Non-Hermitian systems subject to classical noise

No quantum system can ever be truly isolated, for this reason the study of Open Quantum Systems is of both fundamental and practical interest. Non Hermitian systems can account for dissipation and decoherence, while showing new phenomena like exceptional points and PT symmetry. The experimental realization of these systems is subject to all sorts of noise. Motivated by this fact, in this study we consider the effect of classical noise on the dynamics of Non-Hermitian Hamiltonians. Using tools from stochastic calculus, we find the evolution for the noise-averaged density matrix to evolve with an exotic Liouvillian. Furthermore we also characterize the evolution of the fluctuations around the noise-averaged density matrix. This allows us to replicate noisy Non-Hermitian evolution seen experimentally and find several exceptional points, not shown by the standard Lindbladian. Non-Hermitian dynamics and exceptional points show many exciting potential applications, therefore our results shed light on the experimental realization of such systems, as well as on the role of stochasticity in Non-Hermitian extensions of Quantum Mechanics.