Fig. 2: Theory of lattices with stochastic dissipation.
From: Coexistence of dynamical delocalization and spectral localization through stochastic dissipation
a, Eigenstate population scheme of the analytic model. The exponentially localized eigenstates of a lattice with dissipative disorder exhibit eigenvalues λn with different imaginary parts. Initially, the left state is dominant. If \({\mathrm{Im}}(\lambda _n) > {\mathrm{Im}}(\lambda _0)\), the state at site n will become dominant at some time tchange, which depends on the localization lengths l0,ln and the distance d of the two states. Around tchange, there is a rapid spatial transition of the most dominantly populated eigenstate from the left to the right. b, Analytically (equation (2)) and numerically (equations (3) and (4)) extracted spreading coefficient s(W) as a function of the non-Hermitian disorder strength W. Our analytical predictions agree very well with the numerical data for strong disorder, where the model assumptions hold. The error bars (see Supplementary Section 4) capture ±1 s.d. of s(W). For weaker disorder, our numerical data suggest that the spreading coefficient increases as the eigenstates become less localized. Ballistic and diffusive spreading are shown for comparison.
