Enhanced tunneling in a magnetic field

As known, a probability of quantum tunneling through a static potential barrier $U(x)$ can be substantially reduced by a static magnetic field $H_{z}$. This happens due to increase of the effective barrier height caused by Landau's gauge potential in a magnetic field (the same potential results in Landau levels). There is an exponentially small current in the direction of tunneling, $x$. An underbarrier current in the direction perpendicular to tunneling, $y$, is not small. If the potential barrier $U(x,y)$ depends also on the coordinate $y$, a new unexpected scenario can occur. Now the partial de Broglie waves, generated under the barrier, are not collected to the current in the $y$ direction only but can be reflected by the potential $U(x,y)$. An interference of those underbarrier waves after reflections can result in a peak of the particle density at a classically allowed region close to the conventional exit point from under the barrier. At the certain magnetic field, $H_{z}=H_{R}$, the peak amplitude is not exponentially small (Euclidean resonance). The same phenomenon can occur in tunneling through nonstationary barriers and is expected for photon tunneling when a refractive index is slightly inhomogeneous in the tunnel region.