Effect of chaos on relativistic quantum tunnelling (Vol. 43 No. 6)

Tunnelling rates and local density of states for massless Dirac fermion in integrable and chaotic double-well systems where Φ and Χ are two components of Dirac spinor.

What can classical chaos do to a quantum system is a fundamental issue, which is highly relevant to a number of branches in physics. The field, named quantum chaos, has been active for at least three decades, where the focus has been on non-relativistic quantum systems described by the Schrodinger equation. With respect to relativistic quantum systems governed by the Dirac equation, Berry and Mondragon were the first to investigate the energy-level statistics of a chaotic neutrino billiard.

The present work presents an astonishing case of how chaos may affect relativistic quantum tunnelling dynamics. By developing an efficient method to solve the Dirac equation in the setting where relativistic quantum particles can tunnel between two symmetric cavities through a potential barrier, it appears that chaotic cavities can mostly suppress the spread in the tunnelling rate. Specifically, when the classical dynamics is integrable, the tunnelling rate for any given energy can assume values in a range that increases with energy (fig. upper panel). However, when the cavities allow fully chaotic dynamics, spread in the tunnelling rate is strongly reduced (lower panel). This suppression can be explained by the emergence of certain class of pointer states (fig.). A remarkable feature, which does not arise in non-relativistic quantum tunnelling systems, is that substantial tunnelling exists even when the particle energy nears zero. This is a consequence of the relativistic quantum phenomenon of Klein tunnelling. The authors found similar results in tunnelling devices made of graphene, implying that the field of relativistic quantum chaos can be highly relevant to the development of such devices.

Xuan Ni, Liang Huang, Ying-Cheng Lai and L. M. Pecora, ‘Effect of chaos on relativistic quantum tunnelling’, EPL, 98, 50007 (2012)