If the particles inside the material collide within a very small time, we will have a very small time uncertainty Delta t (time uncertainty is the uncertainty on the instant of time, where the Event does happen) also. By Heisenberg's uncertainty relation
Delta E * Delta t >= hbar/2
the energy uncertainty Delta E becomes large also. We therefore can estimate the particle in some Energy state around the energy it would classicaly have (we have a band broadness given by Delta E). I know the Quantum Zeno effect, where extremely frequent interaction of a particle with some other will undergo (almost) no time Evolution. Because Delta E is very big in this case, collisions with classical Energy transfer epsilon will have no significant and observable effect when
epsilon < Delta E.
So only collisions with really high value of epsilon do contribute to observable effects, however, These Kind of collisions are rare. Therefore, there will be very little temporal changes observed.
Question: Let the particle be trapped in an external potential with higher Magnitude than the particle's kinetic Energy expected classical and "on-shell". If the Energy spectrum of a particle is broadening in a material with very high collision frequencies, will there be a higher probability for Quantum Tunneling out of the potential?
I think yes, for a short time. Matter-antimatter pairs can Pop out for a very short time, These pair is consisting of virtual particles. But virtual particles have effects on the Dynamics. Maybe there are also effects outside the barrier due to virtual particles Tunneling out (how would this effect look like?)?
Which other quantum effects we observe in material with high collision frequency? Maybe also vacuum polarization even if the characteristic energy scales for that effect are far lower?
Yes, Patrick Linker .
I believe we do observe quantum tunneling in material with high collision frequency but they will not be observable or not at least observable with our current technology. During the collision the time gap will be extremely small and thus will affect the emission of collided substituents. As their collision will create disturbance in surrounding and thus this disturbance will create favorable condition for creation of matter antimatter pair, which will diminished as breaking virtual particles.
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