High-energy tunneling in complex time

Ludovic D. C. Jaubert, Marcus A. M. de Aguiar

Semiclassical approximations for tunneling processes usually involve complex trajectories or complex times. In this paper we use a previously derived approximation involving only real trajectories propagating in real time to describe the scattering of a Gaussian wavepacket by a finite square potential barrier. We show that the approximation describes both tunneling and interferences very accurately in the limit of small Plank's constant. We use these results to estimate the tunneling time of the wavepacket and find that, for high energies, the barrier slows down the wavepacket but that it speeds it up at energies comparable to the barrier height.

Max Meynig, Hal M. Haggard

Kiran Mathew, Moncy V. John

Ludovic D. C. Jaubert, Marcus A. M. de Aguiar

Semiclassical approximations for tunnelling processes usually involve complex trajectories or complex times. In this paper, we use a previously derived approximation involving only real trajectories propagating in real time to describe the scattering of a Gaussian wavepacket by a finite square potential barrier. We show that the approximation describes both tunnelling and interferences very accurately in the limit of small Planck’s constant. We use these results to estimate the tunnelling time of the wavepacket and find that, for high energies, the barrier slows down the wavepacket but that it speeds it up at energies comparable to the barrier height. PACS numbers: 03.65.Sq, 31.15.Gy (Some figures in this article are in colour only in the electronic version.) 1.

Joachim Ankerhold

E.‐M. Ilgenfritz, H. Perlt

The authors investigate tunnelling through a potential barrier in quantum mechanics extending Feynman's path integral to complex time paths. This problem has gained new interest in the context of baryon number violating processes in the standard electroweak model, where the transitions between topological sectors must be described at high energies and temperatures. The authors reduce the number of degrees of freedom to one in order to test their method. It is found that a path in the complex time plane consisting of purely real or imaginary steps minimizes the real and imaginary parts of the action simultaneously. Jumps from real to imaginary time increments are situated at the turning points of the classical problem. Possible extensions to field theory are discussed.