The concept of time in quantal tunneling processes is reexamined. We find that the Wigner–Eisenbud definition of real time and the definition of imaginary time may be understood in terms of stationary phase analysis in complex time of the microcanonical flux–flux correlation function. This analysis explains why the real time should not be used to justify adiabatic approximations for perpendicular degrees of freedom at tunneling energies. A semiclassical analysis shows that, as suggested by Buettiker and Landauer, the imaginary time should be used to determine the validity of the adiabatic approximation for tunneling processes. Numerical examples for the hydrogen exchange reaction are provided. The implications on adiabatic and sudden approximations in reactive scattering are discussed. A theory unifying the two approaches is outlined.The concept of time in quantal tunneling processes is reexamined. We find that the Wigner–Eisenbud definition of real time and the definition of imaginary time may be understood in terms of stationary phase analysis in complex time of the microcanonical flux–flux correlation function. This analysis explains why the real time should not be used to justify adiabatic approximations for perpendicular degrees of freedom at tunneling energies. A semiclassical analysis shows that, as suggested by Buettiker and Landauer, the imaginary time should be used to determine the validity of the adiabatic approximation for tunneling processes. Numerical examples for the hydrogen exchange reaction are provided. The implications on adiabatic and sudden approximations in reactive scattering are discussed. A theory unifying the two approaches is outlined.

The Journal of Chemical PhysicsAug 1, 198551 citations

Deciphering Quantum Tunneling Dynamics: Insights from Sub-Barrier Interactions and Complex Time Analysis

Xiwang Liu, Xiaokai Li, Yichong Lin +7 more

Quantum tunneling, a quintessential quantum phenomenon, challenges classical intuitions by allowing particles to pass through seemingly insurmountable barriers. This study delves into the intricate dynamics of electron tunneling, focusing on the critical role of sub-barrier interactions and complex time processes. Through a combination of experimental measurements and simulations based on Feynman’s path integral of complex time trajectories, we reveal that the sub-barrier potential interaction introduces an asymmetric electron wave packet probability distribution along the real time axis and a marked delay at the tunneling exit. The energy-dependent behavior of this delay in electronic tunneling agrees with that observed in the previous atomic tunneling studies, suggesting a universal mechanism underlying quantum tunneling across different scales. Our findings underscore the necessity of incorporating both the wave and particle aspects of quantum entities to fully comprehend tunneling dynamics, which holds promise for an intuitive interpretation of complex-number quantum processes.Quantum tunneling, a quintessential quantum phenomenon, challenges classical intuitions by allowing particles to pass through seemingly insurmountable barriers. This study delves into the intricate dynamics of electron tunneling, focusing on the critical role of sub-barrier interactions and complex time processes. Through a combination of experimental measurements and simulations based on Feynman’s path integral of complex time trajectories, we reveal that the sub-barrier potential interaction introduces an asymmetric electron wave packet probability distribution along the real time axis and a marked delay at the tunneling exit. The energy-dependent behavior of this delay in electronic tunneling agrees with that observed in the previous atomic tunneling studies, suggesting a universal mechanism underlying quantum tunneling across different scales. Our findings underscore the necessity of incorporating both the wave and particle aspects of quantum entities to fully comprehend tunneling dynamics, which holds promise for an intuitive interpretation of complex-number quantum processes.

Ultrafast ScienceOct 13, 20252 citations

Complex tunneling dynamics

Ciann‐Dong Yang

Chaos Solitons & FractalsJun 22, 200631 citations

High-energy tunneling in complex time

Thomas M. Gould, Erich R. Poppitz

Prepared forJan 1, 19930 citations

Traversal time in macroscopic quantum tunneling

Paolo Moretti, Daniela Mugnai, Anedio Ranfagni +1 more

We present an interpretation of traversal time results in Josephson junctions, based on a stochastic model of tunneling processes which include dissipative effects. With the use of semiclassical analysis, the experiments performed up until now have supplied a time duration of the order of ${10}^{2}\mathrm{ps}$ (a remarkably long time, even considering the macroscopic nature of the systems under examination). According to our interpretation, this duration is only the imaginary part of a complex quantity, the real part of which (presumably the true physical duration) lies in the range of a few picoseconds.We present an interpretation of traversal time results in Josephson junctions, based on a stochastic model of tunneling processes which include dissipative effects. With the use of semiclassical analysis, the experiments performed up until now have supplied a time duration of the order of ${10}^{2}\mathrm{ps}$ (a remarkably long time, even considering the macroscopic nature of the systems under examination). According to our interpretation, this duration is only the imaginary part of a complex quantity, the real part of which (presumably the true physical duration) lies in the range of a few picoseconds.

Physical Review ADec 1, 19998 citations

{10}^{2}\mathrm{ps}

(a remarkably long time, even considering the macroscopic nature of the systems under examination). According to our interpretation, this duration is only the imaginary part of a complex quantity, the real part of which (presumably the true physical duration) lies in the range of a few picoseconds.