Soliton-antisoliton pair production

Solitons are stable in the excited states because of the favourable balance of energies. In the vicinity of the soliton the dimerization is reduced, so the elastic energy is reduced. This reduction in elastic energy more than compensates the increase in kinetic energy associated with localizing the wavefunction near the vicinity of the solitons. 

We saw that the soliton in the ground state of an odd-site chain is either neutral with spin-1/2 for the undoped chain (5°), or charged with spin 0 for the singly doped chain S ). We now discuss the types of solitons present in the excited states of an even-site chain. Suppose that an even-site chain is instantaneously excited from the ground state to the or 2Ag states. This is a vertical transition, with the soliton-antisoliton separation initially zero. Within a time 27r/o o a soliton-antisoliton pair is created and separates a distance Their 

let us consider the singlet, state. We write this as. 

For a single soliton, as in the groimd state of a odd-site chain, (pn = tpn- This is plotted in Fig. 4.4. The probability distribution functions associated with the localized functions pn and are also plotted in Fig. 4.11. 

Finally, it is easily shown that the 2 Ag state, defined as, 2 Ag) =cL cLjl/) 

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