Euclidean resonance in a magnetic field

TL;DR

This paper explores Euclidean resonance in a magnetic field, revealing how specific conditions enable long-distance tunneling by forming potential wells that facilitate resonance phenomena.

Contribution

It introduces the concept of Euclidean resonance in magnetic fields, linking it to potential well formation and long-distance tunneling, which was not previously understood.

Findings

Euclidean resonance depends on potential shape perpendicular to tunneling

Resonance allows for long-distance underbarrier motion

Potential wells form where kinetic energy becomes negative

Abstract

An analogy between Wigner resonant tunneling and tunneling across a static potential barrier in a static magnetic field is found. Whereas in the process of Wigner tunneling an electron encounters a classically allowed regions, where a discrete energy level coincides with its energy, in the magnetic field a potential barrier is a constant in the direction of tunneling. Along the tunneling path the certain regions are formed, where, in the classical language, the kinetic energy of the motion perpendicular to tunneling is negative. These regions play a role of potential wells, where a discrete energy level can coincide with the electron energy. Such phenomenon, which occurs at the certain magnetic field, is called Euclidean resonance and substantially depends on a shape of potential forces in the direction perpendicular to tunneling. Under conditions of Euclidean resonance a long distance underbarrier motion is possible.