134 research outputs found
Asymmetric kink scattering in a two-component scalar field theory model
Producción CientÃficaIn 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(Ï•1, Ï•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 . 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 EconomÃa, Ciencia y Competitividad (grant MTM2014-57129-C2-1-P)Junta de Castilla y Leon (grant VA057U16
Kink dynamics in the MSTB model
Producción CientÃficaIn 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
-dimensional space-time the defects are classically degenerate in mass
kinks, but in 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
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 - or -dimensional -component scalar
field theory model. Application of these formulae to the BPS kinks or domain
walls of the 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
Higgs phase in a gauge non-linear -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 nonlinear
-model. If , , is the quantized
magnetic flux of the two species of BPS vortex solutions, linearly
independent vortex zero modes for each species are found and described. The
existence of two species of moduli spaces of dimension of these stringy
topological defects is thus locally shown.Comment: 17 pages, 28 figure
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 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
models.Comment: 23 pages, 4 figures, to be published in Annals of Physic
Reflection, transmutation, annihilation and resonance in two-component kink collisions
[EN] In this paper, the study of collisions between kinks arising in the family of MSTB models is addressed. Phenomena such as elastic kink reflection, mutual annihilation, kink-antikink transmutation and inelastic reflection are found and depend on the impact velocity
Non-topological kink scattering in a two-component scalar field theory model
In this paper the scattering between the non-topological kinks arising in a
family of two-component scalar field theory models is analyzed. A winding
charge is carried by these defects. As a consequence, two different classes of
kink scattering processes emerge: (1) collisions between kinks that carry the
same winding number and (2) scattering events between kinks with opposite
winding number. The variety of scattering channels is very rich and it strongly
depends on the collision velocity and the model parameter. For the first type
of events, four distinct scattering channels are found: \textit{kink
reflection} (kinks collide and bounce back), \textit{one-kink (partial)
annihilation} (the two non-topological kinks collide causing the annihilation
of one half of each kink and the subsequent recombination of the other two
halves, giving rise to a new non-topological kink with the opposite winding
charge), \textit{winding flip kink reflection} (kinks collide and emerge with
the opposite winding charge) and \textit{total kink annihilation} (kinks
collide and decay to the vacuum configuration). For the second type of events,
the scattering channels comprise \textit{bion formation} (kink and antikink
form a long-living bound state), \textit{kink-antikink passage} (kinks collide
and pass each other) and \textit{kink-antikink annihilation} (kink and antikink
collide and decay to the vacuum configuration).Comment: 22 pages, 17 figure
Kink dynamics in a system of two coupled scalar elds in two space-time dimensions
[EN] In this paper we examine the scattering processes among the members of a rich family of kinks which arise in a (1+1)-dimensional relativistic two scalar field theory. These kinks carry two different topological charges that determine the mutual interactions between the basic energy lumps (extended particles) described by these topological defects. Processes like topological charge exchange, kink–antikink bound state formation or kink repulsion emerge depending on the charges of the scattered particles. Two-bounce resonant windows have been found in the antikink–kink scattering processes, but not in the kink–antikink interactions
Kink dynamics in a system of two coupled scalar fields in two space–time dimensions
[EN] In this paper we examine the scattering processes among the members of a rich family of kinks which arise in a (1+1)-dimensional relativistic two scalar field theory. These kinks carry two different topological charges that determine the mutual interactions between the basic energy lumps (extended particles) described by these topological defects. Processes like topological charge exchange, kink–antikink bound state formation or kink repulsion emerge depending on the charges of the scattered particles. Two-bounce resonant windows have been found in the antikink–kink scattering processes, but not in the kink–antikink interactions
Two Species of Vortices in a massive Gauged Non-linear Sigma Model
Non-linear sigma models with scalar fields taking values on
complex manifolds are addressed. In the simplest
case, where the target manifold is the sphere, we describe the
scalar fields by means of stereographic maps. In this case when the
symmetry is gauged and Maxwell and mass terms are allowed, the
model accommodates stable self-dual vortices of two kinds with different
energies per unit length and where the Higgs field winds at the cores around
the two opposite poles of the sphere. Allowing for dielectric functions in the
magnetic field, similar and richer self-dual vortices of different species in
the south and north charts can be found by slightly modifying the potential.
Two different situations are envisaged: either the vacuum orbit lies on a
parallel in the sphere, or one pole and the same parallel form the vacuum
orbit. Besides the self-dual vortices of two species, there exist BPS domain
walls in the second case. Replacing the Maxwell contribution of the gauge field
to the action by the second Chern-Simons secondary class, only possible in
-dimensional Minkowski space-time, new BPS topological defects of two
species appear. Namely, both BPS vortices and domain ribbons in the south and
the north charts exist because the vacuum orbit consits of the two poles and
one parallel. Formulation of the gauged model in a
Reference chart shows a self-dual structure such that BPS semi-local vortices
exist. The transition functions to the second or third charts break the
semi-local symmetry, but there is
still room for standard self-dual vortices of the second species. The same
structures encompassing complex scalar fields are easily generalized to
gauged models.Comment: 39 pages, 23 figures (extended version), to be published in JHE
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