Non-topological Solitons Research Articles

One-dimensional soliton system of gaugedQ-ball and anti-Q-ball

The (1+1)-dimensional gauge model of two complex self-interacting scalar fields that interact with each other through an Abelian gauge field and a quartic scalar interaction is considered. It is shown that the model has nontopological soliton solutions describing soliton systems consisting of two Q-ball components possessing opposite electric charges. The two Q-ball components interact with each other through the Abelian gauge field and the quartic scalar interaction. The interplay between the attractive electromagnetic interaction and the repulsive quartic interaction leads to the existence of symmetric and nonsymmetric soliton systems. Properties of these systems are investigated by analytical and numerical methods. The symmetric soliton system exists in the whole allowable interval of the phase frequency, whereas the nonsymmetric soliton system exists only in some interior subinterval. Despite the fact that these soliton systems are electrically neutral, they nevertheless possess nonzero electric fields in their interiors. It is found that the nonsymmetric soliton system is more preferable from the viewpoint of energy than the symmetric one. Both symmetric and nonsymmetric soliton systems are stable to the decay into massive scalar bosons.

Gravitating solitons and black holes with synchronised hair in the four dimensional O(3) sigma-model

We consider the O(3) non-linear sigma-model, composed of three real scalar fields with a standard kinetic term and with a symmetry breaking potential in four space-time dimensions. We show that this simple, geometrically motivated model, admits both self-gravitating, asymptotically flat, non-topological solitons and hairy black holes, when minimally coupled to Einstein’s gravity, without the need to introduce higher order kinetic terms in the scalar fields action. Both spherically symmetric and spinning, axially symmetric solutions are studied. The solutions are obtained under a ansatz with oscillation (in the static case) or rotation (in the spinning case) in the internal space. Thus, there is symmetry non-inheritance: the matter sector is not invariant under the individual spacetime isometries. For the hairy black holes, which are necessarily spinning, the internal rotation (isorotation) must be synchronous with the rotational angular velocity of the event horizon. We explore the domain of existence of the solutions and some of their physical properties, that resemble closely those of (mini) boson stars and Kerr black holes with synchronised scalar hair in Einstein-(massive, complex)-Klein-Gordon theory.

Charge-screened nontopological solitons in a spontaneously broken U(1) gauge theory

We construct, numerically, stationary and spherically symmetric nontopological soliton solutions in the system composed of a complex scalar field, a U(1) gauge field, and a complex Higgs scalar field that causes spontaneous symmetry braking. It is shown that the charge of the soliton is screened by counter charge everywhere.

Cogenesis of LIGO primordial black holes and dark matter

In this letter, we propose a novel scenario which simultaneously explains $\mathcal{O}(10)M_\odot$ primordial black holes (PBHs) and dark matter in the minimally supersymmetric standard model. Gravitational waves (GWs) events detected by LIGO-Virgo collaboration suggest an existence of black holes as heavy as $\sim 30M_\odot$. In our scenario, as seeds of the PBHs, we make use of the baryon number perturbations which are induced by the special type of Affleck-Dine mechanism. Furthermore, the scenario does not suffer from the stringent constraints from CMB $\mu$-distortion due to the Silk damping and pulsar timing. We find the scenario can explain not only the current GWs events consistently, but also dark matter abundance by the non-topological solitons formed after Affleck-Dine mechanism, called Q-balls.

Direct Observation of Zhang-Li Torque Expansion of Magnetic Droplet Solitons.

Magnetic droplets are nontopological dynamical solitons that can be nucleated in nanocontact based spin torque nano-oscillators (STNOs) with perpendicular magnetic anisotropy free layers. While theory predicts that the droplet should be of the same size as the nanocontact, its inherent drift instability has thwarted attempts at observing it directly using microscopy techniques. Here, we demonstrate highly stable magnetic droplets in all-perpendicular STNOs and present the first detailed droplet images using scanning transmission X-ray microscopy. In contrast to theoretical predictions, we find that the droplet diameter is about twice as large as the nanocontact. By extending the original droplet theory to properly account for the lateral current spread underneath the nanocontact, we show that the large discrepancy primarily arises from current-in-plane Zhang-Li torque adding an outward pressure on the droplet perimeter. Electrical measurements on droplets nucleated using a reversed current in the antiparallel state corroborate this picture.

Nucleon properties in the Polyakov quark-meson model

We study the nucleon as a nontopological soliton in a quark medium as well as in a nucleon medium in terms of the Polyakov quark meson (PQM) model with two flavors at finite temperature and density. The constituent quark masses evolving with the temperature at various baryon chemical potentials are calculated and the equations of motion are solved according to the proper boundary conditions. The PQM model predicts an increasing size of the nucleon and a reduction of the nucleon mass in both hot environment. However, the phase structure is different from each other in quark and nucleon mediums. There is a crossover in the low-density region and a first-order phase transition in the high-density region in quark medium, whereas there exists a crossover characterized by the overlap of the nucleons in nucleon medium.

On the solitary wave solutions to the longitudinal wave equation in MEE circular rod

This study investigates the longitudinal wave equation in a magneto-electro-elastic circular rod by using the extended sinh-Gordon equation expansion method. Topological, non-topological and singular soliton solutions are extracted. To illustrate the physical appearance of the obtained solutions, 2D, 3D and the contour graphs to some of the obtained solutions are plotted. The reported results may be useful in explaining the physical meaning of the studied models and other nonlinear physical models arising in nonlinear sciences.

A two-dimensional soliton system of vortex and Q-ball

The (2+1)-dimensional gauge model describing two complex scalar fields that interact through a common Abelian gauge field is considered. It is shown that the model has a soliton solution that describes a system consisting of a vortex and a Q-ball. This two-dimensional system is electrically neutral, nevertheless it possesses a nonzero electric field. Moreover, the soliton system has a quantized magnetic flux and a nonzero angular momentum. Properties of this vortex-Q-ball system are investigated by analytical and numerical methods. It is found that the system combines properties of topological and nontopological solitons.

D term and the structure of pointlike and composed spin-0 particles

This work deals with form factors of the energy-momentum tensor (EMT) of spin-0 particles and the unknown particle property D-term related to the EMT, and is divided into three parts. The first part explores free, weakly and strongly interacting theories to study EMT form factors with the following findings. (i) The free Klein-Gordon theory predicts for the D-term D = -1. (ii) Even infinitesimally small interactions can drastically impact D. (iii) In strongly interacting theories one can encounter large negative D though notable exceptions exist, which includes Goldstone bosons of chiral symmetry breaking. (iv) Contrary to common belief one cannot arbitrarily add "total derivatives" to the EMT. Rather the EMT must be defined in an unambiguous way. The second part deals with the interpretation of EMT form factors in terms of 3D-densities with following results. (i) The 3D-density formalism is internally consistent. (ii) The description is subject to relativistic corrections which are acceptably small in phenomenologically relevant situations including nucleon and nuclei. (iii) The free field result D=-1 persists when a spin-0 boson is not point-like but "heuristically given some internal structure." The third part investigates the question, whether such "giving of an extended structure" can be implemented dynamically, and has the following insights. (i) We construct a consistent microscopic theory which, in a certain parametric limit, interpolates between extended and point-like solutions. (ii) This theory is exactly solvable which is rare in 3+1 dimensions, admits non-topological solitons of Q-ball-type, and has a Gaussian field amplitude. (iii) The interaction of this theory belongs to a class of logarithmic potentials which were discussed in literature, albeit in different contexts including beyond standard model phenomenology, cosmology, and Higgs physics.

Nontopological first-order vortices in a gauged CP(2) model with a dielectric function

We consider nontopological first-order solitons arising from a gauged $CP(2)$ model in the presence of the Maxwell term multiplied by a nontrivial dielectric function. We implement the corresponding first-order scenario by proceeding the minimization of the total energy, this way introducing the corresponding energy lower-bound, such a construction being only possible due to a differential constraint including the dielectric function itself and the self-interacting potential defining the model. We saturate the aforementioned bound by focusing our attention on those solutions fulfilling a particular set of two coupled first-order differential equations. In the sequel, in order to solve these equations, we choose the dielectric function explicitly, also calculating the corresponding self-interacting potential. We impose appropriate boundary conditions supporting nontopological solitons, from which we verify that the energy of final structures is proportional to the magnetic flux they engender, both quantities being not quantized, as expected. We depict the new numerical solutions, whilst commenting on the main properties they present.

Topological and non-topological soliton solution of the 1 + 3 dimensional Gross-Pitaevskii equation with quadratic potential term

This paper carries out the integration of the 1 + 3 dimensional Gross-Pitaevskii equation (GPE) in presence of quadratic potential term to ob tain the 1-soliton solutions. The solitary wave ansatz method is employed to integrate the considered equation. Parametric conditions for the existence of the soliton solutions are determined. Both non-topological (bright) and topological (dark) solitonsolutions are reported and we observed that the existence condition for bright and dark soliton solutions are opposite to each other. Finally, the two integrals of motion of the governing model equation have been extracted

Recrudescence of massive fermion production by oscillons

We bring together the physics of preheating, following a period of inflation, and the dynamics of non-topological solitons, namely oscillons. We show that the oscillating condensate that makes up an oscillon can be an efficient engine for producing heavy fermions, just as a homogeneous condensate is known for doing the same. This then allows heavy fermions to be produced when the energy scale of the Universe has dropped below the scale naturally associated to the fermions.

A practical method in calculating one loop quantum fluctuations to the energy of the non-topological soliton

I have used a practical method to calculate the one-loop quantum correction to the energy of the non-topological soliton in Friedberg-Lee model. The quantum effects which come from the quarks of the Dirac sea scattering with the soliton bag are calculated by a summation of the discrete and continuum energy spectrum of the Dirac equation in the background field of soliton. The phase shift of the continuum spectrum is numerically calculated in an efficient way and all the divergences are removed by the same renormalization procedure.

Travelling wave solutions of generalized Klein–Gordon equations using Jacobi elliptic functions

This paper obtains exact travelling wave solutions of five various forms of the generalized nonlinear Klein–Gordon equations using Jacobi elliptic functions. Topological and non-topological soliton solutions are obtained as well as Jacobi elliptic function solutions. It is acquired constraint conditions for the existence of solitons.

Reissner–Nordstrom–anti–de Sitter nontopological solitons in broken Einstein-Maxwell-Higgs theory

Results are presented from numerical simulations of the Einstein-Maxwell-Higgs equations with a broken U(1) symmetry. Coherent nontopological soliton solutions are shown to exist that separate an anti--de Sitter (AdS) true vacuum interior from a Reissner-Nordstrom (RN) false vacuum exterior. The stability of these bubble solutions is tested by perturbing the charge of the coherent solution and evolving the time-dependent equations of motion. In the weak gravitational limit, the short-term stability depends on the sign of $(\ensuremath{\omega}/Q){\ensuremath{\partial}}_{\ensuremath{\omega}}Q$, similar to $Q$-balls. The long-term end state of the perturbed solutions demonstrates a rich structure and is visualized using ``phase diagrams.'' Regions of both stability and instability are shown to exist for ${\ensuremath{\kappa}}_{g}\ensuremath{\lesssim}0.015$, while solutions with ${\ensuremath{\kappa}}_{g}\ensuremath{\gtrsim}0.015$ were observed to be entirely unstable. Threshold solutions are shown to demonstrate time-scaling laws, and the space separating true and false vacuum end states is shown to be fractal in nature, similar to oscillons. Coherent states with superextremal charge-to-mass ratios are shown to exist and observed to collapse or expand, depending on the sign of the charge perturbation. Expanding superextremal bubbles induce phase transitions to the true AdS vacuum, while collapsing superextremal bubbles can form nonsingular strongly gravitating solutions with superextremal RN exteriors.

Astrophysical constraints on dark-matter Q -balls in the presence of baryon-violating operators

Supersymmetric extensions of the standard model predict the existence of non-topological solitons, $Q$-balls. Assuming the standard cosmological history preceded by inflation, $Q$-balls can form in the early universe and can make up the dark matter. The relatively large masses of such dark-matter particles imply a low number density, making direct detection very challenging. The strongest limits come from the existence of neutron stars because, if a baryonic $Q$-ball is captured by a neutron star, the $Q$-ball can absorb the baryon number releasing energy and eventually destroying a neutron star. However, in the presence of baryon number violating higher-dimension operators, the growth of a $Q$-ball inside a neutron star is hampered once the $Q$-ball reaches a certain size. We re-examine the limits and identify some classes of higher-dimensional operators for which supersymmetric $Q$-balls can account for dark matter. The present limits leave a wide range of parameters available for dark matter in the form of supersymmetric $Q$-balls.

Supermassive dark-matter Q-balls in galactic centers?

Though widely accepted, it is not proven that supermassive compact objects (SMCOs) residing in galactic centers are black holes. In particular, the Milky Way's SMCO can be a giant nontopological soliton, Q-ball, made of a scalar field: this fits perfectly all observational data. Similar but tiny Q-balls produced in the early Universe may constitute, partly or fully, the dark matter. This picture explains in a natural way, why our SMCO has very low accretion rate and why the observed angular size of the corresponding radio source is much smaller than expected. Interactions between dark-matter Q-balls may explain how SMCOs were seeded in galaxies and resolve well-known problems of standard (non-interacting) dark matter.

Control and manipulation of a magnetic skyrmionium in nanostructures

A magnetic skyrmionium is a nontopological soliton, which has a doughnut-like out-of-plane spin texture in thin films, and can be phenomenologically viewed as a coalition of two topological magnetic skyrmions with opposite topological numbers. Due to its zero topological number ($Q=0$) and doughnut-like structure, the skyrmionium has its distinctive characteristics as compared to the skyrmion with $Q=\pm 1$. Here we systematically study the generation, manipulation and motion of a skyrmionium in ultrathin magnetic nanostructures by applying a magnetic field or a spin-polarized current. It is found that the skyrmionium moves faster than the skyrmion when they are driven by the out-of-plane current, and their velocity difference is proportional to the driving force. However, the skyrmionium and skyrmion exhibit an identical current-velocity relation when they are driven by the in-plane current. It is also found that a moving skyrmionium is less deformed in the current-in-plane geometry compared with the skyrmionum in the current-perpendicular-to-plane geometry. Furthermore we demonstrate the transformation of a skyrmionium with $Q=0$ into two skyrmions with $Q=+1$ in a nanotrack driven by a spin-polarized current, which can be seen as the unzipping process of a skyrmionium. We illustrate the energy and spin structure variations during the skyrmionium unzipping process, where linear relations between the spin structure and energies are found. These results could have technological implications in the emerging field of skyrmionics.

Magnetic droplet nucleation boundary in orthogonal spin-torque nano-oscillators.

Static and dynamic magnetic solitons play a critical role in applied nanomagnetism. Magnetic droplets, a type of non-topological dissipative soliton, can be nucleated and sustained in nanocontact spin-torque oscillators with perpendicular magnetic anisotropy free layers. Here, we perform a detailed experimental determination of the full droplet nucleation boundary in the current–field plane for a wide range of nanocontact sizes and demonstrate its excellent agreement with an analytical expression originating from a stability analysis. Our results reconcile recent contradicting reports of the field dependence of the droplet nucleation. Furthermore, our analytical model both highlights the relation between the fixed layer material and the droplet nucleation current magnitude, and provides an accurate method to experimentally determine the spin transfer torque asymmetry of each device.

Nontopological soliton in the Polyakov quark-meson model

Within a mean field approximation, we study a nontopological soliton solution of the Polyakov quark-meson model in the presence of a fermionic vacuum term with two flavors at finite temperature and density. The profile of the effective potential exhibits a stable soliton solution below a critical temperature $T\leq T_{\chi}^c$ for both the crossover and the first-order phase transitions, and these solutions are calculated here with appropriate boundary conditions. However, it is found that only if $T\leq T^c_d$,the energy of the soliton $M_N$ is less than the energy of the three free constituent quarks $3M_q$. As $T> T^c_d$, there is an instant delocalization phase transition from hadron matter to quark matter. The phase diagram together with the location of a critical end point (CEP) has been obtained in $T$ and $\mu$ plane. We notice that two critical temperatures always satisfy $T^c_d\leq T_{\chi}^c$. Finally, we present and compare the result of thermodynamic pressure at zero chemical potential with lattice data.