Theory ofU(1)gaugedQ-balls revisited

Some properties ofU(1)gaugedQ-balls

“…In [7] it was shown that the same relation also holds for U(1) gauged Q-balls. We will use it for an extra check of our numerical results.…”

“…2 Note that the correction to the background nongauged solution in [3] grows with r, which indicates the breakdown of the linear approximation at some r (moreover, as it was shown in [7], such a breakdown of the linear approximation for the correction is inherent to models of gauged Q-balls). Thus, the divergence of total energy in the linear approximation cannot be used as an indication of the absence of a solution to the full set of nonlinear equations.…”

“…do not differ considerably from those of ordinary nongauged Q-balls (see paper [7], in which this issue was examined in detail). Meanwhile, the most interesting cases are those in which backreaction of the gauge field cannot be neglected.…”

“…Later this subject was examined in the well-known paper [4], in which gauged Q-balls (for simplicity, from here on, we call U(1) gauged Q-balls "gauged Q-balls") were examined analytically and numerically. One can also recall papers [5,6,7], where gauged Q-balls were examined mainly from a theoretical point of view, as well as papers [8,9,10,11,12], where solutions for gauged Q-ball were obtained numerically.…”

Schrödinger Equations with Logarithmic Self-Interactions: From Antilinear PT-Symmetry to the Nonlinear Coupling of Channels

“…One of the best known examples is provided by [16,17] in which the toy models are considered in the form of the nonlinear logarithmic Schrödinger Equation (5) with the wave-function solutions ψ ∈ L 2 ( d ) studied in an interval of time t ∈ (t 0 , t 1 ). This equation, along with its relativistic analogue, finds multiple applications in the physics of quantum fields and particles [49][50][51][52][53][54][55], extensions of quantum mechanics [16,56], optics and transport or diffusion phenomena [57][58][59][60], nuclear physics [61,62], the theory of dissipative systems and quantum information [63][64][65][66][67][68], the theory of superfluidity [69][70][71][72] and the effective models of the physical vacuum and classical and quantum gravity [73][74][75][76], where one can utilize the well-known fluid/gravity analogy between inviscid fluids and pseudo-Riemannian manifolds [77][78][79][80][81]. The relativistic analogue of Equation (5) is obtained by replacing the derivative part with the d'Alembert operator and is not considered here.…”