Instability of Solitons in imaginary coupling affine Toda Field Theory

Affine Toda field theory with a pure imaginary coupling constant is a non-hermitian theory. Therefore the solutions of the equation of motion are complex. However, in $1+1$ dimensions it has many soliton solutions with remarkable properties, such as real total energy/momentum and mass. Several authors calculated quantum mass corrections of the solitons by claiming these solitons are stable. We show that there exists a large class of classical solutions which develops singularity after a finite lapse of time. Stability claims, in earlier literature, were made ignoring these solutions. Therefore we believe that a formulation of quantum theory on a firmer basis is necessary in general and for the quantum mass corrections of solitons, in particular.Comment: 17 pages, latex, no figure

Direct Energy Cascade in Two-Dimensional Compressible Quantum Turbulence

We numerically study two-dimensional quantum turbulence with a Gross--Pitaevskii model. With the energy initially accumulated at large scale, quantum turbulence with many quantized vortex points is generated. Due to the lack of enstrophy conservation in this model, direct energy cascade with a Kolmogorov--Obukhov energy spectrum $E(k) \propto k^{-5/3}$ is observed, which is quite different from two-dimensional incompressible classical turbulence in the decaying case. A positive value for the energy flux guarantees a \emph{direct} energy cascade in the inertial range (from large to small scales). After almost all the energy at the large scale cascades to the small scale, the compressible kinetic energy realizes the thermodynamic equilibrium state without quantized vortices.Comment: 14 pages, 10 figure

Holographic classification of Topological Insulators and its 8-fold periodicity

Using generic properties of Clifford algebras in any spatial dimension, we explicitly classify Dirac hamiltonians with zero modes protected by the discrete symmetries of time-reversal, particle-hole symmetry, and chirality. Assuming the boundary states of topological insulators are Dirac fermions, we thereby holographically reproduce the Periodic Table of topological insulators found by Kitaev and Ryu. et. al, without using topological invariants nor K-theory. In addition we find candidate Z_2 topological insulators in classes AI, AII in dimensions 0,4 mod 8 and in classes C, D in dimensions 2,6 mod 8.Comment: 19 pages, 4 Table

Time-reversal symmetric Kitaev model and topological superconductor in two dimensions

A time-reversal invariant Kitaev-type model is introduced in which spins (Dirac matrices) on the square lattice interact via anisotropic nearest-neighbor and next-nearest-neighbor exchange interactions. The model is exactly solved by mapping it onto a tight-binding model of free Majorana fermions coupled with static Z_2 gauge fields. The Majorana fermion model can be viewed as a model of time-reversal invariant superconductor and is classified as a member of symmetry class DIII in the Altland-Zirnbauer classification. The ground-state phase diagram has two topologically distinct gapped phases which are distinguished by a Z_2 topological invariant. The topologically nontrivial phase supports both a Kramers' pair of gapless Majorana edge modes at the boundary and a Kramers' pair of zero-energy Majorana states bound to a 0-flux vortex in the \pi-flux background. Power-law decaying correlation functions of spins along the edge are obtained by taking the gapless Majorana edge modes into account. The model is also defined on the one-dimension ladder, in which case again the ground-state phase diagram has Z_2 trivial and non-trivial phases.Comment: 17 pages, 9 figure

Non-canonical folding of Dynkin diagrams and reduction of affine Toda theories

The equation of motion of affine Toda field theory is a coupled equation for $r$ fields, $r$ is the rank of the underlying Lie algebra. Most of the theories admit reduction, in which the equation is satisfied by fewer than $r$ fields. The reductions in the existing literature are achieved by identifying (folding) the points in the Dynkin diagrams which are connected by symmetry (automorphism). In this paper we present many new reductions. In other words the symmetry of affine Dynkin diagrams could be extended and it leads to non-canonical foldings. We investigate these reductions in detail and formulate general rules for possible reductions. We will show that eventually most of the theories end up in $a_{2n}^{(2)}$ that is the theory cannot have a further dimension $m$ reduction where $m<n$.Comment: 26 pages, Latex2e, usepackage `graphics.sty', 15 figure

Medium effects of magnetic moments of baryons on neutron stars under strong magnetic fields

We investigate medium effects due to density-dependent magnetic moments of baryons on neutron stars under strong magnetic fields. If we allow the variation of anomalous magnetic moments (AMMs) of baryons in dense matter under strong magnetic fields, AMMs of nucleons are enhanced to be larger than those of hyperons. The enhancement naturally affects the chemical potentials of baryons to be large and leads to the increase of a proton fraction. Consequently, it causes the suppression of hyperons, resulting in the stiffness of the equation of state. Under the presumed strong magnetic fields, we evaluate relevant particles' population, the equation of state and the maximum masses of neutron stars by including density-dependent AMMs and compare them with those obtained from AMMs in free space

Stereotypical escape behavior in Caenorhabditis elegans allows quantification of nociceptive stimuli levels

Experiments of pain with human subjects are difficult, subjective, and ethically constrained. Since the molecular mechanisms of pain transduction are reasonably conserved among different species, these problems are partially solved by the use of animal models. However, animals cannot easily communicate to us their own pain levels. Thus progress depends crucially on our ability to quantitatively and objectively infer the perceived level of noxious stimuli from the behavior of animals. Here we develop a quantitative model to infer the perceived level of thermal nociception from the stereotyped nociceptive response of individual nematodes Caenorhabditis elegans stimulated by an IR laser. The model provides a method for quantification of analgesic effects of chemical stimuli or genetic mutations in C. elegans. We test the nociception of ibuprofen-treated worms and a TRPV (transient receptor potential) mutant, and we show that the perception of thermal nociception for the ibuprofen treated worms is lower than the wild-type. At the same time, our model shows that the mutant changes the worm's behavior beyond affecting nociception. Finally, we determine the stimulus level that best distinguishes the analgesic effects and the minimum number of worms that allow for a statistically significant identification of these effects.Comment: 16 pages, 7 figure

Characterization Of Thermal Stresses And Plasticity In Through-Silicon Via Structures For Three-Dimensional Integration

Through-silicon via (TSV) is a critical element connecting stacked dies in three-dimensional (3D) integration. The mismatch of thermal expansion coefficients between the Cu via and Si can generate significant stresses in the TSV structure to cause reliability problems. In this study, the thermal stress in the TSV structure was measured by the wafer curvature method and its unique stress characteristics were compared to that of a Cu thin film structure. The thermo-mechanical characteristics of the Cu TSV structure were correlated to microstructure evolution during thermal cycling and the local plasticity in Cu in a triaxial stress state. These findings were confirmed by microstructure analysis of the Cu vias and finite element analysis (FEA) of the stress characteristics. In addition, the local plasticity and deformation in and around individual TSVs were measured by synchrotron x-ray microdiffraction to supplement the wafer curvature measurements. The importance and implication of the local plasticity and residual stress on TSV reliabilities are discussed for TSV extrusion and device keep-out zone (KOZ).Microelectronics Research Cente