Microscopic Description of Exceptional Points in Open Quantum Systems

Exceptional points (EPs) are discrete points in the parameter space of a given dissipative system at which two or more eigenstates coalesce. In recent years, the EPs have been studied in a wide range of physical contexts, including experiments involving microwave cavities and simple electric circuits. While the eigenstate coalescence can be modeled using a simple phenomenological finite matrix, this approach ignores the continuum degrees of freedom that describe the detailed environmental influence in open systems. In this presentation, we apply an exact description starting from the microscopic Hamiltonian to show the eigenvalues are described by a characteristic fractional power expansion near the EP [Int. J. Theor. Phys. 51, 3536 (2012)]. We further show the usual diagonalization scheme fails at the EP and the Hamiltonian can only be reduced to Jordan block form [J. Math. Phys. 58, 092101 (2017)]. Finally, we briefly show that near the EP the usual exponential decay scheme is replaced by either modified exponential or pure non-exponential decay; we note the phenomenological model is incapable of predicting the non-exponential dynamics [J. Math. Phys. 58, 062101 (2017)].