Büttiker–Landauer tunneling time through one-dimensional barriers of arbitrary shape

Abstract A convenient formalism, based on the surface Green's functions is developed that allows one to obtain a general expression for the Buttiker–Landauer tunneling time through one-dimensional barriers of arbitrary shape. It is shown that transmission, reflection and dwell times can be expressed in terms of the scattering-matrix elements. Although the results are based on the Larmor clock approach, there are indications that they will be applicable to a wide range of clocks. A relation between functional derivatives of the barrier potential and partial derivatives with respect to the incident energy is established. Finally, an analytical expression for escape time of an electron from a finite disordered region is derived and the connection to thelocal scattering-matrix elementsis discussed.