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The following qualitative differences exist between the two approaches: in [33], the dominant peak broadens for α 6 and the second peak does not develop, but gives rise to a flat shoulder in the optical conductivity spectrum at α ≈ 6. As α increases beyond α ≈ 6, the DSG results for the OC do not produce the broad phonon sideband spectrum of the RES-transition that was qualitatively predicted in [29] and obtained with DQMC. Figure 5 shows that already for α = 1 noticeable differences arise between Reσ(Ω) calculated with perturbation theory to O(α), resp.

11, upper panel, with open circles and squares, respectively. The PD-scaling relation for the polaron ground-state energy as derived in [102] is given by (52). In Fig. 11, lower panel, the available data for the free energy from [38] are plotted in the following form, inspired by the lhs and the rhs parts of (52): F2D (α) (squares) and 23 F3D 3πα (open triangles). As follows from the figure, 4 the path integral Monte Carlo results for the polaron free energy in 2D and 3D very closely follow the PD-scaling relation of the form given by (52): F2D (α) ≡ 2 F3D 3 3πα 4 .

Density is found as shown in Fig. 21. Such a suppression is expected because of the screening of the Fr¨ ohlich interaction with increasing polaron density. 1 Ground-State Properties of Interacting Polarons in a Quantum Dot For a spherical quantum dot, a system of N electrons (or holes), with mutual Coulomb repulsion and interacting with the bulk phonons is analysed in [142, 144] using the variational inequality for identical particles (see [145, 146] and Subsect. 1). A parabolic confinement potential, characterised by the frequency parameter Ω0 , is assumed.

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