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Inspired by the universal operator growth hypothesis, we extend the formalism of Krylov construction in dissipative open quantum systems connected to a Markovian bath. Our construction is based upon the modification of the Liouvillian superoperator by the appropriate Lindbladian, thereby following the vectorized Lanczos algorithm and the Arnoldi iteration. This is well justified due to the incorporation of non-Hermitian effects due to the environment. We study the growth of Lanczos coefficients in the transverse field Ising model (integrable and chaotic limits) for boundary amplitude damping and bulk dephasing. Although the direct implementation of the Lanczos algorithm fails to give physically meaningful results, the Arnoldi iteration retains the generic nature of the integrability and chaos as well as the signature of non-Hermiticity through separate sets of coefficients (Arnoldi coefficients) even after including the dissipative environment. Our results suggest that the Arnoldi iteration is meaningful and more appropriate in dealing with open systems.

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This study presents a robust technique to estimate the maximum power point (MPP) of a double-diode model (DDM) photovoltaic (PV) module. The MPP of the DDM PV module under different environmental conditions (DECs) are estimated by using the simple and computationally efficient Levenberg-Marquardt method. The variation of double diode PV module parameters with the change of temperature and irradiation is analysed. The MPP of the DDM PV array at non-standard test condition obtained from the proposed method is verified with the MPP obtained experimentally and by MATLAB simulation. A comparative study of MPP of a DDM PV module estimated from the proposed method with different existing methods is performed for different operating conditions. The maximum measurement error in power generation of a DDM PV module for different methods under DEC is presented which indicates better performance of the proposed method for the estimation of MPP of a DDM PV module.