Conservation of Statistics and Generalized Grassmann Numbers

Conservation of statistics requires that fermions be coupled to Grassmann external sources. Correspondingly, conservation of statistics requires that parabosons, parafermions and quons be coupled to external sources that are the appropriate generalizations of Grassmann numbers.Comment: 10 pages, late

N-quantum approach to quantum field theory at finite T and μ\mu: the NJL model

We extend the N-quantum approach to quantum field theory to finite temperature ($T$) and chemical potential ($\mu$) and apply it to the NJL model. In this approach the Heisenberg fields are expressed using the Haag expansion while temperature and chemical potential are introduced simultaneously through a generalized Bogoliubov transformation. Known mean field results are recovered using only the first term in the Haag expansion. In addition, we find that at finite T and in the broken symmetry phase of the model the mean field approximation can not diagonalize the Hamiltonian. Inclusion of scalar and axial vector diquark channels in the SU(2)$_{rm f}$ $otimes$ SU(3)$_{\rm c}$ version of the model can lead to a lowering of the vacuum energy density. We discuss how to go beyond the mean field approximation by including higher order terms in the Haag expansion.Comment: 14 pages including 2 eps figures. Modified sentences on the lowering of the vacuum energy densit

The Voltage-Current Characteristic of high T_c DC SQUID: theory, simulation, experiment

The analytical theory for the voltage-current characteristics of the large inductance (L>100 pH) high-T_c DC SQUIDs that has been developed previously is consistently compared with the computer simulations and the experiment. The theoretical voltage modulation for symmetric junctions is shown to be in a good agreement with the results of known computer simulations. It is shown that the asymmetry of the junctions results in the increase of the voltage modulation if the critical current is in excess of some threshold value (about 8 microAmps). Below this value the asymmetry leads to the reduction of the voltage modulation as compared to the symmetric case. The comparison with the experiment shows that the asymmetry can explain a large portion of experimental values of the voltage modulation which lie above the theoretical curve for symmetric DC SQUID. It also explains experimental points which lie below the curve at small critical currents. However, a significant portion of these values which lie below the curve cannot be explained by the junction asymmetry.Comment: 22 pages, 14 figure

Neutrino statistics and non-standard commutation relations

Recently it was suggested that the neutrino may violate the Pauli exclusion Principle (PEP). This renews interest in the systematic search for bilinear commutation relations that could describe deviations from PEP. In the context of this search we prove a no-go theorem which forbids a finite occupancy limit for an arbitrary system with a bilinear commutation relation. In other words, either the upper limit on the occupancy number is 1 (the ordinary fermionic case) or there is no upper limit at all. Some examples of the latter class include the usual Bose statistics, as well as non-standard quon statistics and infinite statistics.Comment: 11 pages, RevTeX

Functional Neuroimaging Investigation of the Neural Mechanisms for Successful Feeling-of-Knowing Judgments

A feeling-of-knowing (FOK) is a sense of knowing that an item would be recognizable if seen again later, despite one’s current inability to recall that item from memory. An FOK judgment occurs after a memory search and is a prediction of future recognition. The current study aimed to: (1) determine the brain regions involved in successful (accurate) and unsuccessful (inaccurate) episodic FOKs; (2) replicate the ability of FOKs to predict recognition outcomes and recollection/know (R/K) judgments; (3) explore the different effects of familiarity and recollection on high and low FOKs; and (4) determine the effect of overlearning on FOKs and their ability to predict recognition and R/K outcomes. Nine younger adults (ages 18-26) participated in 2 experimental sessions (encoding and testing), separated by a 48-hour delay (n = 4 for fMRI data). The amount of exposure to the studied items (1 versus 3 presentations) was manipulated. Statistically significant results include (1) a repetition effect such that the words that were repeated during encoding have higher mean recall, mean FOK rating, mean recognition accuracy, and mean R/K than those words presented only once; (2) activity in the ventral lateral prefrontal cortex (PFC) for successful or accurate FOKs; (3) activity in the anterior PFC for accurate high FOKs; and (4) activity in the PFC and anterior cingulate for correctly recognized and remembered items. In future, additional participants are necessary to conduct further and more detailed analyses.Hertzog, Chris - Faculty Mentor ; Schumacher, Eric - Committee Member/Second Reade