Quantum propagator for some classes of three-dimensional three-body systems

In this work we solve exactly a class of three-body propagators for the most general quadratic interactions in the coordinates, for arbitrary masses and couplings. This is done both for the constant as the time-dependent couplings and masses, by using the Feynman path integral formalism. Finally the energy spectrum and the eigenfunctions are recovered from the propagators.Comment: 16 pages, no figure

Multikink solutions and deformed defects

At the present work we consider an application of the deformation procedure that enable us to construct, systematically, scalar field models supporting multikinks. We introduce a new deformation function in order to realize this task. We exemplify the procedure with three different starting models already known in the literature, and the resulting deformed models have rich vacua structures which are responsible for the appearance of multikink configurations

Coupled scalar fields Oscillons and Breathers in some Lorentz Violating Scenarios

In this work we discuss the impact of the breaking of the Lorentz symmetry on the usual oscillons, the so-called flat-top oscillons, and the breathers. Our analysis is performed by using a Lorentz violation scenario rigorously derived in the literature. We show that the Lorentz violation is responsible for the origin of a kind of deformation of the configuration, where the field configuration becomes oscillatory in a localized region near its maximum value. Furthermore, we show that the Lorentz breaking symmetry produces a displacement of the oscillon along the spatial direction, the same feature is present in the case of breathers. We also show that the effect of a Lorentz violation in the flat-top oscillon solution is responsible by the shrinking of the flat-top. Furthermore, we find analytically the outgoing radiation, this result indicates that the amplitude of the outgoing radiation is controlled by the Lorentz breaking parameter, in such away that this oscillon becomes more unstable than its symmetric counterpart, however, it still has a long living nature

On the study of oscillons in scalar field theories: A new approach

In this work we study configurations in one-dimensional scalar field theory, which are time-dependent, localized in space and extremely long-lived called oscillons. It is investigated how the action of changing the minimum value of the field configuration representing the oscillon affects its behavior. We find that one of the consequences of this procedure, is the appearance of a pair of oscillon-like structures presenting different amplitudes and frequencies of oscillation. We also compare our analytical results to numerical ones, showing excellent agreement

Analytical Multi-kinks in smooth potentials

In this work we present an approach which can be systematically used to construct nonlinear systems possessing analytical multi-kink profile configurations. In contrast with previous approaches to the problem, we are able to do it by using field potentials which are considerably smoother than the ones of Doubly Quadratic family of potentials. This is done without losing the capacity of writing exact analytical solutions. The resulting field configurations can be applied to the study of problems from condensed matter to brane world scenarios

Information-Entropic for Travelling Solitons in Lorentz and CPT Breaking Systems

In this work we group three research topics apparently disconnected, namely solitons, Lorentz symmetry breaking and entropy. Following a recent work [Phys. Lett. B 713 (2012) 304], we show that it is possible to construct in the context of travelling wave solutions a configurational entropy measure in functional space, from the field configurations. Thus, we investigate the existence and properties of travelling solitons in Lorentz and CPT breaking scenarios for a class of models with two interacting scalar fields. Here, we obtain a complete set of exact solutions for the model studied which display both double and single-kink configurations. In fact, such models are very important in applications that include Bloch branes, Skyrmions, Yang-Mills, Q-balls, oscillons and various superstring-motivated theories. We find that the so-called Configurational Entropy (CE) for travelling solitons, which we name as travelling Configurational Entropy (TCE), shows that the best value of parameter responsible to break the Lorentz symmetry is one where the energy density is distributed equally around the origin. In this way, the information-theoretical measure of travelling solitons in Lorentz symmetry violation scenarios opens a new window to probe situations where the parameters responsible for breaking the symmetries are random. In this case, the TCE selects the best value

Lorentz Violation and Topologically Trapped Charge Carriers in 2D Materials

The full spectrum of two-dimensional fermion states in a scalar soliton trap with a Lorentz breaking background is investigated in the context of the novel 2D materials, where the Lorentz symmetry should not be strictly valid. The field theoretical model with Lorentz breaking terms represents Dirac electrons in one valley and in a scalar field background. The Lorentz violation comes from the difference between the Dirac electron and scalar mode velocities, which should be expected when modelling the electronic and lattice excitations in 2D materials. We extend the analytical methods developed in the context of 1+1 field theories to explore the effect of the Lorentz symmetry breaking in the charge carrier density of 2D materials in the presence of a domain wall with a kink profile. The width and the depth of the trapping potential from the kink is controlled by the Lorentz violating term, which is reflected analytically in the band structure and properties of the trapped states. Our findings enlarge previous studies of the edge states obtained with domain wall and in strained graphene nanoribbon in a chiral gauge theory