Speaker
Description
Recent experimental measurements of the transition path time distributions of proteins demonstrate that these distributions are experimentally measurable. The folding unfolding dynamics of proteins is classical mechanical in nature but the experiments motivated the development of a quantum theory of transition path time distributions [1-3]. The formalism was applied to define a tunneling flight time which is found to vanish for symmetric and asymmetric Eckart barriers and a rectangular barrier, irrespective of the barrier width and height. This generalized the Hartman effect. Yet, special relativity is not violated [4].
The same approach has led to an understanding that the transition path time distribution can be used in the context of a new concept - time averaged weak values [5]. This approach has led to the formulation of a time averaged weak value commutator and uncertainty principle [6]. The latter is of special note since it leads to the derivation of a weak value time-energy uncertainty principle [5]. This insight is applied to scattering on a potential. We find that it is possible to determine both the location and the momentum of a quantum particle at the price of total uncertainty with respect to the time of arrival at the location.
Finally, we find that the concept of time averaging leads to the conclusion that it is possible to determine the complex weak value of Hermitian operators without resorting to weak measurement [7].
References:
[1] E. Pollak, Quantum Tunneling - The Longer the Path the Less Time it Takes, J. Phys. Chem. Lett. 8, 352 (2017).
[2] E. Pollak, Transition path time distribution, tunneling times, friction and uncertainty, Phys. Rev. Lett. 118, 07041 (2017).
[3] E. Pollak, Thermal quantum transition path time distributions, time averages and quantum tunneling times, Phys. Rev. A 95, 042108 (2017).
[4] J. Petersen and E. Pollak, Tunneling flight time, chemistry and special relativity, J. Phys. Chem. Lett. 8, 4017-4022 (2017).
[5] E. Pollak and S. Miret-Artés, Time averaging of weak values - consequences for time-energy and coordinate-momentum uncertainty, preprint, submitted to New J. Phys..
[6] E. Pollak and S. Miret-Artés, Uncertainty relations for time averaged weak values, to be published.
[7] E. Cohen and E. Pollak, Determination of weak values of hermitian operators using only strong measurement, preprint, arXiv:1804.11298, to be published.
