Time evolution of decay of two identical quantum particles

An analytical solution for the time evolution of decay of two identical noninteracting quantum particles seated initially within a potential of finite range is derived using the formalism of resonant states. It is shown that the wave function, and hence also the survival and nonescape probabilities, for factorized symmetric and entangled symmetric or antisymmetric initial states evolve in a distinctive form along the exponentially decaying and nonexponential regimes. Our findings show the influence of the Pauli exclusion principle on decay. We exemplify our results by solving exactly the $s$-wave $\delta$ shell potential model.

Figure 1

Plot of the $\ln S\left(t\right)$ (lower solid line) and $\ln P\left(t\right)$ (upper solid line) as a function of time in lifetime units for the factorized symmetric state using Eq. (10). The inset shows a calculation of the same quantities at short times using the purely exponential contributions (solid lines) and its corresponding comparison with exact calculations in terms of Moshinsky functions (dotted lines); see text.

Figure 2

Plot of the $\ln S\left(t\right)$ (lower solid line) and $\ln P\left(t\right)$ (upper solid line) as a function of time in lifetime units for the entangled symmetric state using Eq. (25). The inset shows a calculation at short times of the same quantities using the purely exponential contributions (solid lines) and the corresponding comparison with exact calculations in terms of Moshinsky functions (dotted lines); see text.

Figure 3

Plot of the $\ln S\left(t\right)$ (lower solid line) and $\ln P\left(t\right)$ (upper solid line) as a function of time in lifetime units for the entangled antisymmetric state using Eq. (26). The inset shows a calculation of the same quantities at short times using the purely exponential contributions (solid lines) and the corresponding comparison with exact calculations in terms of Moshinsky functions (dotted lines); see text.