and immmunohistochemistry to perform 3D reconstruction of tertiary dendrites, which can be analyzed for differences in spine types and the colocalization of synaptic markers within these spines. In CA1, stress increased the densities of long-thin and mushroom spines and the colocalization of GluA2/PSD-95 within these spines. Conversely, in CA3, stress decreased the densities of filopodia and stubby spines, with a concomitant reduction in the colocalization of GluA2/PSD-95 within these spines. In the outer molecular layer (OML) of the dentate gyrus (DG), stress increased both stubby and long-thin spines, together with greater GluA2/PSD-95 colocalization. These data reflect the rapid effects of stress on inducing morphological changes within specific hippocampal subfields, highlighting a potential mechanism by which stress can modulate memory consolidation and retrieval