Related papers: The $\phi^4$ model with the BPS preserving defect
We find supersymmetric extensions of the half-BPS soliton-impurity models in (1+1) dimensions which preserve half of the $\mathcal{N}=1$ supersymmetry. This is related to the fact that in the bosonic sector (i.e., the half-BPS…
We find a family of (half) self-dual impurity models such that the self-dual (BPS) sector is exactly solvable, for any spatial distribution of the impurity, both in the topologically trivial case and for kink (or antikink) configurations.…
In this work we consider a model where the potential has two topological sectors connecting three adjacent minima, as occurs with the $\phi^6$ model. In each topological sector, the potential is symmetric around the local maximum. For…
We show that BPS-impurity theories may support BPS kink-kink solutions i.e., an energetically degenerated family of solutions describing two kinks at any mutual distance. This requires a singular impurity. As an example we consider the…
The $\varphi^4$-theory is ubiquitous as a low-energy effective description of processes in all fields of physics ranging from cosmology and particle physics to biophysics and condensed matter theory. The topological defects, or kinks, in…
We study a generalized $\phi^4$ model that gives rise to BPS kink/antikink configurations with compacton-like profiles. One observes that the positive parameter controlling the generalizing function promotes an infinity degenerescence of…
We study the non-integrable $\phi^{6}$ model on the half-line. The model has two topological sectors. We chose solutions from just one topological sector to fix the initial conditions. The scalar field satisfies a Neumann boundary condition…
We investigate the propagation of fronts in an inhomogeneous medium within the framework of the $\phi^4$ model. The inhomogeneity is modeled either as an interface separating regions with different dissipation or as a finite layer with…
An exactly solvable one-dimensional Hubbard model with a single Anderson impurity embedded at the boundary is constructed in the framework of the quantum inverse scattering method. The model is solved exactly by the nested Bethe ansatz…
We investigate quantum impurity problems, where a local magnetic moment is coupled to the spin density of a bosonic environment, leading to bosonic versions of the standard Kondo and Anderson impurity models. In a physical situation, these…
This work deals with systems of two real scalar fields coupled to impurity functions, meant to model inhomogeneities often encountered in real physical applications. We investigate the theoretical properties of these systems and some of the…
Antikink-kink ( $\bar{\rm K} $$ {\rm K}$) collisions in the $\phi^6$ model exhibit resonant scattering although the $\phi^6$ kinks do not support any bound states to which energy could be transferred. In Phys. Rev. Lett. 107 (2011) 091602…
We consider a two-dimensional Lorentz-invariant field model with a $\phi^{4}$ potential modified by a term that introduces asymmetries at the manifold space. In this framework, the model recovers its original symmetry only when $p=0$. The…
We find the exact quasiparticle spectrum for the continuum Kondo problem of $k$ species of electrons coupled to an impurity of spin $S$. In this description, the impurity becomes an immobile quasiparticle sitting on the boundary. The…
We study boundary scattering in the $\phi^4$ model on a half-line with a one-parameter family of Neumann-type boundary conditions. A rich variety of phenomena is observed, which extends previously-studied behaviour on the full line to…
We show that the BPS property is a generic feature of field theories in (1+1) dimensions, which does not put any restriction on the action. Here, by BPS solutions we understand static solutions which i) obey a lower-order Bogomolny-type…
In this study, based on the $\varphi^4$ model, a new model (called the $B\varphi^4$ model) is introduced in which the potential form for the values of the field whose magnitudes are greater than $1$ is multiplied by the positive number $B$.…
We study kink-antikink scattering in a one-parameter variant of the $\phi^4$ theory where the model parameter controls the static intersoliton force. We interpolate between the limit of no static force (BPS limit) and the regime where the…
In the framework of the Bose-Hubbard model, we show that two-particle surface bound states embedded in the continuum (BIC) can be sustained at the edge of a semi-infinite one-dimensional tight-binding lattice for any infinitesimally-small…
We discuss a solvable model describing an Anderson like impurity in a BCS superconductor. The model can be mapped onto an Ising field theory in a boundary magnetic field, with the Ising fermions being the quasi-particles of the Bogoliubov…