Asymmetric kink scattering in a two-component scalar field theory model

Producción CientíficaIn this paper the kink scattering in a two-component scalar field theory model in (1+1)-Minkowskian space-time is addressed. The potential term U(fi_1; fi_2) is given by a polynomial of fourth degree in the first field component and of sixth degree in the second one. The novel characteristic of this model is that the kink variety describes two different types of extended particles. These particles are characterized by its topological charge but also by a new feature determined by a discrete charge L = 0,1,-1. For this reason, the kink scattering involves a very rich variety of processes, which comprises kink annihilation, reflection, charge exchange, transmutation, etc. It has been found that not only the final velocity of the scattered kinks, but also the final nature of the emerging lumps after the collision are very sensitive on the initial velocities. Asymmetric scattering processes arise when Type I and Type II particles are obliged to collide. In this case, ten different final scenarios are possible. Symmetric scattering events are also discussed.In this paper the kink scattering in a two-component scalar field theory model in (1+1)-Minkowskian space-time is addressed. The potential term U(ϕ1, ϕ2) is given by a polynomial of fourth degree in the first field component and of sixth degree in the second one. The novel characteristic of this model is that the kink variety describes two different types of extended particles. These particles are characterized by its topological charge but also by a new feature determined by a discrete charge . For this reason, the kink scattering involves a very rich variety of processes, which comprises kink annihilation, reflection, charge exchange, transmutation, etc. It has been found that not only the final velocity of the scattered kinks, but also the final nature of the emerging lumps after the collision are very sensitive on the initial velocities. Asymmetric scattering processes arise when Type I and Type II particles are obliged to collide. In this case, ten different final scenarios are possible. Symmetric scattering events are also discussed.Ministerio de Economía, Ciencia y Competitividad (grant MTM2014-57129-C2-1-P)Junta de Castilla y Leon (grant VA057U16

Kink dynamics in the MSTB model

Producción CientíficaIn this paper kink scattering processes are investigated in the Montonen–Sarker–Trullinger–Bishop (MSTB) model. The MSTB model is in fact a one-parametric family of relativistic scalar field theories living in a one-time one-space Minkowski space-time which encompasses two coupled scalar fields. Among the static solutions of the model two kinds of topological kinks are distinguished in a precise range of the family parameter. In that regime there exists one unstable kink exhibiting only one non-null component of the scalar field. Another type of topological kink solutions, stable in this case, includes two different kinks for which the two components of the scalar field are non-null. Both one-component and two-component topological kinks are accompanied by their antikink partners. The decay of the unstable kink to one of the stable solutions plus radiation is numerically computed. The pair of stable two-component kinks living respectively on upper and lower semi-ellipses in the field space belongs to the same topological sector in the configuration space and provides an ideal playground to address several scattering events involving one kink and either its own antikink or the antikink of the other stable kink. By means of numerical analysis we shall find and describe interesting physical phenomena. Bion (kink–antikink oscillations) formation, kink reflection, kink–antikink annihilation, kink transmutation and resonances are examples of these types of events. The appearance of these phenomena emerging in the kink–antikink scattering depends critically on the initial collision velocity and the chosen value of the coupling constant parametrizing the family of MSTB models.MINDECO grant MTM2014-57129-C2-1-P and Junta de Castilla y León grants VA057U16 and BU229P18

Quantum-induced interactions in the moduli space of degenerate BPS domain walls

In this paper quantum effects are investigated in a very special two-scalar field model having a moduli space of BPS topological defects. In a $(1+1)$-dimensional space-time the defects are classically degenerate in mass kinks, but in $(3+1)$ dimensions the kinks become BPS domain walls, all of them sharing the same surface tension at the classical level. The heat kernel/zeta function regularization method will be used to control the divergences induced by the quantum kink and domain wall fluctuations. A generalization of the Gilkey-DeWitt-Avramidi heat kernel expansion will be developed in order to accommodate the infrared divergences due to zero modes in the spectra of the second-order kink and domain wall fluctuation operators, which are respectively $N\times N$ matrix ordinary or partial differential operators. Use of these tools in the spectral zeta function associated with the Hessian operators paves the way to obtain general formulas for the one-loop kink mass and domain wall tension shifts in any $(1+1)$- or $(3+1)$-dimensional $N$-component scalar field theory model. Application of these formulae to the BPS kinks or domain walls of the $N=2$ model mentioned above reveals the breaking of the classical mass or surface tension degeneracy at the quantum level. Because the main parameter distinguishing each member in the BPS kink or domain wall moduli space is essentially the distance between the centers of two basic kinks or walls, the breaking of the degeneracy amounts to the surge in quantum-induced forces between the two constituent topological defects. The differences in surface tension induced by one-loop fluctuations of BPS walls give rise mainly to attractive forces between the constituent walls except if the two basic walls are very far apart. Repulsive forces between two close walls only arise if the coupling is approaches the critical value from below.Comment: 34 pages, 7 figures, to appear in JHE

Visual Localisation of Mobile Devices in an Indoor Environment under Network Delay Conditions

Current progresses in home automation and service robotic environment have highlighted the need to develop interoperability mechanisms that allow a standard communication between the two systems. During the development of the DHCompliant protocol, the problem of locating mobile devices in an indoor environment has been investigated. The communication of the device with the location service has been carried out to study the time delay that web services offer in front of the sockets. The importance of obtaining data from real-time location systems portends that a basic tool for interoperability, such as web services, can be ineffective in this scenario because of the delays added in the invocation of services. This paper is focused on introducing a web service to resolve a coordinates request without any significant delay in comparison with the sockets

On a family of (1+1)-dimensional scalar field theory models: kinks, stability, one-loop mass shifts

In this paper we construct a one-parametric family of (1+1)-dimensional one-component scalar field theory models supporting kinks. Inspired by the sine-Gordon and $\phi^4$ models, we look at all possible extensions such that the kink second-order fluctuation operators are Schr\"odinger differential operators with P\"oschl-Teller potential wells. In this situation, the associated spectral problem is solvable and therefore we shall succeed in analyzing the kink stability completely and in computing the one-loop quantum correction to the kink mass exactly. When the parameter is a natural number, the family becomes the hierarchy for which the potential wells are reflectionless, the two first levels of the hierarchy being the sine-Gordon and $\phi^4$ models.Comment: 23 pages, 4 figures, to be published in Annals of Physic

Higgs phase in a gauge U(1)\mathbf{U}(1) non-linear CP1\mathbf{CP}^1-model. Two species of BPS vortices and their zero modes

In this paper zero modes of fluctuation are dissected around the two species of BPS vortices existing in the critical Higgs phase, where the scalar and vector meson masses are equal, of a gauged $\mathbb{U}(1)$ nonlinear $\mathbb{CP}^1$-model. If $2\pi n$, $n\in \mathbb{Z}$, is the quantized magnetic flux of the two species of BPS vortex solutions, $2n$ linearly independent vortex zero modes for each species are found and described. The existence of two species of moduli spaces of dimension $2n$ of these stringy topological defects is thus locally shown.Comment: 17 pages, 28 figure

Instability and Trade in Currency Areas

In a currency area, when a country faces a positive shock inflation goes up, real interest rate decreases and competitiveness deteriorates. We show that the stability of equilibrium depends on the rationality of expectations and budget balance of the public sector.Publicad

Instability and trade in currency areas

We present a model of a currency area in which labor markets of country members are isolated but there is trade among these countries. When a country experiences a negative (resp. positive) shock, inflation goes down (up). This causes two effects. On the one hand the real interest rate of this country increases (decreases). On the other hand the goods produced in this country become more (less) competitive. We show that the stability of the system depends on several factors, including a large competitive effect, how inflation expectations are formed and fiscal policy. In general, stability requires a trade-off between the rationality of expectations and budget balance