A stationary body that is out of thermal equilibrium with its environment, and for which the electric susceptibility is nonreciprocal, experiences a quantum torque. This arises from the spatially nonsymmetric electrical response of the body to its interaction with the nonequilibrium thermal fluctuations of the electromagnetic field: the nonequilibrium nature of the thermal field fluctuations results in a net energy flow through the body, and the spatially nonsymmetric nature of the electrical response of the body to its interaction with these field fluctuations causes that energy flow to be transformed into a rotational motion. We establish an exact, closedform, analytical expression for this torque in the case that the environment is the vacuum and the material of the body is described by a damped oscillator model, where the nonreciprocal nature of the electric susceptibility is induced by an external magnetic field, as for magnetooptical media. We also generalise this expression to the context in which the body is slowly rotating. By exploring the hightemperature expansion of the torque, we are able to identify the separate contributions from the continuous spectral distribution of the nonreciprocal electric susceptibility, and from the resonance modes. In particular, we find that the torque persists in the limiting case of zero damping parameter, due to the contribution of the resonance modes. We also consider the lowtemperature expansion of the torque. This work extends our previous consideration of this model to an external magnetic field of arbitrary strength, thereby including nonlinear magnetic field effects.
 NSFPAR ID:
 10348027
 Date Published:
 Journal Name:
 The Journal of Chemical Physics
 Volume:
 157
 Issue:
 5
 ISSN:
 00219606
 Page Range / eLocation ID:
 054103
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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