In this paper we explore the five-dimensional $f(T,B)$ teleparallel modified gravity with $f_1(T,B)=T+k_1{B}^{n_1}$ and $f_2(T,B)=B+k_2{T}^{n_2}$ in the brane scenario. Asymptotically, the bulk geometry converges to an ${\mathrm{AdS}}_5$ spacetime whose cosmological constant is produced by parameters that control torsion and the boundary term. The analysis of the energy density condition reveals a splitting brane process satisfying the weak and strong energy conditions for some values of the parameters $n_{1,2}$ and $k_{1,2}$. In addition, we investigate the behavior of the gravitational perturbations in this scenario. In the bulk, the torsion keeps a gapless nonlocalizable and stable tower of massive modes. Inside the brane core, the torsion produces new barriers and potential wells leading to small amplitude massive modes and a massless mode localized for some values of the parameters $n_{1,2}$ and $k_{1,2}$.

We investigate quantum information by a theoretical measurement approach of an Aharanov–Bohm (AB) ring with Yukawa interaction in curved space with disclination. We obtained the so-called Shannon entropy through the eigenfunctions of the system. The quantum states considered come from Schrödinger theory with the AB field in the background of curved space. With this entropy, we can explore the quantum information at the position space and reciprocal space. Furthermore, we discussed how the magnetic field, the AB flux, and the topological defect influence the quantum states and the information entropy.

To investigate possible topological vortex structures in generalized models, we developed a perturbative generation approach for scalar-vector theories. We demonstrate explicitly that the dielectric permeability functions must have a nonpolynomial shape, i.e., the form of the logarithmic function. Based on this result, we built models in $(2+1)D$ with logarithmic dielectric permeability in order to investigate the presence of topological vortex structures in a Maxwell model. This type of scalar-vector models is important because it can generate stationary field solutions in theories describing the dynamics of the scalar field. As examples, we chose models of the complex scalar field coupled to the Maxwell field. Subsequently, we investigated the model’s Bogomol’nyi equations to describe the field configurations. Then, we demonstrate numerically, for an ansatz with rotational symmetry, that the solutions of the complex scalar field generating minimum energy configurations are topological structures depending on the parameters obtained in the perturbative generation of the vector-scalar theory.

In this research article, we use the Shannon’s formalism to investigate the quantum information entropy of a particle trapped by the Aharonov–Bohm-type field. For quantum information study, it is necessary to investigate the eigenstates of the quantum system, i.e. the wave functions and energies of the quantum states. We assumed that the particle is in principle, confined in a cylindrical box in the presence of Aharonov–Bohm-type effect due to dislocation defect. Analysis of the quantum information entropy, reveals that the dislocation influences the eigenstates and, consequently, the quantum information of the system.

In this paper we study the thick brane scenario constructed in the recently proposed $$f(T,{\mathscr {T}})$$f ( T , T ) theories of gravity, where T is called the torsion scalar and $${\mathscr {T}}$$T is the trace of the energy–momentum tensor. We use the first-order formalism to find analytical solutions for models that include a scalar field as a source. In particular, we describe two interesting case in which in the first we obtain a double-kink solution, which generates a splitting in the brane. In the second case, proper management of a kink solution obtained generates a splitting in the brane intensified by the torsion parameter, evinced by the energy density components satisfying the weak and strong energy conditions. In addition, we investigate the behavior of the gravitational perturbations in this scenario. The parameters that control the torsion and the trace of the energy–momentum tensor tend to shift the massive modes to the core of the brane, keeping a gapless non-localizable and stable tower of massive modes and producing more localized massless modes.

We investigate the presence of topological structures and multiple phase transitions in the O(3)-sigma model with the gauge field governed by Maxwell’s term and subject to a so-called Gausson’s self-dual potential. To carry out this study, it is numerically shown that this model supports topological solutions in 3-dimensional spacetime. In fact, to obtain the topological solutions, we assume a spherically symmetrical ansatz to find the solutions, as well as some physical behaviors of the vortex, as energy and magnetic field. It is presented a planar view of the magnetic field as an interesting configuration of a ring-like profile. To calculate the differential configurational complexity (DCC) of structures, the spatial energy density of the vortex is used. In fact, theDCCis important because it provides us with information about the possible phase transitions associated with the structures located in the Maxwell–Gausson model in 3D. Finally, we note from theDCCprofile an infinite set of kink-like solutions associated with the parameter that controls the vacuum expectation value.