http://hdl.handle.net/10366/116215 Wed, 22 Apr 2026 11:04:54 GMT 2026-04-22T11:04:54Z http://hdl.handle.net/10366/146573 [EN] Solutions of the one-dimensional Schrödinger equation are found when point interactions of the type aδ(x − q) + bδ'(x − q) are placed either in a couple of points or in a regular lattice. The results obtained in the present study are a first step toward a rigorous mathematical model of real metamaterials is Solid State Physics. Sun, 01 Jan 2017 00:00:00 GMT http://hdl.handle.net/10366/146573 2017-01-01T00:00:00Z http://hdl.handle.net/10366/146572 [EN] We investigate a special class of the PT-symmetric quantum models being perfectly invisible zero-gap systems with a unique bound state at the very edge of continuous spectrum of scattering states. The family includes the PT-regularized two particle Calogero systems (conformal quantum mechanics models of de Alfaro-Fubini-Furlan) and their rational extensions whose potentials satisfy equations of the KdV hierarchy and exhibit, particularly, a behaviour typical for extreme waves. We show that the two simplest Hamiltonians from the Calogero subfamily determine the fluctuation spectra around the PT-regularized kinks arising as traveling waves in the field-theoretical Liouville and SU(3) conformal Toda systems. Peculiar properties of the quantum systems are reflected in the associated exotic nonlinear supersymmetry in the unbroken or partially broken phases. The conventional N=2 supersymmetry is extended here to the N=4 nonlinear supersymmetry that involves two bosonic generators composed from Lax-Novikov integrals of the subsystems, one of which is the central charge of the superalgebra. Jordan states are shown to play an essential role in the construction. Tue, 12 Dec 2017 00:00:00 GMT http://hdl.handle.net/10366/146572 2017-12-12T00:00:00Z http://hdl.handle.net/10366/146571 [EN] We study the spectrum of the 1D Dirac Hamiltonian encompassing the bound and scattering states of a fermion distorted by a static background built from δ-function potentials. After introducing the most general Dirac-δ potential for the Dirac equation we distinguish between “mass-spike” and “electrostatic” δ-potentials. Differences in the spectra arising depending on the type of δ-potential are studied in deep detail. Fri, 16 Aug 2019 00:00:00 GMT http://hdl.handle.net/10366/146571 2019-08-16T00:00:00Z http://hdl.handle.net/10366/146570 [EN] We investigate how the Lax-Novikov integral in the perfectly invisible PT-regularized zero-gap quantum conformal and superconformal mechanics systems affects on their (super)-conformal symmetries. We show that the expansion of the conformal symmetry with this integral results in a nonlinearly extended generalized Shrödinger algebra. The PT-regularized superconformal mechanics systems in the phase of the unbroken exotic nonlinear N= 4 super-Poincaré symmetry are described by nonlinearly super-extended Schrödinger algebra with the osp(2|2) sub-superalgebra. In the partially broken phase, the scaling dimension of all odd integrals is indefinite, and the osp(2|2) is not contained as a sub-superalgebra. Fri, 25 Jan 2019 00:00:00 GMT http://hdl.handle.net/10366/146570 2019-01-25T00:00:00Z http://hdl.handle.net/10366/146568 [EN] 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(ϕ1, ϕ2) 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. Thu, 01 Aug 2019 00:00:00 GMT http://hdl.handle.net/10366/146568 2019-08-01T00:00:00Z http://hdl.handle.net/10366/146567 [EN] In 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. Thu, 06 Jun 2019 00:00:00 GMT http://hdl.handle.net/10366/146567 2019-06-06T00:00:00Z http://hdl.handle.net/10366/146566 [EN] Pareas snakes possess outstanding asymmetry in the mandibular tooth number, which has probably been caused by its evolution to improve the feeding on the predominant dextral snails. Gene mutation can generate chiral inversion on the snail body. A sinistral snail population can thrive in this ecological context. The interactions between dextral/sinistral snails and Pareas snakes are modeled in this paper by using a new generalized functional response of Holling type II. Distinct Pareas species show different bilateral asymmetry degrees. This parameter plays an essential role in the model and determines the evolution of the populations. Stability of the solutions is analyzed for different regimes in the space of parameters. Sun, 01 Sep 2019 00:00:00 GMT http://hdl.handle.net/10366/146566 2019-09-01T00:00:00Z http://hdl.handle.net/10366/146565 [EN] We consider different methods of calculating the (fractional) fermion number of solitons based on the heat kernel expansion. We derive a formula for the localized 𝜂 function that provides a more systematic version of the derivative expansion for spectral asymmetry and compute the fermion number in a multi flavor extension of the Goldstone–Wilczek model. We also propose an improved expansion of the heat kernel that allows the tackling of the convergence issues and permits an automated computation of the coefficients. Thu, 20 Jun 2019 00:00:00 GMT http://hdl.handle.net/10366/146565 2019-06-20T00:00:00Z http://hdl.handle.net/10366/146563 [EN] In this letter the fractional fermion number of thick domain walls is computed. The analysis is achieved by developing the heat kernel expansion of the spectral eta function of the Dirac Hamiltonian governing the fermionic fluctuations around the domain wall. A formula is derived showing that a non null fermion number is always accompanied by a Hall conductivity induced on the wall. In the limit of thin and impenetrable walls the chiral bag boundary conditions arise, and the Hall conductivity is computed for this case as well. Thu, 10 Oct 2019 00:00:00 GMT http://hdl.handle.net/10366/146563 2019-10-10T00:00:00Z http://hdl.handle.net/10366/146562 [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. Mon, 26 Feb 2018 00:00:00 GMT http://hdl.handle.net/10366/146562 2018-02-26T00:00:00Z http://hdl.handle.net/10366/146560 [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. Thu, 15 Feb 2018 00:00:00 GMT http://hdl.handle.net/10366/146560 2018-02-15T00:00:00Z http://hdl.handle.net/10366/146475 [EN] In this paper the domain wall solutions of a Ginzburg-Landau non-linear 𝕊2-sigma hybrid model are exactly calculated. There exist two types of basic domain walls and two families of composite domain walls. The domain wall solutions have been identified by using a Bogomolny arrangement in a system of sphero-conical coordinates on the sphere 𝕊2. The stability of all the domain walls is also investigated. Fri, 29 Jun 2018 00:00:00 GMT http://hdl.handle.net/10366/146475 2018-06-29T00:00:00Z http://hdl.handle.net/10366/133154 [EN]The bipartite ground state entanglement in a finite linear harmonic chain of particles is numerically investigated. The particles are subjected to an external on-site periodic potential belonging to a family parametrized by the unit interval encompassing the sine-Gordon potential at both ends of the interval. Strong correspondences between the soliton entanglement entropy and the kink energy distribution profile as functions of the sub-chain length are found. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10366/133154 2014-01-01T00:00:00Z http://hdl.handle.net/10366/133153 [EN] It is shown that the Confluent Heun Equation (CHEq) reduces for certain conditions of the parameters to a particular class of Quasi-Exactly Solvable models, associated with the Lie algebra $sl (2,{\mathbb R})$. As a consequence it is possible to find a set of polynomial solutions of this quasi-exactly solvable version of the CHEq. These finite solutions encompass previously known polynomial solutions of the Generalized Spheroidal Equation, Razavy Eq., Whittaker-Hill Eq., etc. The analysis is applied to obtain and describe special eigen-functions of the quantum Hamiltonian of two fixed Coulombian centers in two and three dimensions. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10366/133153 2014-01-01T00:00:00Z http://hdl.handle.net/10366/133152 [EN] By applying Darboux-Crum transformations to the quantum one-gap Lam ́e system, we introduce an arbitrary countable number of bound states into forbidden bands. The perturbed potentials are reflectionless and contain two types of soliton defects in the periodic background. The bound states with finite number of nodes are supported in the lower forbidden band by the periodicity defects of the potential well type, while the pulse type bound states in the gap have infinite number of nodes and are trapped by defects of the compression modulations nature.We investigate the exotic nonlinear N= 4 supersymmetric structure in such paired Schrödinger systems, which extends an ordinary N= 2 supersymmetry and involves two bosonic generators composed from Lax-Novikov integrals of the subsystems. One of the bosonic integrals has a nature of a central charge, and allows us to liaise the obtained systems with the stationary equations of the Korteweg-de Vries and modified Korteweg-de Vrieshierarchies. This exotic supersymmetry opens the way for the construction of self-consistent condensates based on the Bogoliubov-de Gennes equations and associated with them new solutions to the Gross-Neveu model. They correspond to the kink or kink-antikink defects of the crystalline background independence on whether the exotic supersymmetry is unbroken or spontaneously broken. Wed, 01 Jan 2014 00:00:00 GMT http://hdl.handle.net/10366/133152 2014-01-01T00:00:00Z http://hdl.handle.net/10366/133151 [EN]The effects induced by the quantum vacuum fluctuations of one massless real scalar field on a configuration of two partially transparent plates are investigated. The physical properties of the infinitely thin plates are simulated by means of Dirac-$\delta-\delta^\prime$ point interactions. It is shown that the distortion caused on the fluctuations by this external background gives rise to a generalization of Robin boundary conditions. The $T$-operator for potentials concentrated on points with non defined parity is computed with total generality. The quantum vacuum interaction energy between the two plates is computed using the $TGTG$ formula to find positive, negative, and zero Casimir energies. The parity properties of the $\delta-\delta^\prime$ potential allow repulsive quantum vacuum force between identical plates. Thu, 01 Jan 2015 00:00:00 GMT http://hdl.handle.net/10366/133151 2015-01-01T00:00:00Z