Miret-Artés Salvador, Dumont Randall S, Rivlin Tom, Pollak Eli
Instituto de Física Fundamental, CSIC, Serrano 123, 28006 Madrid, Spain.
Department of Chemistry and Chemical Biology, McMaster University, Hamilton, ON L8S 4M1, Canada.
Entropy (Basel). 2021 Dec 13;23(12):1675. doi: 10.3390/e23121675.
In this work, our purpose is to show how the symmetry of identical particles can influence the time evolution of free particles in the nonrelativistic and relativistic domains as well as in the scattering by a potential δ-barrier. For this goal, we consider a system of either two distinguishable or indistinguishable (bosons and fermions) particles. Two sets of initial conditions have been studied: different initial locations with the same momenta, and the same locations with different momenta. The flight time distribution of particles arriving at a 'screen' is calculated in each case from the density and flux. Fermions display broader distributions as compared with either distinguishable particles or bosons, leading to earlier and later arrivals for all the cases analyzed here. The symmetry of the wave function seems to speed up or slow down the propagation of particles. Due to the cross terms, certain initial conditions lead to bimodality in the fermionic case. Within the nonrelativistic domain, and when the short-time survival probability is analyzed, if the cross term becomes important, one finds that the decay of the overlap of fermions is faster than for distinguishable particles which in turn is faster than for bosons. These results are of interest in the short time limit since they imply that the well-known quantum Zeno effect would be stronger for bosons than for fermions. Fermions also arrive earlier and later than bosons when they are scattered by a δ-barrier. Although the particle symmetry does affect the mean tunneling flight time, in the limit of narrow in momentum initial Gaussian wave functions, the mean times are not affected by symmetry but tend to the phase time for distinguishable particles.
在这项工作中，我们的目的是展示全同粒子的对称性如何影响非相对论和相对论领域中自由粒子的时间演化，以及在由δ势垒引起的散射中的时间演化。为了实现这个目标，我们考虑一个由两个可区分或不可区分（玻色子和费米子）的粒子组成的系统。我们研究了两组初始条件：具有相同动量的不同初始位置，以及具有不同动量的相同位置。在每种情况下，根据密度和通量计算到达“屏幕”的粒子的飞行时间分布。与可区分粒子或玻色子相比，费米子显示出更宽的分布，导致在此处分析的所有情况下更早和更晚到达。波函数的对称性似乎加快或减慢了粒子的传播。由于交叉项，某些初始条件在费米子情况下导致双峰性。在非相对论领域内，当分析短时间生存概率时，如果交叉项变得重要，人们会发现费米子重叠的衰减比可区分粒子更快，而可区分粒子又比玻色子更快。这些结果在短时间极限内很有趣，因为它们意味着著名的量子芝诺效应对于玻色子比对于费米子更强。当费米子被δ势垒散射时，它们也比玻色子更早和更晚到达。尽管粒子对称性确实会影响平均隧穿飞行时间，但在动量初始高斯波函数很窄的极限情况下，平均时间不受对称性影响，而是趋向于可区分粒子的相位时间。
