Relativistic Formulation of Quantum Tunneling

Dai-Yu Xu, Towe Wang, Xun Xue

Mohsen Razavy

In this revised and expanded edition, in addition to a comprehensible introduction to the theoretical foundations of quantum tunneling based on different methods of formulating and solving tunneling problems, different semiclassical approximations for multidimensional systems are presented. Particular attention is given to the tunneling of composite systems, with examples taken from molecular tunneling and also from nuclear reactions. The interesting and puzzling features of tunneling times are given extensive coverage, and the possibility of measurement of these times with quantum clocks are critically examined. In addition by considering the analogy between evanescent waves in waveguides and in quantum tunneling, the times related to electromagnetic wave propagation have been used to explain certain aspects of quantum tunneling times. These topics are treated in both non-relativistic as well as relativistic regimes. Finally, a large number of examples of tunneling in atomic, molecular, condensed matter and nuclear physics are presented and solved.

Boris Mikhailovich Karnakov, V. D. Mur, Vladimir S Popov

Enderalp Yakaboylu

Tunnel-ionization is investigated in the framework of relativistic quantum mechanics. \nFor an arbitrary constant electromagnetic field a gauge invariant energy \noperator is introduced in order to identify the classically forbidden region for \ntunnel-ionization. Furthermore, relativistic features of tunnel-ionization are explored. \nA one-dimensional intuitive picture predicts that the ionized electron wave \npacket in the relativistic regime experiences a momentum shift along the laser’s \npropagation direction. This is shown to be consistent with the well-known strong \nfield approximation. Furthermore, spin dynamics in tunnel-ionization process \nis discussed in the standard as well as in the dressed strong field approximation. \nNext, the tunneling time delay is investigated for tunnel-ionization by extending \nthe definition of the Wigner time delay. Later, this concept is redefined in terms of \nthe phase of the fixed energy propagator. The developed formalism is applied to \nthe deep-tunneling and the near-threshold-tunneling regimes. It is shown that in \nthe latter case signatures of the tunneling time delay can be measurable at remote \ndistance. Finally, the path-dependent formulation of gauge theory is discussed. It \nis demonstrated that this equivalent formulation of gauge theory leads to a canonical \ngauge fixing, in which the Feynman path integral becomes more intuitive and \nthe calculation of the quasiclassical propagator is considerably simplified

Mohsen Razavy