Properties of a sinusoidally driven thermostat

This analytical and numerical study explores, from a deterministic perspective, the response of a particle in contact with a heat bath to an external force that varies sinusoidally in time. The heat bath is represented as a deterministic Nosé-Hoover thermostat. Such an idealized model encompasses features found in a variety of physical problems in which the coherent influence of an external agent competes against the thermalization tendencies of the surrounding medium, e.g., a charged particle in a thermal plasma that is acted on by a powerful electromagnetic wave. It is found that, independently of the coupling strength to the thermostat, average power can only be extracted from the sinusoidal force when the oscillatory velocity exceeds the thermal velocity. It follows from this property that a candidate heat bath whose temperature is raised solely through the application of a sinusoidal force (e.g., radio-frequency heating), reaches, in a finite time, a unique final temperature determined by the force parameters. The transition boundary separating the two domains of power transfer is shown to be dominated by chaotic behavior. The combined response to a sinusoidal force and a dc force are also considered and the relevant regions of power transfer are delineated.