A strange weak value in spontaneous pair productions via a supercritical step potential

Abstract

We consider a case when a weak value is introduced as a physical quantity rather than as an average of weak measurements. The case we treat is a time evolution of a particle by the 1 + 1-dimensional Dirac equation. In particular, in a spontaneous pair production via a supercritical step potential, a quantitative explanation can be given by a weak value for the group velocity of the particle. We also show that the condition for the pair production (supercriticality) corresponds to the condition when the weak value takes a strange value (superluminal velocity). 10

A weak-value model for virtual particles supplying the electric current in graphene: the minimal conductivity and the Schwinger mechanism

“…Our result shows one of the interesting cases in which a weak value emerges as a real value of a physical quantity like [17]. In addition, aside from the issue of a weak value, it also gives a new insight into graphene in the sense that the creation process is related to virtual particles allowed by the uncertainty relations.…”

“…In [17], we showed the case when a group velocity of a quantum particle was given by a weak value in the 1 + 1 dimensional Dirac equation, which was applied to a transmission through a supercritical step potential. In this paper, we show that this weak-value formalism is also valid for describing the creation process of an electric carrier in graphene.…”

“…In addition to the applications mentioned above, weak measurements have offered interesting approaches for the foundation of quantum mechanics such as quantum paradoxes [35][36][37][38][39] and the violation of the Leggett-Garg inequality [40][41][42][43]. Apart from weak measurements, a weak value has been useful for explaining quantum phenomena [17,18,[44][45][46][47]. Then, the significance of a weak value itself has also been discussed in the context of a measurement [48][49][50][51] and the validity for a description of quantum mechanics [43,[52][53][54][55][56].…”

When a negative weak value −1 plays the counterpart of a probability 1

“…Weak value has been observed as an ensemble average via weak measurement so far, while weak value can also appear as a physical value in some cases [13][14][15][16][17]. In fact we have experimentally estimated weak values by the statistical procedure.…”

Negation of photon loss provided by negative weak value

“…Although the weak value of −1 cannot be interpreted as a conventional probability, any weak value can be observed by weak measurements; it also naturally appears in a quantum phenomenon as a value of a physical quantity [31][32][33][34][35]. Recently we have also showed that positive and negative weak values are associated with symmetrical operations [36].…”