Semiclassical formula for quantum tunneling in asymmetric doublewell potentials
Abstract
Despite the fact that quantum tunneling has been studied since the advent of quantum mechanics, the literature appears to contain no simple (textbook) formula for tunneling in generic asymmetric doublewell potentials. In the regime of strong localization, I derive a succinct analytical formula based on the WentzelKramersBrillouin semiclassical approach. Two different examples of asymmetric potentials are discussed: the cases when the two localized levels are degenerate and when they are not degenerate. For the first case, I also discuss a timedependent problem showing the quantum Zeno effect.
 Publication:

Physical Review A
 Pub Date:
 July 2012
 DOI:
 10.1103/PhysRevA.86.012106
 arXiv:
 arXiv:1205.0366
 Bibcode:
 2012PhRvA..86a2106R
 Keywords:

 03.65.Xp;
 03.65.Sq;
 03.75.Lm;
 74.50.+r;
 Tunneling traversal time quantum Zeno dynamics;
 Semiclassical theories and applications;
 Tunneling Josephson effect BoseEinstein condensates in periodic potentials solitons vortices and topological excitations;
 Tunneling phenomena;
 point contacts weak links Josephson effects;
 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 (9 pages, 7 figures)