介观互感耦合阻尼并联双谐振电路的量子涨落

The Quantum Fluctuations of Mesoscopic Parallel Damped Double Resonance Mutual Inductance Coupled Circuit

对介观互感耦合阻尼并联电路作双模耦合阻尼谐振子处理,将其量子化。通过三次幺正变换,将体系的哈密顿量对角化。在此基础上给出了体系的本征能谱,研究了Fock态、真空态下各回路电流和电压的量子涨落。

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.