Possible Exotic Phases in the One-Dimensional Extended Hubbard Model

We investigate numerically the ground state phase diagram of the one-dimensional extended Hubbard model, including an on--site interaction U and a nearest--neighbor interaction V. We focus on the ground state phases of the model in the V >> U region, where previous studies have suggested the possibility of dominant superconducting pairing fluctuations before the system phase separates at a critical value V=V_PS. Using quantum Monte Carlo methods on lattices much larger than in previous Lanczos diagonalization studies, we determine the boundary of phase separation, the Luttinger Liquid correlation exponent K_rho, and other correlation functions in this region. We find that phase separation occurs for V significantly smaller than previously reported. In addition, for negative U, we find that a uniform state re-enters from phase separation as the electron density is increased towards half filling. For V < V_PS, our results show that superconducting fluctuations are not dominant. The system behaves asymptotically as a Luttinger Liquid with K_rho < 1, but we also find strong low-energy (but gapped) charge-density fluctuations at a momentum not expected for a standard Luttinger Liquid.

Linking brain to mind in normal behavior and schizophrenia

In order to understand schizophrenia, a linking hypothesis is needed that shows how brain mechanisms lead to behavioral functions in normals, and also how breakdown in these mechanisms lead to behavioral symptoms in schizophrenia. Such a linking hypothesis is now available that complements the discussion offered by Phillips and Silverstein.

Consciousness CLEARS the Mind

A full understanding of consciouness requires that we identify the brain processes from which conscious experiences emerge. What are these processes, and what is their utility in supporting successful adaptive behaviors? Adaptive Resonance Theory (ART) predicted a functional link between processes of Consciousness, Learning, Expectation, Attention, Resonance, and Synchrony (CLEARS), includes the prediction that "all conscious states are resonant states." This connection clarifies how brain dynamics enable a behaving individual to autonomously adapt in real time to a rapidly changing world. The present article reviews theoretical considerations that predicted these functional links, how they work, and some of the rapidly growing body of behavioral and brain data that have provided support for these predictions. The article also summarizes ART models that predict functional roles for identified cells in laminar thalamocortical circuits, including the six layered neocortical circuits and their interactions with specific primary and higher-order specific thalamic nuclei and nonspecific nuclei. These prediction include explanations of how slow perceptual learning can occur more frequently in superficial cortical layers. ART traces these properties to the existence of intracortical feedback loops, and to reset mechanisms whereby thalamocortical mismatches use circuits such as the one from specific thalamic nuclei to nonspecific thalamic nuclei and then to layer 4 of neocortical areas via layers 1-to-5-to-6-to-4.