Quantum dynamics of a damped free particle

C. Aslangul , N. Pottier , D. Saint-James

We investigate the exact quantum dynamics of a free particle damped through its interaction with an harmonic bath, when the effective coupling strength behaves as ωδ at low frequency. We find that various regimes can occur depending on the value of δ and of the temperature. At large times, the mean square displacement is shown either to diverge as tv, the exponent v being never greater than 2 or to tend towards a finite value, indicating a confinement in the broad sense. In addition, for δ < 1, an oscillation (absent in the uncoupled system) is found : due to the friction on the dominant low-frequency modes and to the existence of retardation effects, the particle is forced to relax in the mean towards its initial location, the net dynamical effect of the bath being similar to that of an applied potential. In the limit δ → 0, the particle is frozen.

Mots clés: quantum statistical mechanics; quantum theory; thermodynamics

Domaines: Articles anciens

C. Aslangul, N. Pottier, D. Saint-James. Quantum dynamics of a damped free particle. Journal de Physique, 1987, 48 (11), pp.1871-1880. ⟨10.1051/jphys:0198700480110187100⟩. ⟨jpa-00210629⟩