Theoretical Physics

3

Authors: M. Socolovsky

The existence of the Aharonov-Bohm (A − B) effect with its associated U(1)-bundle A−B, and the uniqueness -up to homotopy- of a continuous function S2 ! C, induce a unique map -up to isomorphism- between the Hopf bundles with zero and unit Chern number, respectively 0 : S1 ! S2 ×S1 ! S2 and 1 : S1 ! S3 ! S2. This establishes a tight relation between 0 and 1 through A−B, and therefore between the A − B effect and the hypothetical unit magnetic charge when the Dirac connection in 1 is considered.

8

Authors: S. Khondaker, N. A. Chowdhury, A. Mannan, A. A. Mamun

The propagation of ion-acoustic waves (IAWs) in a collisionless unmagnetized selfgravitating degenerate quantum plasma system (SG-DQPS) has been studied theoretically for the first time. A nonlinear Schrödinger equation is derived by using the reductive perturbation method to study the nonlinear dynamics of the IAWs in the SG-DQPS. It is found that for kc > k (kc < k) (where kc is critical value of the propagation constant k which determines the stable and unstable region of IAWs) the IAWs are modulationally unstable (stable), and that kc depends on the ratio of the electron number density to light ion number density. It is also observed that the self-gravitating bright envelope solitons are modulationally stable. The results obtained from our present investigation are useful for understanding the nonlinear propagation of the IAWs in astrophysical compact objects like white dwarfs and neutron stars.