Adaptive Spectral Condensation in Open Quantum Systems

Hydrodynamic collective behavior in driven-dissipative quantum systems is typically understood as a consequence of microscopic conservation laws or externally imposed symmetries.Here we demonstrate a distinct mechanism: an adaptive nonlinear feedback dynamically reorganizes the Liouvillian spectrum into an emergent low-dimensional non-Hermitian hydrodynamic manifold. Using exact Liouvillian diagonalization, Dynamic Mode Decomposition (DMD) {schmid2010dynamic, kutz2016dynamic}, pseudospectral analysis, and finite-size scaling across more than 10³ stochastic realizations, we show that the system develops a robust spectral condensation characterized by the emergence of slow collective modes separated from the dissipative bulk.The microscopic Liouvillian spectrum quantitatively matches the data-driven DMD generator, establishing a direct hydrodynamic correspondence between microscopic open-system dynamics and emergent collective evolution. Near the condensation threshold, the Liouvillian becomes strongly non-normal, exhibiting transient amplification, enhanced Petermann factors, pseudospectral inflation, and near-defective spectral geometry. We further identify a robust collapse of transient dynamics under dissipative gap rescaling, consistent with an emergent non-Hermitian scaling structure that is largely independent of microscopic feedback details across the system sizes studied (N=2–8). These results indicate that adaptive driven-dissipative dynamics can self-organize into robust low-dimensional non-Hermitian collective sectors and collective spectral self-organization. Kernel-deformation analyses across multiple Hamiltonian classes, dissipative channels, and nonlinear feedback architectures further demonstrate that the emergent hydrodynamic sector is robust against variations in the microscopic feedback functional form.