Soliton Configurations Research Articles

Decoupling of Field Equations in Einstein and Modified Gravity

This paper is concerned with giving the proof that there is a general decoupling property of vacuum and nonvacuum gravitational field equations in Einstein gravity and f(R, T)-modifications. The constructions are possible in terms of geometric and physical objects adapted to certain nonholonomic 2+2 splitting with local fibred structure. This allows us to generate exact and/or parametric depending solutions with generic off–diagonal metrics and generalized, or Levi–Civita, connections. Different classes of modified spacetimes are determined by corresponding generating and integration functions depending, in general, on all space and time coordinates and may possess, or not, Killing symmetries. The initial data sets for the Cauchy problem and their global properties are analyzed. There are formulated the criteria of evolution with spacetime splitting and decoupling of fundamental field equations. Examples of exact solutions defining ellipsoid deformations of black hole metrics and solitonic configurations are provided.

Fully resonant soliton interactions in the Whitham–Broer–Kaup system based on the double Wronskian solutions

With the aim of exploring whether the (1+1)-dimensional coupled nonlinear evolution equations admit abundant soliton interactions, like the cases in the Kadomtsev–Petviashvili II equation, we in this paper study the double Wronskian solutions to the Whitham–Broer–Kaup (WBK) system. We give the parametric condition for two double Wronskians to generate the non-singular, non-trivial and irreducible soliton solutions. Via the asymptotic analysis of two double Wronskians, we show that the soliton solutions of the WBK system is in general linearly combined of fully resonant (M,N)- and (M−1,N+1)-soliton configurations. It turns out that the WBK system can exhibit various complex soliton structures which are different pairwise combinations of elastic, confluent and divergent interactions. From a combinatorial viewpoint, we also explain that the asymptotic solitons of a [(M,N),(M−1,N+1)]-soliton solution are identified by a pair of Grassmannian permutations.

8-Spinors and structure of solitons in generalized Mie electrodynamics

A generalization of Mie electrodynamics is considered. It includes a 8-spinor field and higher powers of the Mie invariant AμAμ. Particular topological properties of 8-spinors are indicated and are associated with the existence of the remarkable Brioschi identity of eight squares, which permits deriving a natural 8-spinor unification of the Skyrme model of baryons and the Faddeev model of leptons, these particles being treated as topological solitons. Two types of soliton configurations admitted by the model are constructed. These are charged static and neutral lightlike (luxons) ones.

Observing various phase transitions in the holographic model of superfluidity

We study the gravity duals of supercurrent solutions in the anti--de Sitter (AdS) black hole background with general phase structure to describe both the first- and the second-order phase transitions at finite temperature in strongly interacting systems. We argue that the conductivity and the pair susceptibility can be possible phenomenological indications to distinguish the order of phase transitions. We extend our discussion to the AdS soliton configuration. Different from the black hole spacetime, in the probe limit, the first-order phase transition cannot be brought by introducing the spatial component of the vector potential of the gauge field in the AdS soliton background.

Field theory on the world sheet: improvements and generalizations

This article is the continuation of a project of investigating planar ϕ 3 model in various dimensions. The idea is to reformulate them on the world sheet, and then to apply the classical (meanfield) approximation, with two goals: to show that the ground state of the model is a solitonic configuration on the world sheet, and the quantum fluctuations around the soliton lead to the formation of a transverse string. After a review of some of the earlier work, we introduce and discuss several generalizations and new results. In 1 + 2 dimensions, a rigorous upper bound on the solitonic energy is established. A ϕ 4 interaction is added to stabilize the original ϕ 3 model. In 1 + 3 and 1 + 5 dimensions, an improved treatment of the ultraviolet divergences is given. And significantly, we show that our approximation scheme can be imbedded into a systematic strong coupling expansion. Finally, the spectrum of quantum fluctuations around the soliton confirms earlier results: in 1 + 2and 1 + 3dimensions,a transverse string is formed on the world sheet.

Soliton configurations in generalized Mie electrodynamics

The generalization of the Mie electrodynamics within the scope of the effective 8-spinor field model is suggested, with the Lagrangian including Higgs-like potential and higher degrees of the invariant AµAµ. Using special Brioschi 8-spinor identity, we show that the model includes the Skyrme and the Faddeev models as particular cases. We investigate the large-distance asymptotic of static solutions and estimate the electromagnetic contribution to the energy of the localized charged configuration.

Traveling solitons in Lorentz andCPTbreaking systems

In this work we present a class of traveling solitons in Lorentz and $CPT$ breaking systems. In the case of Lorentz violating scenarios, as far as we know, only static solitonic configurations were analyzed up to now in the literature. Here it is shown that it is possible to construct some traveling solitons which cannot be mapped into static configurations by means of Lorentz boosts due to explicit breaking. In fact, the traveling solutions cannot be reached from the static ones by using something similar to a Lorentz boost in those cases. Furthermore, in the model studied, a complete set of exact solutions is obtained. The solutions present a critical behavior controlled by the choice of an arbitrary integration constant.

Various types of phase transitions in the AdS soliton background

We study the basic holographic insulator and superconductor phase transition in the AdS soliton background by generalizing the spontaneous breaking of a global U(1) symmetry to occur via Stückelberg mechanism. We construct the soliton solutions with backreaction and examine the effects of the backreaction on the condensation of the scalar hair in the generalized Stückelberg Lagrangian. We disclose rich physics in various phase transitions. In addition to the AdS soliton configuration, we also examine the property of the phase transition in the AdS black hole background.

Radiation of Terahertz Electromagnetic Waves from Build-In Nano Josephson Junctions of Cuprate High-Tc Superconductors

The nano-scale intrinsic Josephson junctions in highly anisotropic cuprate superconductors have potential for generation of terahertz electromagnetic waves. When the thickness of a superconductor sample is much smaller than the wavelength of electromagnetic waves in vacuum, the superconductor renders itself as a cavity. Unlike conventional lasers, the presence of the cavity does not guarantee a coherent emission because of the internal degree of freedom of the superconductivity phase in long junctions. We study the excitation of terahertz wave by solitons in a stack of intrinsic Josephson junctions, especially for relatively short junctions. Coherent emission requires a rectangular configuration of solitons. However such a configuration is unstable against weak fluctuations, contrarily solitons favor a triangular lattice corresponding to an out phase oscillation of electromagnetic waves. To utilize the cavity, we propose to use an array of stacks of short intrinsic Josephson junctions to generate powerful terahertz electromagnetic waves. The cavity synchronizes the plasma oscillation in different stacks and the emission intensity is predicted to be proportional to the number of stacks squared.

Signature of the black hole phase transition in quasinormal modes

We study the perturbation of the scalar field interacting with the Maxwell field in the background of d-dimensional charged AdS black hole and AdS soliton. Different from the single classical field perturbation, which always has the decay mode in the black hole background, we observe the possible growing mode when the perturbation of the scalar field strongly couples to the Maxwell field. Our results disclose the signature of how the phase transition happens when the interaction among classical fields is strong. The sudden change of the perturbation to growing mode is also observed in the AdS soliton with electric potential. However in the magnetic charged AdS soliton background, we observe the consistent perturbation behavior when the interaction between scalar field and Maxwell field is considered. This implies that for the magnetic charged AdS soliton configuration, unlike the situation with electric potential, there is no scalar field condensation which causes the phase change.

Nontopological soliton configuration in the system of two interacting scalar fields with the global Abelian symmetry

The system of two interacting scalar fields with the global Abelian symmetry and renormalized Lagrangian is considered. A nontopological soliton solution of the Q-ball type is shown to exist in this system. The total analytical description of soliton fields is performed for the thin-wall regime. A numerical solution for the system of nonlinear differential equations is given for the general case.

Phase transitions between solitons and black holes in asymptotically [formula omitted] spaces

We employ a thermodynamic analysis to determine the phase structure of Eguchi–Hanson solitons, Schwarzschild–AdS/Zk black holes and thermal AdS/Zk. The Euclidean actions are calculated by two equable means: the first uses the Eguchi–Hanson soliton as the thermal background while the second makes use of minimal boundary counterterms in the action necessary to render individual actions finite. The Euclidean actions are then utilised to determine the phase structure in arbitrary odd dimension; it is found that there is a Hawking–Page phase transition and also a phase transition between the black hole and soliton. There is found to be no smooth phase transition governed by an order parameter between AdS/Zk and the soliton but nevertheless AdS/Zk changes phase by tunneling to the lower energy soliton configuration.

Solutions of coupled BPS equations for two-family Calogero and matrix models

We consider a large $N$, two-family Calogero and matrix model in the Hamiltonian, collective-field approach. The Bogomol'nyi limit appears and the solutions to the coupled Bogomol'nyi-Prasad-Sommerfeld equations are given by the static soliton configurations. We find all solutions close to constant and construct exact one-parameter solutions in the strong-weak dual case. Full classification of these solutions is presented.

Solitons via Lie-Bäcklund transformation for 5D low-energy string theory

We apply a non-linear matrix transformation of Lie-Backlund type on a seed soliton configuration in order to obtain a new solitonic solution in the framework of the 5D low-energy effective field theory of the bosonic string. The seed solution represents a stationary axisymmetric two-soliton configuration previously constructed through the inverse scattering method and consists of a massless gravitational field coupled to a non-trivial chargeless dilaton and to an axion field endowed with charge. We apply a fully parameterized non-linear matrix transformation of Ehlers type on this massless solution and get a massive rotating axisymmetric gravitational soliton coupled to charged axion and dilaton fields. We discuss on some physical properties of both the initial and the generated solitons and fully clarify the physical effect of the non-linear normalized Ehlers transformation on the seed solution, in particular, the generated field configuration acquires mass and charge terms, and does not possess some of the bizarre properties that the initial ISM solitonic solution does.

Note on generalized Janus configurations

We study several aspects of generalized Janus configuration, which includes a theta term. We investigate the vacuum structure of the theory and find that unlike the Janus configuration without theta term there is no nontrivial vacuum. We also discuss BPS soliton configuration both by supersymmetry analysis and from energy functional. The half BPS configurations could be realized by introducing transverse (p,q)-strings in original brane configuration corresponding to generalized Janus configuration. It turns out the BPS soliton could be taken as modified dyon. We discuss the solution of half BPS equations for the sharp interface case. Moreover we construct less supersymmetric Janus configuration with theta term.

Continuously deformable topological structure

Some time ago, Bazeia and collaborators [D. Bazeia, J. Menezes, R. Menezes, Phys. Rev. Lett. 91 (2003) 241601], introduced a model consisting of a self-interacting scalar field, where the solitonic static configuration presents a kind of static two kinks profile. Here we present a novel model having this not much usual and interesting property. The implications, and possible advantages, of this new exactly solvable non-linear system are addressed. In particular, the consequences for some D-dimensional defects and cosmological scenarios such as the brane worlds are explored.

Unbounded Multi-Magnon and Spike

We generalize the one magnon solution in R X S^2 to unbounded M magnon and find the corresponding solitonic string configuration in the string sigma model. This configuration gives rise to the expected dispersion relation obtained from the spin chain model in the large 't Hooft coupling limit. After considering (M,M) multi-magnon or spike on R X S^2 X S^2 as a subspace of AdS(5)XS^5 or AdS(4)XCP^3, we investigate the dispersion relation and the finite size effect for (M,M) multi-magnon or spike.

147 fs, 51 MHz soliton fiber laser at 156 μm with a fiber-connector-type SWNT/P3HT saturable absorber

We fabricated a fiber-connector-type saturable absorber in which SWNTs and P3HT (poly-3-hexylthiophene) were coated on the fiber connector end. This saturable absorber allowed us to realize a short laser cavity length. We used a soliton cavity configuration to generate the shortest pulse (147 fs) at the highest repetition rate (51 MHz) yet obtained with carbon nanotubes (CNT) related saturable absorbers.

NoncommutativeQ-lumps

$Q$-lumps associated with the noncommutative $\mathbb{C}{P}^{N}$ model in $2+1$ dimensions are constructed. These are solitonic configurations which are time dependent and rotate with constant angular frequency. Energy of the $Q$-lumps is $E=2\ensuremath{\pi}k+\ensuremath{\alpha}|Q|$, and we find that in a regime in which the noncommutativity parameter $\ensuremath{\theta}$ is related to the moduli determining the size of the lumps, it can be viewed to depend on $\ensuremath{\theta}$ via the Noether charge $Q$. We present a collective coordinate-type analysis signalling that $\mathbb{C}{P}^{1}$ $Q$-lumps remain stable under small radiative perturbations.

Cosmology of the closed string tachyon

The spacetime physics of bulk closed string tachyon condensation is studied at the level of a two-derivative effective action. We derive the unique perturbative tachyon potential consistent with a full class of linearized tachyonic deformations of supercritical string theory. The solutions of interest deform a general linear dilaton background by the insertion of purely exponential tachyon vertex operators. In spacetime, the evolution of the tachyon drives an accelerated contraction of the universe and, absent higher-order corrections, the theory collapses to a cosmological singularity in finite time, at arbitrarily weak string coupling. When the tachyon exhibits a null symmetry, the worldsheet dynamics is known to be exact and well defined at tree level. We prove that if the two-derivative effective action is free of nongravitational singularities, higher-order corrections always resolve the spacetime curvature singularity of the null tachyon. The resulting theory provides an explicit mechanism by which tachyon condensation can generate or terminate the flow of cosmological time in string theory. Additional particular solutions can resolve an initial singularity with a tachyonic phase at weak coupling, or yield solitonic configurations that localize the universe along spatial directions.