Numerical Evidence of Luttinger and Fermi Liquid Behaviour in the 2D Hubbard Model

The two dimensional Hubbard model with a single spin-up electron interacting with a finite density of spin-down electrons is studied using the quantum Monte Carlotechnique, a new conjugate gradient method for the evaluation of the Edwards wavefunction ansatz, and the standard second order perturbation theory. We performed simulations up to 242 sites at $U/t=4$ reaching the zero temperature properties with no ``fermion sign problem'' and found a surprisingly good accuracy of the Edwards wavefunction ansatz at low density or low doping. The conjugate gradient method was then applied to system up to 1922 sites and infinite $U$ for the Edwards state. Fermi liquid theory seems to remain stable in 2D for all cases studied with the exception of the half filling case where a ``Luttinger like behavior'' survives in the Hubbard model , yielding a vanishing quasiparticle weight in the thermodynamic limit.Comment: 10 pages + 4 pictures, RevTex, SISSA 121/93/CM/M

Megascopic Quantum Phenomena. A Critical Study of Physical Interpretations

A megascopic revalidation is offered providing responses and resolutions of current inconsistencies and existing contradictions in present-day quantum theory. As the core of this study we present an independent proof of the Goldstone theorem for a quantum field formulation of molecules and solids. Along with phonons two types of new quasiparticles appear: rotons and translons. In full analogy with Lorentz covariance, combining space and time coordinates, a new covariance is necessary, binding together the internal and external degrees of freedom, without explicitly separating the centre-of-mass, which normally applies in both classical and quantum formulations. The generally accepted view regarding the lack of a simple correspondence between the Goldstone modes and broken symmetries, has significant consequences: an ambiguous BCS theory as well as a subsequent Higgs mechanism. The application of the archetype of the classical spontaneous symmetry breaking, i.e. the Mexican hat, as compared to standard quantum relations, i.e. the Jahn-Teller effect, superconductivity or the Higgs mechanism, becomes a disparity. In short, symmetry broken states have a microscopic causal origin, but transitions between them have a teleological component. The different treatments of the problem of the centre of gravity in quantum mechanics and in field theories imply a second type of Bohr complementarity on the many-body level opening the door for megascopic representations of all basic microscopic quantum axioms with further readings for teleonomic megascopic quantum phenomena, which have no microscopic rationale: isomeric transitions, Jahn-Teller effect, chemical reactions, Einstein-de Haas effect, superconductivity-superfluidity, and brittle fracture.Comment: 117 pages, 17 sections, final revised version from 20 May 2019 but uploaded after the DOI was know

Barriers to Non-Viral Vector-Mediated Gene Delivery in the Nervous System

Efficient methods for cell line transfection are well described, but, for primary neurons, a high-yield method different from those relying on viral vectors is lacking. Viral transfection has several drawbacks, such as the complexity of vector preparation, safety concerns, and the generation of immune and inflammatory responses when used in vivo. However, one of the main problems for the use of non-viral gene vectors for neuronal transfection is their low efficiency when compared with viral vectors. Transgene expression, or siRNA delivery mediated by non-viral vectors, is the result of multiple processes related to cellular membrane crossing, intracellular traffic, and/or nuclear delivery of the genetic material cargo. This review will deal with the barriers that different nanoparticles (cationic lipids, polyethyleneimine, dendrimers and carbon nanotubes) must overcome to efficiently deliver their cargo to central nervous system cells, including internalization into the neurons, interaction with intracellular organelles such as lysosomes, and transport across the nuclear membrane of the neuron in the case of DNA transfection. Furthermore, when used in vivo, the nanoparticles should efficiently cross the blood-brain barrier to reach the target cells in the brain

Speaking out loud: Muslim women, Indian Delights and culinary practices in eThekwini/Durban

I asked, 'Did your mother teach you to cook?' Almost an hour later, time consumed by mutual reminiscences of Indian Delights, stories of the tastes and textures and colours of food and life in Durban, at last when I thought it would never be answered my question swam back up to the surface of our conversation: 'You know, then I lived with my oldest sister, not my mother. Her mother-in-law taught me.' Too heavy a shift of register, the answer dropped into the bubble of conversation we had made around ourselves, imposing another reluctant silence. I could not ask more, not then. Deliverance came through other stories. We talked about the subtly different combinations of spices that women even from the same family choose to use, and the embodied pleasures of walking into a kitchen steamed up with the smells of several dishes all cooking at once. And for the moment we avoided returning to a family narrative of separation, loss and melancholy