When chaos meets relativistic quantum mechanics

Because their low-energy excitations obey relativistic quantum mechanics, Dirac materials have many physical properties that are not typically seen in conventional semiconductors. Recent advances in two-dimensional Dirac materials have stoked interest in a new field called relativistic quantum chaos, which seeks to understand how classical chaos manifests in relativistic quantum systems. The field is not only fundamental to physics but is also integral to developing new solid-state electronic, spintronic and valleytronic devices.

A team of researchers published a review of the findings in this emerging field and potential paths forward in Chaos. The group’s tutorial discusses how classical chaos can be exploited for a variety of uses, including modulating quantum transport in graphene and generating superpersistent currents in Dirac ring domains. The field’s growing literature suggests that relativistic quantum chaos is not simply the standard machinery of quantum chaos applied to relativistic quantum systems, but a new discipline in its own right.

Quantum anomalies are at the forefront of condensed matter physics and pursuits in material science to create topological quantum matters. These newly investigated anomalies are typically relativistic quantum phenomena and induce intriguing exchanges between quantum and classical systems in terms of underlying fundamental symmetries that are relevant to relativistic quantum chaos.

So far, research in the field has revealed a number of counterintuitive phenomena that include chiral scars, unconventional statistics of energy level spacing, manifestations of Klein tunneling, highly robust persistent currents in chaotic Dirac billiards, and relativistic quantum chimera states.

The authors hope their review will help drive interest in uncovering, understanding and exploiting phenomena arising from the rich interplay between classical chaos and relativistic quantum mechanics.

Source: “Relativistic quantum chaos - An emergent interdisciplinary field,” by Ying-Cheng Lai, Hongya Xu, Liang Huang, and Celso Grebogi, Chaos (2018). The article can be accessed at https://doi.org/10.1063/1.5026904 .