Damping and Fluctuations in Systems of Coupled Quantum Oscillators

Hongqi Li

In order to research quantum effect of a mesoscopic parallel circuit with mutual inductance coupled and damped, we adopt the method of damped harmonic oscillator quantization to quantize the circuit. By using unitary transform, the Hamiltonian of the system is diagonalized. Then we can get the energy levels of the circuit. Our results show that one such circuit can be equivalent to double module coupling harmonic oscillator, the quantum fluctuations of the electrical current and voltage not only relate to the parameters and mutual inductance coupling intensity of the circuit, but also to the quantum states of the circuit. And when the coupling intensity is colse to zero, the quantum fluctuations only relate to the inherence frequency of the circuit. Then we can control the quantum noises of the circuit by adjusting the parameters.

Hermann Grabert

Oleg Yu. Dinariev

Qiu Shen-Yu, Cai Shao-Hong, (1)贵州大学物理系，贵阳 550025; (2)贵州大学物理系，贵阳 550025;贵阳财经学院，贵阳 550004

The dissipative mesoscopic coupled circuits are obtained by the method of damped harmonic oscillator quantization . The quantum fluctuations of charge and current in an arbitrary eigenstate of the system have also been given .The result shows that the quantum fluctuations of the charge and current exist in all states, and the fluctuations in the component circuits are corelated.

Anton Amann, Harald Atmanspacher A

Sun Yu-Jing

For the damped inductive coupled electric circuit with time-dependent inductances and capacitances,the system is quantized with the electron-phonon interaction included and the quantum fluctuations are calculated.In the studied coupled circuit,there are resistances both in the component circuits and in the coupling part.When the inductances and the capacitances are independent of time,the physical quantities will first decrease with oscillations and then reach a stable state.At the stable state,if the inductances and capacitances in the two component circuits are the same and the resistances go to zero,the quantum fluctuations will tend to that of the undamped circuit.