Narrow Results

The application of topological defects to the study of different molecular potential models has been a focus of interest in recent times due to its significant role in shaping the behavior and interactions of molecular systems. In lieu of this, the asymptotic iteration method is employed to obtain the eigensolutions of the Schrödinger equation of the modified shifted Morse potential model with topological defect. Vibrational energies for carbon monoxide have been presented numerically for various topological defects and the results are compared with experimental data. With the help of the energy expression of modified shifted Morse potential, the q-deformed partition function and other superstatistical function expressions of modified shifted Morse potential for carbon monoxide within the modified Dirac delta distribution are obtained, using the Euler–MacLaurin’s formula. For various temperature values considered, the superstatistical plots show a high level of dependence on the topological defect parameter and deformation parameter. The superstatistical functions for a deformation parameter of zero correspond to the conventional thermodynamic functions. Our results also agree with the available results in the literature.

In this work, using a description of defects in solids in terms of three-dimensional gravity, we have obtained the changes on the spectrum energy and eigenfunctions of a bound particle, moving in a magnetic field, in a space with a linear topological defect, namely disclination and screw dislocation. We find exact expressions for the energy eigenvalue and eigenfunctions and compare these results with the ones obtained in the previous cases.

The equation of circular loops of cosmic string with time-dependent tension is studied in the Minkowski spacetime and Robertson–Walker universe. We found that, in the case where the tension depends on some power of the cosmic time, cosmic string loops with time-varying tension should not collapse to form a black hole if the power is lower than a critical value.

Inspired by condensed matter physics we propose a new, asymmetric, family of cosmic strings. These strings present a conical curvature singularity plus a surrounding region of alternating positive and negative curvature as the azimuthal angle is changed. Their sources include both positive and negative mass density regions.

We present a brief overview of recently proposed detection schemes for axion, axion-like pseudoscalar particle and topological defect dark matter. We focus mainly on the possibility of using atomic and molecular systems for dark matter detection. For axions and axion-like particles, these methods are complementary probes to ongoing photon–axion interconversion experiments and astrophysical observations. For topological defects, these methods are complementary to conventional astrophysical search schemes based on gravitational signatures.

Einstein introduced cosmological constant in his field equations in an ad hoc manner. Cosmological constant plays the role of vacuum energy of the universe which is responsible for the accelerating expansion of the universe. To give a theoretical support, it remains an elusive goal to modern physicists. We provide a prescription to obtain cosmological constant from the phase transitions of the early universe when topological defects, namely monopole might have existed.

We present a brief overview of a new generation of high-precision laboratory and astrophysical measurements to search for ultralight (sub-eV) axion, axion-like pseudoscalar and scalar dark matter (DM), which form either a coherently oscillating classical field or topological defects (solitons). In these new detection methods, the sought effects are linear in the interaction constant between DM and ordinary matter, which is in stark contrast to traditional searches for DM, where the sought effects are quadratic or higher order in the underlying interaction constants (which are extremely small).

At finite temperatures, the field along a linear stretch of correlation length size is supposed to trace the shortest path in the field space given the two end point values, known as the geodesic rule. In this study, we compute the probability that, the field variations over distances of correlation length follow this rule in theories with $O(2)$ global symmetry. We consider a simple ferromagnetic $O(2)$-spin model and a complex ${\varphi }^4$ theory. The computations are carried out on an ensemble of equilibrium configurations, generated using Monte Carlo simulations. The numerical results suggest a significant deviation to the geodesic rule, relevant for the formation of topological defects during quench in second-order phase transition. Also for the case of $O(2)$-spins in two dimensions, the distribution and density of vortices, have been studied. It is found that, for quench temperatures close to the transition point, the Kibble–Zurek mechanism underestimates the equilibrium density of defects. The exponents corresponding to the width of the distributions are found to be smaller than Kibble mechanism estimates and match only when there is no deviation from the geodesic rule.

In this paper, we consider a charged relativistic spin-1 oscillator under the influence of an internal magnetic flux in a $(2+1)$-dimensional spacetime induced by a spinning point source. In order to analyze the effects of the internal magnetic flux and spin of the point source on the relativistic dynamics of such a vector field, we seek a non-perturbative solution of the associated spin-1 equation derived as an excited state of Zitterbewegung. By performing an analytical solution of the resulting equation, we determine exact results for the system in question. Accordingly, we analyze the effects of spin of the point source and internal magnetic flux on the relativistic dynamics of the considered test field. We see that the spin of such a field can be altered by the magnetic flux and this means that the considered system may behave as a fermion or boson according to the varying values of the magnetic flux, in principle. We observe that the internal magnetic flux and the spin of the point source impact on the relativistic energy levels and probability density functions. Also, our results indicate that the spin of the point source breaks the symmetry of the energy levels corresponding to particle–antiparticle states.

We investigate the quantum scattering of an electron by a topological defect called dispiration, with an externally applied magnetic field along its axis. The Aharonov–Bohm effect for bound states is analyzed and it is demonstrated that the wave function and the energy spectra associated with the particle depend on the features of the dispiration as well as on the magnetic flux. We also calculate Berry's phase associated to the dynamics of electrons in this background.

We consider a neutral particle with permanent electric dipole moment interacting with a field configuration induced by the noninertial effects of the Fermi–Walker reference frame in the presence of a disclination and discuss the influence of curvature on the Landau–He–McKellar–Wilkens quantization.

In this paper, we have investigated bound state solutions for a scalar particle described in the space–time of a chiral cosmic string subjected to rotational effects in a Kaluza–Klein theory. We saw that combinations between the parameters that describe the generalized space–time impose upper and lower limits for the radial coordinate leading to well-established boundary conditions.

We study the problem of vortex nucleation in rotating two-dimensional Bose–Einstein condensate confined in a harmonic trap. We show that, within the Gross–Pitaevskii theory with the boundary condition of vanishing of the order parameter at infinity, topological defects nucleation occurs via the creation of vortex-antivortex pairs far from the cloud center, where the modulus of the order parameter is small. Then vortices move toward the center of the cloud and antivortices move in the opposite direction but never disappear. We also discuss the role of surface modes.

In this paper we review the theory of unconventional quantum critical points that are beyond the Landau's paradigm. Three types of unconventional QCPs will be discussed: (1) The transition between topological order and semiclassical spin ordered phase; (2) The transition between topological order and valence bond solid phase; (3) The direct second order transition between different competing orders. We focus on the field theory and universality class of these unconventional QCPs. Relation of these QCPs with recent numerical simulations and experiments on quantum frustrated magnets are also discussed.

A network of optical parametric oscillators (OPOs) is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising/XY ground state as the system transitions from below to above the lasing threshold. We study the behavior of this “Ising machine” for three canonical problems: a 1D ferromagnetic spin chain, a 2D square lattice and problems where next-nearest-neighbor couplings give rise to frustration. If the pump turn-on time is finite, topological defects form (domain walls for the Ising model, winding number and vortices for XY) and their density can be predicted from a numerical model involving a linear “growth stage” and a nonlinear “saturation stage”. These predictions are compared against recent data for a 10,000-spin 1D Ising machine.

In this paper we study the Landau levels arising within the relativistic dynamics of a neutral particle which possesses a permanent magnetic dipole moment interacting with an external electric field in the curved space–time background with the presence of a torsion field. We use the Aharonov–Casher effect to couple this neutral particle with the electric field in this curved background. The eigenfunction and eigenvalues of the Hamiltonian are obtained. We show that the presence of the topological defect breaks the infinite degeneracy of the relativistic Landau levels arising in this system. We study the nonrelativistic limit of the eigenvalues and compare these results with cases studied earlier.

We investigate the analog effect of the Aharonov–Bohm effect for bound states in two relativistic quantum systems in a spacetime with a spacelike dislocation. We assume that the topological defect has an internal magnetic flux. Then, we analyze the interaction of a charged particle with a uniform magnetic field in this topological defect spacetime, and thus, we extend this analysis to the confinement of a hard-wall potential and a linear scalar potential. Later, the interaction of the Klein–Gordon oscillator with a uniform magnetic field is analyzed. We first focus on the effects of torsion that stem from the spacetime with a spacelike dislocation and the geometric quantum phase. Then, we analyze the effects of torsion and the geometric quantum phase under the presence of a hard-wall potential and a linear scalar potential.

We consider an elastic medium with a disclination and investigate the topological effects on the interaction of a spinless electron with radial electric fields through the WKB (Wentzel, Kramers, Brillouin) approximation. We show how the centrifugal term of the radial equation must be modified due to the influence of the topological defect in order that the WKB approximation can be valid. Then, we search for bound states solutions from the interaction of a spinless electron with the electric field produced by this linear distribution of electric charges. In addition, we search for bound states solutions from the interaction of a spinless electron with radial electric field produced by uniform electric charge distribution inside a long non-conductor cylinder.

In this work, we solve the radial Schrödinger wave equation in three dimensions under Aharonov–Bohm (AB)-flux field with potential superposition of generalized q-deformed Hulthen potential, Coulomb potential, and inverse quadratic Yukawa potential in a point-like defect. We determine the approximate eigenvalue solution using the parametric Nikiforov–Uvarov (NU) method and analyze the effects of topological defect and the magnetic flux field with this superposed potential. We show an analogous of the AB effect because the eigenvalue solution depends on the geometric quantum phase and bound state solutions are possible under condition. Finally, we utilize the approximate eigenvalue solution to some molecular potential models, such as Deng–Fan potential and inverse quadratic Hulthen potential and analyze the effects on the energy levels and the radial wave functions.

In recent years, the extension of the notion of symmetry using the picture of topological defects and its applications have been actively studied. One direction is the so-called non-invertible symmetry, in which non-invertible topological defects are treated as symmetry. We have constructed non-invertible topological defects from duality in 4D lattice pure ℤ₂ gauge theory. This work is in collaboration with Y.Nagoya and S.Yamaguchi.