The Transition Path Time Distribution - Protein Folding, Quantum Mechanics, Tunneling Times and Uncertainty

The recent experimental measurement of the transition path time distributions of proteins [1] presents theory with several challenges. Foremost, why do the fits of the experimental data to a theoretical expression lead to barrier heights which are much lower than the free energies of activation of the observed transitions? Secondly, what is the transition path time distribution, without invoking the Smoluchowski limit. Thirdly, what are the properties of a quantum transition path time distribution and may they be used to present a new parafigm for understanding the concpet of time in quantum mechanics? In this talk I will introduce the concept of a transition path barrier to explain the experimental results [2] as well as the concept of a quantum mechanical transition path time probability distribution. The properties of these distribution, including quantum tunneling times and its relation to position momentum uncertainty will be discussed.

[1] Neupane K., Foster D.A.N., Dee D.R., Yu H., Wang F., Woodside M.T.; Direct Observation of Transition Paths During the Folding of Proteins and Nucleic Acids, Science (2016) Vol. 352, 239-242

[2] Pollak E. , The transition path time distribution and the transition path free energy barrier, Phys. Chem. Chem. Phys. (2016) Vol. 18, 28872 – 28882