Thoughts about disordered thinking: measuring and quantifying the laws of order and disorder

Peer ReviewedPostprint (author's final draft

θ\theta Effects in Chern-Simons QED2+1{\rm QED}_{2+1} with a Four-Fermi Interaction

We investigate the effects of the Chern-Simons coupling on the high energy behavior in the $(2+1)$-dimensional Chern-Simons QED with a four-Fermi interaction. Using the $1/N$ expansion we discuss the Chern-Simons effects on the critical four-Fermi coupling at $O(1/N)$ and the $\beta$ function around it. High-energy behavior of Green's functions is also discussed. By explicit calculation, we find that the radiative correction to the Chern-Simons coupling vanishes at $O(1/N)$ in the broken phase of the dynamical parity symmetry. We argue that no radiative corrections to the Chern-Simons term arise at higher orders in the $1/N$ expansion.Comment: 13 pages, 6 figures not included, LaTeX, SNUTP 92-9

Nature of 45 degree vortex lattice reorientation in tetragonal superconductors

The transformation of the vortex lattice in a tetragonal superconductor which consists of its 45 degree reorientation relative to the crystal axes is studied using the nonlocal London model. It is shown that the reorientation occurs as two successive second order (continuous) phase transitions. The transition magnetic fields are calculated for a range of parameters relevant for borocarbide superconductors in which the reorientation has been observed

Equation of state for the 2+1 dimensional Gross-Neveu model at order 1/N

We calculate the equation of state of the Gross-Neveu model in 2+1 dimensions at order 1/N, where N is the number of fermion species. We make use of a general formula valid for four-fermion theories, previously applied to the model in 1+1 dimensions. We consider both the discrete and continuous symmetry versions of the model. We show that the pion-like excitations give the dominant contribution at low temperatures. The range of validity for such pion dominance is analyzed. The complete analysis from low to high temperatures also shows that in the critical region the role of composite states is relevant, even for quite large N, and that the free-component behaviour at high T starts at about twice the mean field critical temperature.Comment: 19 pages, RevTeX, 10 figures.p

Four Fermion Field Theories and the Chern-Simons Field: A Renormalization Group Study

In (2+1) dimensions, we consider the model of a $N$ flavor, two-component fermionic field interacting through a Chern-Simons field besides a four fermion self-interaction which consists of a linear combination of the Gross-Neveu and Thirring like terms. The four fermion interaction is not perturbatively renormalizable and the model is taken as an effective field theory in the region of low momenta. Using Zimmerman procedure for reducing coupling constants, it is verified that, for small values of the Chern-Simons parameter, the origin is an infrared stable fixed point but changes to ultraviolet stable as $\alpha$ becomes bigger than a critical $\alpha_c$. Composite operators are also analyzed and it is shown that a specific four fermion interaction has an improved ultraviolet behavior as $N$ increases.Comment: 9 pages, revte

Interpretations of Presburger Arithmetic in Itself

Presburger arithmetic PrA is the true theory of natural numbers with addition. We study interpretations of PrA in itself. We prove that all one-dimensional self-interpretations are definably isomorphic to the identity self-interpretation. In order to prove the results we show that all linear orders that are interpretable in (N,+) are scattered orders with the finite Hausdorff rank and that the ranks are bounded in terms of the dimension of the respective interpretations. From our result about self-interpretations of PrA it follows that PrA isn't one-dimensionally interpretable in any of its finite subtheories. We note that the latter was conjectured by A. Visser.Comment: Published in proceedings of LFCS 201

Coexisting Dementia and Depression in Parkinson's Disease

Dementia and depression in patients with Parkinson's disease have been reported separately, but their prevalence is controversial. This study examines the coexistence of these two problems and suggests a common underlying biochemical system. We examined these two entities by retrospective chart review and cerebrospinal fluid biochemistry. We found a prevalence of 10.9% for dementia, 51% for depression, and 5.4% for coincident depression and dementia. In a prospective study of patients with Parkinson's disease we found a continuum of cerebrospinal fluid 5-hydroxyindoleacetic acid concentrations. Patients who were either depressed or demented had lower concentrations of this metabolite than other patients with Parkinson's disease, but patients who were depressed and demented had the lowest levels. These results suggest that the coexistence of dementia and depression represents a unique clinical entity in Parkinson's disease. The serotonergic system may be involved in depression and dementia because evidence of a cumulative effect on this biochemical system is present

Why the lowest Landau level approximation works in strongly type II superconductors

Higher than the lowest Landau level contributions to magnetization and specific heat of superconductors are calculated using Ginzburg - Landau equations approach. Corrections to the excitation spectrum around solution of these equations (treated perturbatively) are found. Due to symmetries of the problem leading to numerous cancellations the range of validity of the LLL approximation in mean field is much wider then a naive range and extends all the way down to $H = {H_{c2}(T)}/13$. Moreover the contribution of higher Landau levels is significantly smaller compared to LLL than expected naively. We show that like the LLL part the lattice excitation spectrum at small quasimomenta is softer than that of usual acoustic phonons. This enhanses the effect of fluctuations. The mean field calculation extends to third order, while the fluctuation contribution due to HLL is to one loop. This complements the earlier calculation of the LLL part to two loop order.Comment: 20 pages, Latex file, three figure