Space–time evolution of the λφ4 model: classical and quantum aspects

A time dependent variational approach is used to derive the equations of motion for the λφ4 model. The simultaneous evolution of the quantum fluctuations and of the classical part of the field is considered in a lattice of 1+1 dimensions. Different initial conditions corresponding to non-equilibrium situations are considered and evolved in time. Such high energy localized configurations expand in the lattice by “bumps” which may change with time. The quantum fluctuations make the peaks be smoother and the expansion faster.