1,432 research outputs found
One-loop kink mass shifts: a computational approach
In this paper we develop a procedure to compute the one-loop quantum
correction to the kink masses in generic (1+1)-dimensional one-component scalar
field theoretical models. The procedure uses the generalized zeta function
regularization method helped by the Gilkey-de Witt asymptotic expansion of the
heat function via Mellin's transform. We find a formula for the one-loop kink
mass shift that depends only on the part of the energy density with no field
derivatives, evaluated by means of a symbolic software algorithm that automates
the computation. The improved algorithm with respect to earlier work in this
subject has been tested in the sine-Gordon and models. The
quantum corrections of the sG-soliton and -kink masses have
been estimated with a relative error of 0.00006% and 0.00007% respectively.
Thereafter, the algorithm is applied to other models. In particular, an
interesting one-parametric family of double sine-Gordon models interpolating
between the ordinary sine-Gordon and a re-scaled sine-Gordon model is
addressed. Another one-parametric family, in this case of models, is
analyzed. The main virtue of our procedure is its versatility: it can be
applied to practically any type of relativistic scalar field models supporting
kinks.Comment: 35 pages, 6 figures, to be published in Nuclear Physics
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
Changing shapes: adiabatic dynamics of composite solitary waves
We discuss the solitary wave solutions of a particular two-component scalar
field model in two-dimensional Minkowski space. These solitary waves involve
one, two or four lumps of energy. The adiabatic motion of these composite
non-linear non-dispersive waves points to variations in shape.Comment: 21 pages, 15 figures. To appear in Physica D: Nonlinear Phenomen
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
One-dimensional solitary waves in singular deformations of SO(2) invariant two-component scalar field theory models
In this paper we study the structure of the manifold of solitary waves in
some deformations of SO(2) symmetric two-component scalar field theoretical
models in two-dimensional Minkowski space. The deformation is chosen in order
to make the analogous mechanical system Hamilton-Jacobi separable in polar
coordinates and displays a singularity at the origin of the internal plane. The
existence of the singularity confers interesting and intriguing properties to
the solitary waves or kink solutions.Comment: 25 pages, 18 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
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
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