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We present an extension of the dynamic electrical model (DEM), which enable us to explain some important features of the perovskite solar cells (PSC), like the shape of the hysteresis and the appearance of the 'bump' in the so called reverse scan, without requiring any additional assumptions. We give analytical expressions in terms of the Lambert's function W for the open circuit voltage, the stationary current, and the instantaneous current, which can be written also in terms of elementary functions for the most part of the ranges of the physical parameters. The initial polarization of the cell, modeled as the charging of a capacitor with voltage dependent capacitance, is consistently determined in the model, from the initial stationary conditions. This is inline with a previously observed sharp increase of the PSC capacitance beyond the open-circuit voltage. Besides the known features, we obtain characteristics that were not yet analyzed experimentally, like the change of the bump from the reverse scan branch of the J-V characteristics to the forward scan, with the increase of the poling voltage (or the increase of the PSC capacitance).

A general fermion system interacting with a time-periodic external field is discussed in the second quantization formalism transposed in the Fock-Floquet space. The method simulates the evolution of the system with the help of an auxiliary parameter which is analog to the time and defines the vectors associated to the states of the system, such that the matrix elements in the Hilbert space have a physical correspondence. Assuming that only the principal quasi-energies have physical relevance, the ground state of the free system is constructed in the occupation-numbers representation and an analog of Wick's theorem is derived. The perturbation series of the Green's functions is subsequently obtained, and the linear response of a given observable is expressed in terms of the correlation functions. The results have formal similarities to those of the standard theory of the many-particle conservative systems.

In this paper the quasi-energies and the reduced Floquet vectors corresponding to a particle in 2-dimensions interacting with a time-dependent, monochromatic, linearly polarized electro-magnetic field, and in the presence of a weak, static, spatial-periodic field, are calculated. The later is treated using the stationary perturbation theory in the extended Hilbert space adapted for the eigenvalue equation of the Floquet Hamiltonian. The results have similarities to those of the quasi-free electron model.

We consider the class of Hamiltonians composed by a quadratic form in the canonical operators and a linear interaction term with time periodic external fields of an arbitrary strength. The Hamiltonian can be made time independent by a unitary transformation in the extended Hilbert space, which has the meaning of a time-dependent translation in the classical phase space. We solve the eigenvalue problem for the Floquet Hamiltonian and we find general expressions for the time-dependent wave functions, of interest for the optical and transport properties of quantum nanostructures.