Effect of quantum subsystem–subsystem coupling in hybrid systems

Abstract

In this paper, we study the effect of quantum subsystem–subsystem coupling on the magnetic-like field that the classical subsystem feels in a quantum–classical hybrid system. The hybrid system is composed of a classical magnetic particle and two coupled spins. We show that (i) when the spin–spin interaction is equal to the magnetic–spin interaction, the magnetic-like field changes sharply. This observation becomes more clear when the distance between the two subsystems is much longer than the magnetic particle's rotating radius. (ii) When the spin–spin interaction is larger than the coupling between the quantum classical systems, the effect that the quantum subsystem acts on in the classical part approaches zero. Some useful applications are also discussed.

Keywords:

• Berry phase

Acknowledgements

This work is supported by NCET of M.O.E. and NSF of China under Grant Nos. 60578014 and 10775023.

Notes

Note

1. It should be emphasised that the restriction of a fixed radius is only for the purpose of predigesting the calculation. It does not affect the result, i.e. when the classical particle moves freely in the xy plane with an instantaneous radius r at the moment, the magnetic-like field is the same as the particle rotates circularly with fixed radius r, but the magnetic-like force are rather different. This results from the fact that the definition of the magnetic-like field in Equation (5) is a function of the coordinates of the classical particle only. The varying radius affects the classical particle through the magnetic-like force given by .