Time dilation in the oscillating decay laws of moving two-mass unstable quantum states

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 ${\mathcal{P}}_p(t)$ 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 ${\alpha }_1$ and ${\alpha }_2$ near the non-vanishing lower bounds ${\mu }_{0,1}$ and ${\mu }_{0,2}$ of the mass spectra, respectively. If the powers ${\alpha }_1$ and ${\alpha }_2$ differ, the long-time survival probability ${\mathcal{P}}_p(t)$ exhibits a dominant inverse-power-law decay and is approximately related to the survival probability at rest ${\mathcal{P}}_0(t)$ by a time dilation. The corresponding scaling factor ${\chi }_{p,k}$ reads $\sqrt{1+p^2/{\mu }_{0,k}^2}$, the power ${\alpha }_k$ being the lower of the powers ${\alpha }_1$ and ${\alpha }_2$. If the two powers coincide and the lower bounds ${\mu }_{0,1}$ and ${\mu }_{0,2}$ differ, the scaling relation is lost and damped oscillations of the survival probability ${\mathcal{P}}_p(t)$ appear over long times. By changing reference frame, the period $T_0$ 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 ${\mu }_{0,1}$ and ${\mu }_{0,2}$.

References in corpus (9)

• Non-exponential decay in quantum field theory and in quantum mechanics: the case of two (or more) decay channels
• No classical limit of quantum decay for broad states
• General properties of the evolution of unstable states at long times
• Hidden evidence of non-exponential nuclear decay
• Nonexponential decay of an unstable quantum system: Small-$Q$-value s-wave decay
• Decay Law of Relativistic Particles: Quantum Theory Meets Special Relativity
• Oscillations in the decay law: A possible quantum mechanical explanation of the anomaly in the experiment at the GSI facility
• Decay law and time dilatation
• Time evolution of an unstable quantum system

Cited by in corpus (3)

• Universality of quantum time dilation
• Regularities in the transformation of the oscillating decay rate in moving unstable quantum systems
• Transformation of intermediate times in the decays of moving unstable quantum systems via the exponential modes