Influence of Dissipation on Quantum Coherence

A quantum mechanical particle which moves in a symmetric double-well potential, and whose interaction with the environment is described in the classical regime by a phenomenological friction coefficient $\eta$, is considered. It is shown that, provided $\frac{\eta {q_0}^2}{\hslash }$ exceeds a critical value of order unity ($\pm q_0$ are the locations of the potential minima), the mean rate of tunneling between the degenerate minima decreases with temperature, leading at $T=0\mathrm{}$ to spontaneous symmetry breaking.