Cluster synchronization in an ensemble of neurons interacting through chemical synapses

In networks of periodically firing spiking neurons that are interconnected with chemical synapses, we analyze cluster state, where an ensemble of neurons are subdivided into a few clusters, in each of which neurons exhibit perfect synchronization. To clarify stability of cluster state, we decompose linear stability of the solution into two types of stabilities: stability of mean state and stabilities of clusters. Computing Floquet matrices for these stabilities, we clarify the total stability of cluster state for any types of neurons and any strength of interactions even if the size of networks is infinitely large. First, we apply this stability analysis to investigating synchronization in the large ensemble of integrate-and-fire (IF) neurons. In one-cluster state we find the change of stability of a cluster, which elucidates that in-phase synchronization of IF neurons occurs with only inhibitory synapses. Then, we investigate entrainment of two clusters of IF neurons with different excitability. IF neurons with fast decaying synapses show the low entrainment capability, which is explained by a pitchfork bifurcation appearing in two-cluster state with change of synapse decay time constant. Second, we analyze one-cluster state of Hodgkin-Huxley (HH) neurons and discuss the difference in synchronization properties between IF neurons and HH neurons.Comment: Notation for Jacobi matrix is changed. Accepted for publication in Phys. Rev.

Magnetoelasticity theory of incompressible quantum Hall liquids

A simple and physically transparent magnetoelasticity theory is proposed to describe linear dynamics of incompressible fractional quantum Hall states. The theory manifestly satisfies the Kohn theorem and the $f$-sum rule, and predicts a gaped intra-Landau level collective mode with a roton minimum. In the limit of vanishing bare mass $m$ the correct form of the static structure factor, $s(q)\sim q^4$, is recovered. We establish a connection of the present approach to the fermionic Chern-Simons theory, and discuss further extensions and applications. We also make an interesting analogy of the present theory to the theory of visco-elastic fluids.Comment: RevTeX 4, 6 pages; expanded version to appear in PRB; more technical details, and discussions of the physics adde

On transport in quantum Hall systems with constrictions

Motivated by recent experimental findings, we study transport in a simple phenomenological model of a quantum Hall edge system with a gate-voltage controlled constriction lowering the local filling factor. The current backscattered from the constriction is seen to arise from the matching of the properties of the edge-current excitations in the constriction ($\nu_{2}$) and bulk ($\nu_{1}$) regions. We develop a hydrodynamic theory for bosonic edge modes inspired by this model, finding that a competition between two tunneling process, related by a quasiparticle-quasihole symmetry, determines the fate of the low-bias transmission conductance. In this way, we find satisfactory explanations for many recent puzzling experimental results.Comment: 4 pages, 4 figure

Structural properties of electrons in quantum dots in high magnetic fields: Crystalline character of cusp states and excitation spectra

The crystalline or liquid character of the downward cusp states in N-electron parabolic quantum dots (QD's) at high magnetic fields is investigated using conditional probability distributions obtained from exact diagonalization. These states are of crystalline character for fractional fillings covering both low and high values, unlike the liquid Jastrow-Laughlin wave functions, but in remarkable agreement with the rotating-Wigner-molecule ones [Phys. Rev. B 66, 115315 (2002)]. The crystalline arrangement consists of concentric polygonal rings that rotate independently of each other, with the electrons on each ring rotating coherently. We show that the rotation stabilizes the Wigner molecule relative to the static one defined by the broken-symmetry unrestricted-Hartree-Fock solution. We discuss the non-rigid behavior of the rotating Wigner molecule and pertinent features of the excitation spectrum, including the occurrence of a gap between the ground and first excited states that underlies the incompressibility of the system. This leads us to conjecture that the rotating crystal (and not the static one) remains the relevant ground state for low fractional fillings even at the thermodynamic limit.Comment: Published version. Typos corrected. REVTEX4. 10 pages with 8 postscript figures (5 in color). For related papers, see http://www.prism.gatech.edu/~ph274cy

A comparison of ultraviolet sensitivities in universal, nonuniversal, and split extra dimensional models

We discuss the origin of ultraviolet sensitivity in extra dimensional theories, and compare and contrast the cutoff dependences in universal, nonuniversal and split five dimensional models. While the gauge bosons and scalars are in the five dimensional bulk in all scenarios, the locations of the fermions are different in different cases. In the universal model all fermions can travel in the bulk, in the nonuniversal case they are all confined at the brane, while in the split scenario some are in the bulk and some are in the brane. A possible cure from such divergences is also discussed.Comment: 9 pages, Latex, no figure, v2: further clarifications and references added, accepted for publication in Phys. Rev.

Optical activity of noncentrosymmetric metals

We describe the phenomenon of optical activity of noncentrosymmetric metals in their normal and superconducting states. The found conductivity tensor contains the linear in wave vector off diagonal part responsible for the natural optical activity. Its value is expressed through the ratio of light frequency to the band splitting due to the spin-orbit interaction. The Kerr rotation of polarization of light reflected from the metal surface is calculated. In the additional file "Erratum" I've pointed out the sign error in arXiv:1001.2113 ( PRB v.81, 094525 (2010)) that leads to the wrong statement about the Kerr effect in light reflection from the surface of media without space parity.Comment: 9 pages + 2 pages of Erratum. arXiv admin note: text overlap with arXiv:0903.330

Relativistic Hall Effect

We consider the relativistic deformation of quantum waves and mechanical bodies carrying intrinsic angular momentum (AM). When observed in a moving reference frame, the centroid of the object undergoes an AM-dependent transverse shift. This is the relativistic analogue of the spin Hall effect, which occurs in free space without any external fields. Remarkably, the shifts of the geometric and energy centroids differ by a factor of 2, and both centroids are crucial for the correct Lorentz transformations of the AM tensor. We examine manifestations of the relativistic Hall effect in quantum vortices, and mechanical flywheels, and also discuss various fundamental aspects of this phenomenon. The perfect agreement of quantum and relativistic approaches allows applications at strikingly different scales: from elementary spinning particles, through classical light, to rotating black-holes.Comment: 5 pages, 3 figures, to appear in Phys. Rev. Let

Temperature dependence of the conductivity of the electronic crystal

We study the temperature dependence of the conductivity of the 2D electronic solid. In realistic samples, a domain structure forms in the solid and each domain randomly orients in the absence of the in-plane field. At higher temperature, the electron transport is governed by thermal activation form of $\sigma_{xx}(T)\propto e^{-\Delta_0/k_BT}$. The impurities will localize the electron states along the edges of the crystal domains. At sufficient low temperature, another transport mechanism called Mott's variable range hopping mechanism, similar to that in a disorder insulator takes effect. We show that as the temperature decreases, a crossover from the fixed range hopping of the transport to the variable range hopping of transport in the 2D electron system may be experimentally observed.Comment: 4 pages,1 figure

Unified hydrodynamics theory of the lowest Landau level

We propose a hydrodynamics theory of collective quantum Hall states, which describes incompressible liquids, hexatic liquid crystals, a bubble solid and a Wigner crystal states within a unified framework. The structure of the theory is uniquely determined by the space-time symmetry, and a symmetry with respect to static shear deformations. In agreement with recent experiments the theory predicts two gapped collective modes for incompressible liquids. We argue that the presence of the above two modes is a universal property of a magnetized two-dimensional collective liquid.Comment: RevTex, 8 pages. Revised and expanded versio