Complex Time Semiclassical Formulation of Dissipative Tunneling Dynamics

Kin’ya Takahashi, Kensuke S. Ikeda

Joachim Ankerhold, Hermann Grabert

The time evolution of the density matrix of a system with potential barrier is determined using path integrals. Describing the quantum dynamics in terms of the semiclassical motion in the complex coordinate plane, a detailed picture of barrier penetration in the time domain and the change-over from thermal activation to quantum tunneling is gained. Deep tunneling is shown to arise from specific fluctuations about the semiclassical real time trajectories.

Markus Saltzer, Joachim Ankerhold

We study to what extent propagation of wave packets through potential barriers can be described semiclassically in real time. By analyzing the semiclassical approximation to the exact path-integral representation of the quantum-mechanical time evolution operator, we show that in the long-time sector it is dominated by quasiclassical fluctuations associated with caustics. Contrary to the description of tunneling in imaginary times, simple tunneling paths even for complex energies do not exist. Our findings lead to an extended semiclassical propagation scheme for wave-packet dynamics which is numerical efficient and accurately describes deep incoherent tunneling through static and externally driven barrier potentials.

Joachim Ankerhold

Niall D. Whelan

Luis Aragón-Muñoz, Guillermo Chacón‐Acosta, Héctor H. Hernández

In this work, we study the quantum tunnel effect through a potential barrier within a semiclassical formulation of quantum mechanics based on expectation values of configuration variables and quantum dispersions as dynamical variables. The evolution of the system is given in terms of a dynamical system for which we are able to determine numerical effective trajectories for individual particles, similar to the Bohmian description of quantum mechanics. We obtain a complete description of the possible trajectories of the system, finding semiclassical reflected, tunneled and confined paths due to the appearance of an effective time-dependent potential.