Ground state properties of dissipative two state system coupled to phonons

We present a systematic analysis of ground state properties of a tunneling system coupled to an Ohmic bath. The nonadiabatic effects induced by coupling with tunneling particle , on the ground state properties of phonons are taken into account. For this we have considered both displacement and deformation of phonons via a variational treatment. The symmetry breaking transition , or the delocalization-localization transition of tunneling particle is presented and is compared with earlier known results. We also show that in the critical regime a gap will be opened near the zero momentum in the spectrum of the phonons. The modified phonon spectrum along with the phonon displacement field correlation functions have been calculated. It is shown that in the critical regime the tunneling system stabilizes the lattice against long wavelength fluctuations.