Phase transitions in Ising model on a Euclidean network

A one dimensional network on which there are long range bonds at lattice distances $l>1$ with the probability $P(l) \propto l^{-\delta}$ has been taken under consideration. We investigate the critical behavior of the Ising model on such a network where spins interact with these extra neighbours apart from their nearest neighbours for $0 \leq \delta < 2$. It is observed that there is a finite temperature phase transition in the entire range. For $0 \leq \delta < 1$, finite size scaling behaviour of various quantities are consistent with mean field exponents while for $1\leq \delta\leq 2$, the exponents depend on $\delta$. The results are discussed in the context of earlier observations on the topology of the underlying network.Comment: 7 pages, revtex4, 7 figures; to appear in Physical Review E, minor changes mad

Regular and Periodic Tachyon Kinks

We search for regular tachyon kinks in an extended model, which includes the tachyon action recently proposed to describe the tachyon field. The extended model that we propose adds a new contribution to the tachyon action, and seems to enrich the present scenario for the tachyon field. We have found stable tachyon kinks of regular profile, which may appropriately lead to the singular kink found by Sen sometime ago. Also, under specific conditions we may find periodic array of kink-antikink configurations.Comment: 10 pages, 1 figure. Version to be published in Mod. Phys. Lett.

Non-BPS D-brane Near NS5-branes

We use tachyon field theory effective action to study the dynamics of a non-BPS Dp-brane propagating in the vicinity of k NS5-branes. For the time dependent tachyon condensation we will concentrate on the case of the large tachyon and the case when a non-BPS D-brane is close to NS5-branes. For spatial dependent tachyon condensation we will argue that the problem reduces to the study of the motion of an array of D(p-1)-branes and D(p-1)-antibranes in the vicinity of k NS5-branes.Comment: 21 page

Tachyon Tube on non BPS D-branes

We report our searches for a single tubular tachyonic solution of regular profile on unstable non BPS D3-branes. We first show that some extended Dirac-Born-Infeld tachyon actions in which new contributions are added to avoid the Derrick's no-go theorem still could not have a single regular tube solution. Next we use the Minahan-Zwiebach tachyon action to find the regular tube solutions with circular or elliptic cross section. With a critical electric field, the energy of the tube comes entirely from the D0 and strings, while the energy associated to the tubular D2-brane tension is vanishing. We also show that fluctuation spectrum around the tube solution does not contain tachyonic mode. The results are consistent with the identification of the tubular configuration as a BPS D2-brane.Comment: Latex 18 page

Inverse cascades in turbulence and the case of rotating flows

We first summarize briefly several properties concerning the dynamics of two-dimensional (2D) turbulence, with an emphasis on the inverse cascade of energy to the largest accessible scale of the system. In order to study a similar phenomenon in three-dimensional (3D) turbulence undergoing strong solid-body rotation, we test a previously developed Large Eddy Simulation (LES) model against a high-resolution direct numerical simulation of rotating turbulence on a grid of $3072^3$ points. We then describe new numerical results on the inverse energy cascade in rotating flows using this LES model and contrast the case of 2D versus 3D forcing, as well as non-helical forcing (i.e., with weak overall alignment between velocity and vorticity) versus the fully helical Beltrami case, both for deterministic and random forcing. The different scaling of the inverse energy cascade can be attributed to the dimensionality of the forcing, with, in general, either a $k_{\perp}^{-3}$ or a $k_{\perp}^{-5/3}$ energy spectrum of slow modes at large scales, perpendicular referring to the direction of rotation. We finally invoke the role of shear in the case of a strongly anisotropic deterministic forcing, using the so-called ABC flow.Comment: 10 pages, 3 figure

Cosmology in scalar tensor theory and asymptotically de-Sitter Universe

We have investigated the cosmological scenarios with a four dimensional effective action which is connected with multidimensional, supergravity and string theories. The solution for the scale factor is such that initially universe undergoes a decelerated expansion but in late times it enters into the accelerated expansion phase. Infact, it asymptotically becomes a de-Sitter universe. The dilaton field in our model is a decreasing function of time and it becomes a constant in late time resulting the exit from the scalar tensor theory to the standard Einstein's gravity. Also the dilaton field results the existence of a positive cosmological constant in late times.Comment: 7 pages, Revtex Style, 6 Postscript figure

The Schrodinger Wave Functional and Closed String Rolling Tachyon

In this short note we apply Schrodinger picture description of the minisuperspace approach to the closed string tachyon condensation. We will calculate the rate of produced closed string and we will show that the density of high massive closed string modes reaches the string density in time of order one in string units.Comment: 12 page

Topological Blocking in Quantum Quench Dynamics

We study the non-equilibrium dynamics of quenching through a quantum critical point in topological systems, focusing on one of their defining features: ground state degeneracies and associated topological sectors. We present the notion of 'topological blocking', experienced by the dynamics due to a mismatch in degeneracies between two phases and we argue that the dynamic evolution of the quench depends strongly on the topological sector being probed. We demonstrate this interplay between quench and topology in models stemming from two extensively studied systems, the transverse Ising chain and the Kitaev honeycomb model. Through non-local maps of each of these systems, we effectively study spinless fermionic $p$-wave paired superconductors. Confining the systems to ring and toroidal geometries, respectively, enables us to cleanly address degeneracies, subtle issues of fermion occupation and parity, and mismatches between topological sectors. We show that various features of the quench, which are related to Kibble-Zurek physics, are sensitive to the topological sector being probed, in particular, the overlap between the time-evolved initial ground state and an appropriate low-energy state of the final Hamiltonian. While most of our study is confined to translationally invariant systems, where momentum is a convenient quantum number, we briefly consider the effect of disorder and illustrate how this can influence the quench in a qualitatively different way depending on the topological sector considered.Comment: 18 pages, 11 figure