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

We consider a case where a weak value is introduced as a physical quantity rather than an average of weak measurements. The case we treat is a time evolution of a particle by 1+1 dimensional Dirac equation. Particularly 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 the condition for the pair production (supercriticality) corresponds to the condition when the weak value takes a strange value (superluminal velocity).Comment: 12 pages, 3 figures, close to published versio

Circuit configurations which can/cannot show super-radiant phase transitions

Several superconducting circuit configurations are examined on the existence of super-radiant phase transitions (SRPTs) in thermal equilibrium. For some configurations consisting of artificial atoms, whose circuit diagrams are however not specified, and an LC resonator or a transmission line, we confirm the absence of SRPTs in the thermal equilibrium following the similar analysis as the no-go theorem for atomic systems. We also show some other configurations where the absence of SRPTs cannot be confirmed.Comment: 12 pages, 6 figure