Effect of low momentum quantum fluctuations on a coherent field structure - art. no. 105011

In the present work the evolution of a coherent held structure of the sine- Gordon equation under quantum fluctuations is studied. The basic equations an derived from the coherent state approximation to the functional Schrodin ger equation for the field. These equations are solved asymptotically and n umerically for three physical situations. The first is the study of the non linear mechanism responsible for the quantum stability of the soliton in th e presence of low momentum fluctuations. The second considers the scatterin g of a wave by the soliton. Finally the third problem considered is the col lision of solitons and the stability of a breather. It is shown that the co mplete integrability of the sine-Gordon equation precludes fusion and split ting processes in this simplified model. The approximate results obtained a re non-perturbative in nature, and are valid for the full nonlinear interac tion in the limit of low momentum fluctuations. It is also found that these approximate results are in good agreement with full numerical solutions of the governing equations. This suggests that a similar approach could be us ed for the baby Skyrme model, which is not completely integrable. In this c ase the higher space dimensionality and the internal degrees of freedom whi ch prevent the integrability will be responsible for fusion and splitting p rocesses. This work provides a starting point in the numerical solution of the full quantum problem of the interaction of the field with a fluctuation .