用热场动力学理论研究介观电路的Wigner函数

利用热场动力学及相干热态表象理论,重构了有限温度下介观RLC电路的Wigner函数,研究了有限温度下介观RLC电路的量子涨落.借助于Weyl-Wigner理论讨论了有限温度下介观RLC电路Wigner函数的边缘分布,并进一步阐明了Wigner函数边缘分布统计平均的物理意义.结果表明: 有限温度下介观RLC电路中电荷和电流的量子涨落随着温度和电阻值的增加而增加,回路中的电荷和电流之间存在着压缩效应,这种量子效应是由于系统零点振动的涨落而引起的; 有限温度下介观RLC电路Wigner函数边缘分布的统计平均正好是储存在介观RLC电路中电容和电感上的能量.

Wigner Function of Mesoscopic Circuit by Virtue of the Thermo Tield Dynamics

By virtue of the thermo field dynamics and the coherent thermo state representation, the Wigner function of mesoscopic RLC circuit at finite temperature was obtained, and the quantum fluctuations of mesoscopic RLC circuit at finite temperature were studied. By means of the Weyl correspondence and Wigner theorem the marginal distribution of Wigner function in mesoscopic RLC circuit was discussed. The physical meaning of marginal distributions' statistical average of the Wigner function was explained. The results show that the quantum fluctuations of both charge and current of mesoscopic RLC circuit at finite temperature increase with the rising of temperature and resistance value, and the mesoscopic RLC circuit has squeezed effects between charge and current, caused by the quantum mechanical zero-point fluctuations; the marginal distributions' statistical averages of the Wigner function are the energy stored in capacity and in inductance of the mesoscopic RLC circuit, respectively.