caused by the D -terms: (1) cannot change the net particle number density in Φ$_{i}$, denoted by n$_{i}$ = i ˙ Φ ∗ $_{i}$Φ$_{i}$ + h.c. , and hence the total baryon/lepton number density stored in the condensate. (2) cannot decrease the total comoving particle number density in φ$_{i}$ , denoted by ˜ n$_{i}$ , thus the total number density of quanta ˜ n = ∑ i ˜ n$_{i}$ in the condensate. As a direct consequence of the conservation of energy density, non-perturbative effects will not increase the average energy of quanta E$_{ave}$ . The theorem also applies to elliptical trajectories, where the condensate will mainly contain particles (or anti-particles), but it will also contain a small mixture of anti-particles (or particles). The theorem is applicable for the subsequent evolution of the plasma formed after the phase of particle production. This implies that possible non-perturbative effects do not lead to the decay of a rotating condensate. They merely redistribute the energy which is initially stored in the condensate among the fields on the D -flat subspace [410]. The marked difference between rotating and an oscillating flat direction case can be un- derstood from the trajectory of motion (i.e. circular for rotation versus linear for oscillation). An oscillating condensate φ , whose trajectory of motion is a line, can be written as φ = ϕ 2 exp( iθ ) + ϕ 2 exp( − iθ ) , (427) This is not surprising since an oscillation is the superposition of two rotations in opposite directions, which carry exactly the same number of particles and anti-particles respectively. Therefore the net particle number density stored in an oscillating condensate is zero. and the conserved charge associated with the global U (1) (corresponding to phase θ ) is given by n = i ˙ $_{φ}$∗$_{φ}$ + h . c . = 0 . (428) Now consider non-perturbative particle production from an oscillating condensate. One can think of this process as a series of annihilations among N particles and N anti-particles in the condensate, N > 1, into an energetic particle-anti-particle pair. This is totally compatible with conservation of charge, see Eq. (428); n = 0 after preheating as well as in the condensate. On the other hand, a (maximally) rotating condensate consists of particles or anti- particles only [410, 411]. Conservation of the net particle number density then implies 199