Abstract
The decay of a moving system is studied in case the system is initially prepared in a two-mass unstable quantum state. The survival probability P_p(t) is evaluated over short and long times in the reference frame where the unstable system moves with constant linear momentum p. The mass distribution densities of the two mass states are tailored as power laws with powers α₁ and α₂ near the non-vanishing lower bounds μ_0,1 and μ_0,2 of the mass spectra, respectively. If the powers α₁ and α₂ differ, the long-time survival probability P_p(t) exhibits a dominant inverse-power-law decay and is approximately related to the survival probability at rest P₀(t) by a time dilation. The corresponding scaling factor χ_p,k reads √1+p²/μ_0,k², the power α_k being the lower of the powers α₁ and α₂. If the two powers coincide and the lower bounds μ_0,1 and μ_0,2 differ, the scaling relation is lost and damped oscillations of the survival probability P_p(t) appear over long times. By changing reference frame, the period T₀ of the oscillations at rest transforms in the longer period T_p according to a factor which is the weighted mean of the scaling factors of each mass, with non-normalized weights μ_0,1 and μ_0,2.