Polaron Problem in Quantum Wells

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The problem of the polaron ground state energy and of effective mass renormalization in quantum wells has been widely discussed in literature [1, 2]. Considerably less attention has been paid to the quantum well polaron lifetime [3], or more generally, to the spectral density function which is closely related to the excitonic absorption lineshape function. We employ the cumulant expansion method which has been proved to be very accurate in the case of three-dimensional po larons [4]. The main idea of this method is to expand the correction to the phase of the time dependent Green's function in powers of the coupling constant. Such an expansion is much faster convergent than a standard perturbation series for the Green's function. In practice, already the lowest order term provides a very reasonable approximation.