We use the effective field theory approach to systematically study the dynamics of classical and quantum systems in an oscillating magnetic field. We find that the fast field oscillations give rise to an effective interaction which is able to confine charged particles as well as neutral particles with a spin magnetic moment. The effect is reminiscent of the renown dynamical stabilization of charges by the oscillating electric field and provides a foundation for a new class of magnetic traps. The properties characteristic to the dynamical magnetic confinement are reviewed.
PT symmetric quantum mechanics for a particle trapped by the generalized non-Hermitian harmonic oscillator potential is studied. It is shown that energy and the expectation value of the position operator
x can not be real simultaneously, if the particle is trapped. Non-vanishing boundary conditions for the trapped particle in
PT symmetric theory are also discussed.
Using the perturbation theory,we solve the ground state of Bose-Einstein condensate in composite potential trap,which is composed of one-dimensional linear harmonic oscillator potential and optical lattice potential.We treat the kinetic energy of particles in composite potential trap as a perturbation and analyse the effect of kinetic term as well as composite potential trap on probability density distribution of particles in ground state of condensate.In the end,we infer the main field of application of perturbation theory.