Semiclassical fluctuations in the quantum phase model

We consider the one-dimensional quantum phase model coupled to a thermal bath at finite temperatures and investigate the competition of quantum and thermal fluctuations. By means of a variational method, we obtain the effective classical Hamiltonian, which manifests a crossover from quantum to classical behaviors of the fluctuations. It is also shown that the peculiar nature of the quantum-phase model restricts the applicability of the otherwise well-working variational method to a certain range of quantum fluctuations.