Optical Analogue of Irreversible Quantum Theories

Foundations of quantum mechanics are designed by their physical interpretation: each observable must be a Hermitian operator to guarantee the reality of its spectrum, and wave functions must belong to a Hilbert space with a conserved probability measure. Recently, extended quantum theories have been developed by replacing the Hermiticity condition with the weaker requirement of a complex space-time-symmetric (PT-S) Hamiltonian with real-valued eigenvalues. In addition, various authors developed time asymmetric (TA) QM with complex energy eigenvalues, which account for irreversible evolution.
PT-S and TA QM are profoundly linked when considering the spontaneous PT-symmetry breaking in optics, but physical realizations of their coupling is lacking. Here we show that dispersive shock waves in nonlocal nonlinear optics are useful tools to simulate the quantization of decay rates predicted by TA QM. We also consider two parallel optical fibers, with gain-loss interaction, that mimic the coupling between PT-S and TA QM.
This work presents several applications in optics and condensed matter physics, including the study of irreversible propagations and decays of phonons in disordered lattices.