Semiclassical Real-Time Tunneling by Multiple Spawning of Classical Trajectories

Abstract

We systematically extend semiclassical real-time propagation methods based on Gaussian wave packets by using the composition property of the time-dependent quantum-mechanical Green function. For the first time, in an application to the problem of barrier tunneling, a semiclassical time-domain calculation of the transmission probability exhibits good agreement with exact quantum mechanical values at energies below the barrier top. Only two insertions of unity are needed for these results in a benchmark model of reactive scattering.

Strong Field Tunnel Ionization by Real-Valued Classical Trajectories

“…From the point of view of SC-IVR, the present work complements alternate procedures for incorporating tunneling effects into these methods [5,6]. It continues recent work [7] to extend SC-IVR methods, which have mostly been restricted to problems of field free and low-field molecular dynamics [3], to the area of strong field physics.…”

Tunneling in two-dimensional systems using a higher-order Herman–Kluk approximation

“…7,8 Although it is sometimes possible to overcome this difficulty by an analysis which provides optimal values for the parameters, 7 this approach has been implemented only for the one-dimensional ͑1D͒ Eckart potential and its application to more general systems seems difficult. A number of additional ways to describe tunneling within the framework of HK-like approximations have been proposed [9][10][11][12][13][14][15][16][17][18] but, in most cases, it is not clear whether they are sufficiently general and numerically efficient for the practical treatment of tunneling in multidimensional systems in the absence of thermal averaging.…”

Quasiclassical and semiclassical wave-packet dynamics in periodic potentials

“…It is noted that several schemes have been devised to improve the performance of semiclassical initial-value representation propagators for systems which exhibit tunneling effects. 42,47,49,50 Let us next consider the results of the quasiclassical method. Overall the results shown in Fig.…”