Wigner surmise for Hermitian and non-Hermitian Chiral random matrices

We use the idea of a Wigner surmise to compute approximate distributions of the first eigenvalue in chiral Random Matrix Theory, for both real and complex eigenvalues. Testing against known results for zero and maximal non-Hermiticity in the microscopic large-N limit we find an excellent agreement, valid for a small number of exact zero-eigenvalues. New compact expressions are derived for real eigenvalues in the orthogonal and symplectic classes, and at intermediate non-Hermiticity for the unitary and symplectic classes. Such individual Dirac eigenvalue distributions are a useful tool in Lattice Gauge Theory and we illustrate this by showing that our new results can describe data from two-colour QCD simulations with chemical potential in the symplectic class

Extent and mechanism of sealing in transected giant axons of squid and earthworms

Transected axons are often assumed to seal at their cut ends by the formation of continuous membrane barriers that allow for the restoration of function in the axonal stumps. We have used several electrophysiological measures (membrane potential, input resistance, injury current density) and several morphological measures (phase-contrast, video-enhanced differential interference contrast, light, and electron microscopies) of living and fixed material to assess the extent and mechanism of sealing within hours after transecting giant axons of squid (Loligo pealeiand Sepioteuthis lessoniana) and earthworms (Lumbricus terrestris). Our electrophysiological data suggest that the proximal and distal ends of transected squid giant axons do not completely seal within 2.5 hr in physiological saline. In contrast, the same set of measures suggest that proximal and distal ends of transected earthworm giant axons seal within 1 hr in physiological saline. Our morphological data show that the cut ends of both squid and earthworm axons constrict, but that a 20- 70-am-diameter opening always remains at the cut end that is filled with vesicles. Axonal transection induces the formation of vesicles that are observed in the axoplasm within minutes in standard salines and that rapidly migrate to the cut ends. These injury-induced vesicles are loosely packed near the cut ends of squid giant axons, which do not functionally seal within 2.5 hr of transection. In contrast, vesicles formed a tightly packed plug at the cut ends of earthworm medial giant axons, which do functionally seal within 1 hr of transection in physiological saline. Since we detect no single continuous membrane that spans the cut end, sealing does not appear to occur by the fusion of constricted axolemmal membrane or the formation of a membranous partition at the cut end. Rather, our data are consistent with the hypothesis that a tightly packed vesicular plug is responsible for sealing of earthworm giant axons.This work was supported in part by NIH Grant NS31256 and ONR Grant N00014-90-J-1137 to H.M.F., an NIAAA fellowship to T.L.K., and an ATP grant to G.D.B.Neuroscienc

Scattering Experiments with Microwave Billiards at an Exceptional Point under Broken Time Reversal Invariance

Scattering experiments with microwave cavities were performed and the effects of broken time-reversal invariance (TRI), induced by means of a magnetized ferrite placed inside the cavity, on an isolated doublet of nearly degenerate resonances were investigated. All elements of the effective Hamiltonian of this two-level system were extracted. As a function of two experimental parameters, the doublet and also the associated eigenvectors could be tuned to coalesce at a so-called exceptional point (EP). The behavior of the eigenvalues and eigenvectors when encircling the EP in parameter space was studied, including the geometric amplitude that builds up in the case of broken TRI. A one-dimensional subspace of parameters was found where the differences of the eigenvalues are either real or purely imaginary. There, the Hamiltonians were found PT-invariant under the combined operation of parity (P) and time reversal (T) in a generalized sense. The EP is the point of transition between both regions. There a spontaneous breaking of PT occurs

Molecular Aspects of Secretory Granule Exocytosis by Neurons and Endocrine Cells

Neuronal communication and endocrine signaling are fundamental for integrating the function of tissues and cells in the body. Hormones released by endocrine cells are transported to the target cells through the circulation. By contrast, transmitter release from neurons occurs at specialized intercellular junctions, the synapses. Nevertheless, the mechanisms by which signal molecules are synthesized, stored, and eventually secreted by neurons and endocrine cells are very similar. Neurons and endocrine cells have in common two different types of secretory organelles, indicating the presence of two distinct secretory pathways. The synaptic vesicles of neurons contain excitatory or inhibitory neurotransmitters, whereas the secretory granules (also referred to as dense core vesicles, because of their electron dense content) are filled with neuropeptides and amines. In endocrine cells, peptide hormones and amines predominate in secretory granules. The function and content of vesicles, which share antigens with synaptic vesicles, are unknown for most endocrine cells. However, in B cells of the pancreatic islet, these vesicles contain GABA, which may be involved in intrainsular signaling.' Exocytosis of both synaptic vesicles and secretory granules is controlled by cytoplasmic calcium. However, the precise mechanisms of the subsequent steps, such as docking of vesicles and fusion of their membranes with the plasma membrane, are still incompletely understood. This contribution summarizes recent observations that elucidate components in neurons and endocrine cells involved in exocytosis. Emphasis is put on the intracellular aspects of the release of secretory granules that recently have been analyzed in detail

Matrix models and QCD with chemical potential

The Random Matrix Model approach to Quantum Chromodynamics (QCD) with non-vanishing chemical potential is reviewed. The general concept using global symmetries is introduced, as well as its relation to field theory, the so-called epsilon regime of chiral Perturbation Theory (echPT). Two types of Matrix Model results are distinguished: phenomenological applications leading to phase diagrams, and an exact limit of the QCD Dirac operator spectrum matching with echPT. All known analytic results for the spectrum of complex and symplectic Matrix Models with chemical potential are summarised for the symmetry classes of ordinary and adjoint QCD, respectively. These include correlation functions of Dirac operator eigenvalues in the complex plane for real chemical potential, and in the real plane for imaginary isospin chemical potential. Comparisons of these predictions to recent Lattice simulations are also discussed