Tunneling Time and the Breakdown of Born-Oppenheimer Approximation

Quantum Tunneling: The Longer the Path, the Less Time it Takes

The standard approaches to tunneling times are replaced by considering time correlation functions. A class of correlation functions that is always positive is identified and used to define quantum mechanical transition time probability distributions. The formalism is used to study the quantum dynamics of a thermal position correlation function of a parabolic barrier Hamiltonian. The transition time probability distribution between two points distributed symmetrically about the barrier top shifts to shorter times as the temperature is reduced and tunneling is increased. A study of the mean transition time as a function of the distance between the center of the initial and final densities shows that when the temperature is sufficiently low and tunneling dominates the dynamics, increasing the length of the path traversed decreases the mean transition time. The introduction of friction to the dynamics does not "destroy" this phenomenon, except when the friction coefficient is very large.

Distribution of residence times as a marker to distinguish different pathways for quantum transport

Electron transport through a nanoscale system is an inherently stochastic quantum mechanical process. Electric current is a time series of electron tunneling events separated by random intervals. Thermal and quantum noise are two sources of this randomness. In this paper we use the quantum master equation to consider the following questions. (i) Given that an electron has tunneled into the electronically unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there are no intermediate tunneling events (the tunneling path)? (ii) Given that an electron tunneled into the unoccupied system from the source electrode at some particular time, how long is it until an electron tunnels out to the drain electrode to leave the system electronically unoccupied, where there are no intermediate tunneling events (a tunneling path)? (iii) What are the distributions of these times? We show that electron correlations suppress the difference between the electron tunneling path and an electron tunneling path.

Distribution of tunnelling times for quantum electron transport

In electron transport, the tunnelling time is the time taken for an electron to tunnel out of a system after it has tunnelled in. We define the tunnelling time distribution for quantum processes in a dissipative environment and develop a practical approach for calculating it, where the environment is described by the general Markovian master equation. We illustrate the theory by using the rate equation to compute the tunnelling time distribution for electron transport through a molecular junction. The tunnelling time distribution is exponential, which indicates that Markovian quantum tunnelling is a Poissonian statistical process. The tunnelling time distribution is used not only to study the quantum statistics of tunnelling along the average electric current but also to analyse extreme quantum events where an electron jumps against the applied voltage bias. The average tunnelling time shows distinctly different temperature dependence for p- and n-type molecular junctions and therefore provides a sensitive tool to probe the alignment of molecular orbitals relative to the electrode Fermi energy.