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*CANCELED*Traversal time for tunneling


The tunneling of particles through classically forbidden regions is a basic quantum phenomenon. We review discussions which investigate the dynamics of this process and in particular attempt to answer the question: “What is the time a particle needs to traverse a classically forbidden region”. Some approaches lead to superluminal velocities. Similar to Brillouin and Sommerfeld we are interested in approaches which yield causal subluminal velocities. In particular we discuss in some detail the propagation of monochromatic fronts of Stevens and Buttiker and Thomas [1].  The use of such fronts to find a sharp traversal time is not possible, however, using frequency band limited sources or short-time Fourier analysis allows to determine a traversal time with the accuracy of the time itself [2].

[1] Markus  Buttiker and Harry Thomas, Ann. Phys. (Leipzig) 7, 602 (1988).

[2] Gonzalo Muga and Markus Buttiker, Phys. Rev. A 62, 023808 (2000).