The unreasonable effectiveness of mathematics in non-Hermitian physics*
Over the past two decades, ideas from mathematics have been increasingly used to engineer, tailor, and control open classical and quantum systems called non-Hermitian or parity-time symmetric systems. Examples of these ideas include unitary dilations, Riemann surfaces with branch cuts, exceptional degeneracies, and change-of-basis induced gauge fields. After a brief history of PT-symmetric theory, I will show how these ideas have been used across different experimental platforms to elucidate different aspects of classical and quantum open systems. .
*With apologies to Eugene Wigner; in collaboration with Anthony Laing group (University of Bristol, UK), Kater Murch group (Washington University, St. Louis), and Roberto Leon’s group (UNAM, Mexico).