Soliton structures

The calculated energies converge rapidly with chain size because of selftrapping, which occurs once the chain size exceeds the spatial extent of the solitonic structures. These will be described in the next section. In Section 10.3 we discuss the extent to which a fully quantum treatment of the lattice degrees of freedom changes this behaviour to better fit the experimental values. 

The isolated single chain binding energy is 2.4 eV. However, as explained in Section 9.4, the unbound pair is strongly screened in a solid state environment by 2.0 eV, whereas the exciton is more weakly screened ( 0.3 eV). This implies that the binding energy of the exciton in the solid state is 0.7 eV, in reasonable agreement with experimental interpretations of Section 10.1. 

The structures of the ground state and the 1 H , l B and 2 A+ states are shown in Fig. 10.4. The 1 H and 2M+ states undergo considerable lattice distortion, whereas the 1 H state shows a weak polaronic distortion of the lattice, very similar to the charged state. In Chapter 7 it was shown that the 1 5,7 and 2 71+ states fit a two-soliton form (defined in eqn (7.19)). In contrast, the 2 t1+ state fits a four-soliton form (defined in eqn (7.20)), indicating the strong triplet-triplet character of that state. 

Further insight into the electronic structure of polyenes and its relation to their geometry can be obtained from the spin-spin correlation function, defined as 

Reprinted with permission from W. Barford, R. J. Bursill, and M. Yu Lavrentiev, Phys. Rev. B 63, 195108, 2001. Copyright 2001 by the American Physical Society. 

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The emergent soliton structures arc obviously very reminiscent of the propagating structures normally associated with one-dimensional class c4 elementary CA, as well as the glider -like structures appearing in Conway s Game of Life (section 3.4.4). There are two noteworthy differences between these systems, however (aside from the fact that we are looking at the spatial derivative here as opposed to a... 

In this chapter we have reported on theoretical investigations of two different regimes of interaction between ultraintense EM radiation and plasmas, as examples of the application of the theoretical models developed in a previous chapter. First, we have studied the existence of localized spatial distributions of EM radiation, which appear in numerical simulations as a result of the injection of an ultrashort and intense laser pulse into an underdense plasma. Such solitonic structures originating from the equilibrium between the EM radiation pressure, the plasma pressure and the ambipolar field associated with the space charge have been described in the framework of both a relativistic kinetic model and a relativistic fluid approach. It has also been shown that... 

According to this result, for E 0, there is a small modulation of the helical structure that is a deflection from the harmonic low without a change in the structure period. With increasing field, the helix becomes distorted stronger and the soliton structure appears. Now a solution of Eq. (13.23) may be found in the... 

The effects of electron-phonon interactions alone were described in Chapter 4. We showed that these interactions lead to a dimerized, semiconducting ground state and to solitonic structures in the excited states. On the other hand, the effects of electron-electron interactions in a polymer with a fixed geometry were described in Chapters 5 and 6. There it was shown that the electronic interactions cause a metal-insulator (or Mott-Hubbard) transition in undimerized chains. Electron-electron interactions also cause Mott-Wannier excitons in the weak-coupling limit of dimerized chains, and to both Mott-Hubbard excitons and spin density wave excitations in the strong coupling limit. 

There are significant deviations between the quantum and adiabatic predictions for the triplet soliton structures. The soliton width in the adiabatic calculation (ca. 10 bond lengths) is much shorter than the corresponding quantum calculation. 

FIGURE 1.22. (a) Schematic representation of soliton structures in polyacetylene, (b) Schematic band structure for neutral, positive, and negative solitons. 

Actual soliton structures in rmAz -Poly(acetylene). 

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