Correlation Functions of (2k-1, 2) Minimal Matter Coupled to 2D Quantum Gravity

We compute N-point correlation functions of non-unitary (2k-1, 2) minimal matter coupled to 2D quantum gravity on a sphere using the continuum Liouville field approach. A gravitational dressing of the matter primary field with the minimum conformal weight is used as the cosmological operator. Our results are in agreement with the correlation functions of the one-matrix model at the k-th critical point.Comment: 9 pages, STUPP-92-13

The Critical Ising Model on a M\"obius Strip

We study the two-dimensional critical Ising model on a M\"obius strip based on a duality relation between conformally invariant boundary conditions. By using a Majorana fermion field theory, we obtain explicit representations of crosscap states corresponding to the boundary states. We also discuss the duality structure of the partition functions.Comment: 6 pages, ptptex, to appear in Prog. Theor. Phy

Nonlinear response for external field and perturbation in the Vlasov system

A nonlinear response theory is provided by use of the transient linearization method in the spatially one-dimensional Vlasov systems. The theory inclusively gives responses to external fields and to perturbations for initial stationary states, and is applicable even to the critical point of a second order phase transition. We apply the theory to the Hamiltonian mean-field model, a toy model of a ferromagnetic body, and investigate the critical exponent associated with the response to the external field at the critical point in particular. The obtained critical exponent is nonclassical value 3/2, while the classical value is 3. However, interestingly, one scaling relation holds with another nonclassical critical exponent of susceptibility in the isolated Vlasov systems. Validity of the theory is numerically confirmed by directly simulating temporal evolutions of the Vlasov equation.Comment: 15 pages, 8 figures, accepted for publication in Phys. Rev. E, Lemma 2 is correcte

Landau like theory for universality of critical exponents in quasistatioary states of isolated mean-field systems

An external force dynamically drives an isolated mean-field Hamiltonian system to a long-lasting quasistationary state, whose lifetime increases with population of the system. For second order phase transitions in quasistationary states, two non-classical critical exponents have been reported individually by using a linear and a nonlinear response theories in a toy model. We provide a simple way to compute the critical exponents all at once, which is an analog of the Landau theory. The present theory extends universality class of the non-classical exponents to spatially periodic one-dimensional systems, and shows that the exponents satisfy a classical scaling relation inevitably by using a key scaling of momentum.Comment: 7 page

Non-mean-field Critical Exponent in a Mean-field Model : Dynamics versus Statistical Mechanics

The mean-field theory tells that the classical critical exponent of susceptibility is the twice of that of magnetization. However, the linear response theory based on the Vlasov equation, which is naturally introduced by the mean-field nature, makes the former exponent half of the latter for families of quasistationary states having second order phase transitions in the Hamiltonian mean-field model and its variances. We clarify that this strange exponent is due to existence of Casimir invariants which trap the system in a quasistationary state for a time scale diverging with the system size. The theoretical prediction is numerically confirmed by $N$-body simulations for the equilibrium states and a family of quasistationary states.Comment: 6 pages, 3 figure

Logarithmic Behaviours in the Feigin-Fuchs Construction of the c=-2 Conformal Field Theory

We obtain logarithmic behaviours of a four-point correlation function in the c=-2 conformal field theory by using the Feigin-Fuchs construction. It becomes an indeterminate form by a naive evaluation, but is obtained by introducing an appropriate regularization procedure.Comment: LaTeX, 7 page

Dynamical pattern formations in two dimensional fluid and Landau pole bifurcation

A phenomenological theory is proposed to analyze the asymptotic dynamics of perturbed inviscid Kolmogorov shear flows in two dimensions. The phase diagram provided by the theory is in qualitative agreement with numerical observations, which include three phases depending on the aspect ratio of the domain and the size of the perturbation: a steady shear flow, a stationary dipole, and four traveling vortices. The theory is based on a precise study of the inviscid damping of the linearized equation and on an analysis of nonlinear effects. In particular, we show that the dominant Landau pole controlling the inviscid damping undergoes a bifurcation, which has important consequences on the asymptotic fate of the perturbation.Comment: 9 pages, 7 figure

Common Hepatic Branch of Vagus Nerve-Dependent Expression of Immediate Early Genes in the Mouse Brain by Intraportal L-Arginine: Comparison with Cholecystokinin-8

Information from the peripheral organs is thought to be transmitted to the brain by humoral factors and neurons such as afferent vagal or spinal nerves. The common hepatic branch of the vagus (CHBV) is one of the main vagus nerve branches, and consists of heterogeneous neuronal fibers that innervate multiple peripheral organs such as the bile duct, portal vein, paraganglia, and gastroduodenal tract. Although, previous studies suggested that the CHBV has a pivotal role in transmitting information on the status of the liver to the brain, the details of its central projections remain unknown. The purpose of the present study was to investigate the brain regions activated by the CHBV. For this purpose, we injected L-arginine or anorexia-associated peptide cholecystokinin-8 (CCK), which are known to increase CHBV electrical activity, into the portal vein of transgenic Arc-dVenus mice expressing the fluorescent protein Venus under control of the activity-regulated cytoskeleton-associated protein (Arc) promotor. The brain slices were prepared from these mice and the number of Venus positive cells in the slices was counted. After that, c-Fos expression in these slices was analyzed by immunohistochemistry using the avidin-biotin-peroxidase complex method. Intraportal administration of L-arginine increased the number of Venus positive or c-Fos positive cells in the insular cortex. This action of L-arginine was not observed in CHBV-vagotomized Arc-dVenus mice. In contrast, intraportal administration of CCK did not increase the number of c-Fos positive or Venus positive cells in the insular cortex. Intraportal CCK induced c-Fos expression in the dorsomedial hypothalamus, while intraportal L-arginine did not. This action of CCK was abolished by CHBV vagotomy. Intraportal L-arginine reduced, while intraportal CCK increased, the number of c-Fos positive cells in the nucleus tractus solitarii in a CHBV-dependent manner. The present results suggest that the CHBV can activate different brain regions depending on the nature of the peripheral stimulus