Charge orders, magnetism and pairings in the cuprate superconductors

We review the recent developments in the field of cuprate superconductors with the special focus on the recently observed charge order in the underdoped compounds. We introduce new theoretical developments following the study of the antiferromagnetic (AF) quantum critical point (QCP) in two dimensions, in which preemptive orders in the charge and superconducting (SC) sectors emerged, that are in turn related by an SU(2) symmetry. We consider the implications of this proliferation of orders in the underdoped region, and provide a study of the type of fluctuations which characterize the SU(2) symmetry. We identify an intermediate energy scale where the SU(2) pairing fluctuations are dominant and argue that they are unstable towards the formation of a Resonant Peierls Excitonic (RPE) state at the pseudogap (PG) temperature $T^{*}$. We discuss the implications of this scenario for a few key experiments.Comment: 16 pages, 17 figure

Coherent delocalization: Views of entanglement in different scenarios

The concept of entanglement was originally introduced to explain correlations existing between two spatially separated systems, that cannot be described using classical ideas. Interestingly, in recent years, it has been shown that similar correlations can be observed when considering different degrees of freedom of a single system, even a classical one. Surprisingly, it has also been suggested that entanglement might be playing a relevant role in certain biological processes, such as the functioning of pigment-proteins that constitute light-harvesting complexes of photosynthetic bacteria. The aim of this work is to show that the presence of entanglement in all of these different scenarios should not be unexpected, once it is realized that the very same mathematical structure can describe all of them. We show this by considering three different, realistic cases in which the only condition for entanglement to exist is that a single excitation is coherently delocalized between the different subsystems that compose the system of interest

Analisis de las dificultades en el aprendizaje autogestionado de un tema de Química

El grupo de alumnos que no regulariza la asignatura durante el cursado, en el próximo año se transforma en recursantes. Para este grupo de alumnos puede ser una opción válida que autogestionen sus aprendizajes por sistema e-learning con el acompañamiento de docentes-tutores. Como primera aproximación de esta modalidad de aprendizaje se seleccionó el tema óxido-reducción encarado a través de la utilización de diagramas de Latimer para evaluar si se logró aprendizaje sobre balanceo de ecuaciones redox, criterios de espontaneidad, procesos de dismutación o desproporción, cálculo de potenciales, entre otros. Es objetivo de este trabajo analizar, con un mismo instrumento de evaluación, las dificultades en la comprensión del tema óxido-reducción usando como estrategia el aprendizaje autogestionado en alumnos recursantes y la forma tradicional en alumnos no recursantes

Generalised eigenfunction expansion and singularity expansion methods for canonical time-domain wave scattering problems

The generalised eigenfunction expansion method (GEM) and the singularity expansion method (SEM) are applied to solve the canonical problem of wave scattering on an infinite stretched string in the time domain. The GEM, which is shown to be equivalent to d'Alembert's formula when no scatterer is present, is also derived in the case of a point-mass scatterer coupled to a spring. The discrete GEM, which generalises the discrete Fourier transform, is shown to reduce to matrix multiplication. The SEM, which is derived from the Fourier transform and the residue theorem, is also applied to solve the problem of scattering by the mass-spring system. The GEM and SEM are also applied to the problem of scattering by a mass positioned a fixed distance from an anchor point, which supports more complicated resonant behavior.Comment: 18 pages, 5 figure

Generalised eigenfunction expansion and singularity expansion methods for two-dimensional acoustic time-domain wave scattering problems

Time-domain wave scattering in an unbounded two-dimensional acoustic medium by sound-hard scatterers is considered. Two canonical geometries, namely a split-ring resonator (SRR) and an array of cylinders, are used to highlight the theory, which generalises to arbitrary scatterer geometries. The problem is solved using the generalised eigenfunction expansion method (GEM), which expresses the time-domain solution in terms of the frequency-domain solutions. A discrete GEM is proposed to numerically approximate the time-domain solution. It relies on quadrature approximations of continuous integrals and can be thought of as a generalisation of the discrete Fourier transform. The solution then takes a simple form in terms of direct matrix multiplications. In parallel to the GEM, the singularity expansion method (SEM) is also presented and applied to the two aforementioned geometries. It expands the time-domain solution over a discrete set of unforced, complex resonant modes of the scatterer. Although the coefficients of this expansion are divergent integrals, we introduce a method of regularising them using analytic continuation. The results show that while the SEM is usually inaccurate at $t=0$, it converges rapidly to the GEM solution at all spatial points in the computational domain, with the most rapid convergence occurring inside the resonant cavity.Comment: 24 pages, 9 figure

Optimal eigenvalues estimate for the Dirac operator on domains with boundary

We give a lower bound for the eigenvalues of the Dirac operator on a compact domain of a Riemannian spin manifold under the \MIT bag boundary condition. The limiting case is characterized by the existence of an imaginary Killing spinor.Comment: 10 page