Friction as a consistent quantum-mechanical concept

A quantum analog of friction (understood as a completely positive, Markovian, translation-invariant, phenomenological model of dissipation) is known to be at odds with detailed balance in the thermodynamic limit. We show that this is not the case for quantum systems with internal (e.g., spin) states nonadiabatically coupled to translational dynamics. For such systems, a quantum master equation is derived which phenomenologically accounts for the frictional effect of a uniform zero-temperature environment. A simple analytical example is provided. Conjectures regarding the finite-temperature case are also formulated. The results are important for efficient simulations of complex molecular dynamics and quantum reservoir engineering applications.

Figure 1

The ball-and-spring model of a quantum damped harmonic oscillator [Eq. (17)] with an additional internal structure represented by the molecular stretching mode $x_2$ (see Sec. 4 for details).