Polaron transformation

This Hamiltonian is diagonalized by the canonical transformation (called Lang-Firsov or polaron ) [95-97]... 

Now let us consider the polaron transformation (146)-(147) applied to the tunneling Hamiltonian... 

To conclude, after the canonical transformation we have two equivalent models (1) the initial model (145) with the eigenstates (160) and (2) the fictional free-particle model (154) with the eigenstates (158). We shall call this second model polaron representation. The relation between the models is established by (155)-(157). It is also clear from the Hamiltonian (148), that the operators < , d. ad. and a describe the initial electrons and vibrons in the fictional model. 

Fourth, Jaime and Salamon (1999) have pointed out that a(T) increases more sharply than exponentially on cooling to rmax in fig. 30 and that the additional entropy transported increases on crossing the () -() phase boundary at tc. This observation is consistent with a progressive transformation from Zener to small polarons in the hole-poor phase as the hole concentration x = 0.30 in this phase is diluted by the trapping of Zener polarons in the hole-rich phase. Such a transformation would double the number of sites available to a polaron and would therefore increase the a of eq. (26) by reducing c = (1 — r)2x toward c = (1 — r)x, where r is the ratio of trapped to free polarons. In the O phase, most of the polarons appear to be small polarons at 7 N. 

Electron back transfer is the opposite process to exciton dissociation and can positively influence the EL intensity, provided energy requirements are fulfilled. A detailed analysis of the transformation within polaron pairs is carried out in [70]. 

Transformation. The transformation of the Hamiltonian (2.1) which yields a weak residual excitation-phonon coupling even when the g are large has been discussed several times (4, 7, 16, 17). It prSduces a uniform shift in the excitation energy levels and a displacement in the equilibrium position of the phonons corresponding to the formation of a polaron. Since the transfer interactions J compete with this tendency to form a localized... 

Besides the mentioned aperiodicity problem the treatment of correlation in the ground state of a polymer presents the most formidable problem. If one has a polymer with completely filled valence and conduction bands, one can Fourier transform the delocalized Bloch orbitals into localized Wannier functions and use these (instead of the MO-s of the polymer units) for a quantum chemical treatment of the short range correlation in a subunit taking only excitations in the subunit or between the reference unit and a few neighbouring units. With the aid of the Wannier functions then one can perform a Moeller-Plesset perturbation theory (PX), or for instance, a coupled electron pair approximation (CEPA) (1 ), or a coupled cluster expansion (19) calculation. The long range correlation then can be approximated with the help of the already mentioned electronic polaron model (11). 

It is interesting to follow the role of the IT effect in this picture. Dressed with phonons, orbital states transform into the so-called IT polaron states. The orbital pseudo spin becomes vibronic pseudo spin (a detailed discussion of this side of the story is given below in Sects. 5.2 and 5.3). Instead of free rotations of the orbital pseudo spin we come to hindered rotations of the vibronic pseudo spin. At each metal site, the equipotential continuum of different orientations of the orbital spin is transformed into alternating bumps and wells of the vibronic pseudo spin. The latter ones correspond to favorable directions of the vibronic pseudo spin along metal-ligand chemical bonds. 

Using the small polaron model, we can easily diagonalize the Hamiltonian (521) with respect to the phonon variables by canonical transformation [compare with expression (255)]... 

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