Ricerc@Sapienza

Foundations of quantum mechanics (QM) are designed by the 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, which do not require such a restrictive mathematical structure, have been developed.
In the late 90s, a broader set of Hamiltonian operators was considered by replacing the Hermiticity condition with the weaker requirement of a space-time reflection symmetry (PT-symmetry). This allows to obtain complex Hamiltonians whose spectra are still real and positive. In the 80s, QM in rigged Hilbert spaces showed that even the reality of the Hamiltonian spectrum is not necessary: the imaginary part of a complex energy takes into account the presence of a time asymmetric (TA) evolution, and describes damping.
Surprisingly, even if these two theories seem unrelated and were conceived independently, their link becomes deeply relevant when one considers the spontaneous PT-symmetry breaking phenomena in optical applications.
The present research aims at an exhaustive first quantization theory able to commit together non-Hermitian and PT-symmetric Hamiltonians with TA-QM. This goal is not only fundamentally important but has a relevant counterpart in studying optical propagation, where experimental tests and applications can be conceived and realized. We formerly showed the way TA-QM describes dispersive shock waves in nonlinear optics, and other scientists elaborated optical analogues of PT-symmetric systems. Our goal is to study the propagation of light in more complex systems, where PT-symmetry and TA evolution are simultaneously present.
This project presents several applications in optics and condensed matter physics, including the study of optical intrinsically irreversible propagation of ultra-short laser pulses interacting with matter and decay of phonons in disordered lattices.