Reduced density matrix approach to phononic dissipation in friction

Understanding mechanisms for energy dissipation from nanoparticles in conta ct with large samples is a central problem in describing friction microscop ically. Calculation of the reduced density matrix appears to be the most su itable method to study such systems that are coupled to a large environment . In this paper, the time evolution of the reduced density matrix has been evaluated for an arbitrary system coupled to a heat reservoir. The formalis m is then applied to study the vibrational relaxation following the stick-s lip motion of an asperity on a surface. The frequency and temperature depen dence of the relaxation time is also determined. Predictions of the reduced density matrix are compared with those obtained by using the Golden Rule a pproach.