We investigate the entanglement for a model of a particle moving in the lattice (many-body system). The interaction between the particle and the lattice is modelled using Hookes law. The Feynman path integral approach is applied to compute the densit
y matrix of the system. The complexity of the problem is reduced by considering two-body system (bipartite system). The spatial entanglement of ground state is studied using the linear entropy. We find that increasing the confining potential implies a large spatial separation between the two particles. Thus the interaction between the particles increases according to Hookes law. This results in the increase in the spatial entanglement.
We report on a theoretical investigation concerning the polaronic effect on the transport properties of a charge carrier in the one-dimensional molecular chain. Our technique is based on the Feynmans path integral approach. Analytical expressions for
the frequency-dependent mobility and effective mass of the carrier are obtained as functions of electron-phonon coupling. The result exhibits the crossover from a nearly free particle to a heavily trapped particle. We find that the mobility depends on temperature and decreases exponentially with increasing temperature at low temperature. It exhibits large-polaronic-like behaviour in the case of weak electron-phonon coupling. These results agree with the phase transition cite{Mish} of transport phenomena related to polaron motion in the molecular chain.
