Emergent Liouvillian exceptional points from exact principles

Recent years have seen a surge of interest in exceptional points in open quantum systems. The natural approach in this area has been the use of Markovian master equations. While the resulting Liouvillian EPs have been seen in a variety of systems and have been associated to numerous exotic effects, it is an open question whether such degeneracies and their peculiarities can persist beyond the validity of master equations. In this work, taking the example of a dissipative double-quantum-dot system, we show that exact Heisenberg equations governing system and bath dynamics exhibit the same EPs as the corresponding master equations. To highlight the importance of this finding, we prove that the paradigmatic property associated to EPs - critical damping, persists well beyond the validity of master equations. Our results demonstrate that Liouvillian EPs can arise from underlying fundamental exact principles, rather than merely as a consequence of approximations involved in deriving master equations.

💡 Research Summary

In this paper the authors address a fundamental question in the theory of open quantum systems: are Liouvillian exceptional points (EPs) merely artifacts of the approximations that lead to Markovian master equations, or do they reflect deeper, exact properties of the underlying dynamics? To answer this, they study a paradigmatic dissipative double‑quantum‑dot (DQD) system, each dot being coupled to its own fermionic reservoir. The total Hamiltonian consists of the system part (dot energies ε_d and inter‑dot tunneling g), the reservoir Hamiltonians (continuum of modes with energies ε_kj), and the tunneling interaction between each dot and its reservoir (amplitudes t_kj).

The authors analyse the problem in two parallel frameworks. First, they solve the Heisenberg equations of motion for the dot operators without invoking any Born or Markov approximations. By assuming a wide‑band limit (WBL) they replace the energy‑dependent tunneling rates by constant Γ_j. The resulting operator dynamics can be written as a linear inhomogeneous differential equation d ̂d(t)/dt = A ̂d(t)+ ̂ξ(t), where A is a 2 × 2 non‑Hermitian matrix
A =