用纠缠态表象导出复杂量子介观电路的特征频率  

Obtaining Characteristic frequencies of complex quantum mesoscopic circuit through the entangled state representation

作　　者：笪诚[1,2] 范洪义[1,3] DA Cheng;FAN Hongyi(The Interdisciplinary Center for Study on Maths, Physics and Engineering, Chaohu University,Hefei, 238000, China;School of Mechanical and Electronic Engineering, Chaohu University, Hefei, 238000, China;Department of Material Science and Engineering, University of Science and Technology of China, Hefei, 230026, China)

机构地区：[1]巢湖学院数理工程研究中心,安徽合肥238000 [2]巢湖学院机械与电子工程学院,安徽合肥238000 [3]中国科学技术大学材料科学与工程系,合肥230026

出　　处：《安徽建筑大学学报》2016年第3期73-80,共8页Journal of Anhui Jianzhu University

基　　金：安徽省高等学校自然科学研究重点项目(项目编号:KJ2016A504);安徽省高等学校省级质量工程教学研究项目(项目编号:2015jyxm327);巢湖学院博士科研启动基金资助项目(项目编号:KYQD-201407)

摘　　要：以讨论有互感和共用电容的两回路介观电路的量子化为例,我们提出复杂量子介观电路的特征频率的概念。在给出该电路正确的量子Hamilton算符后,用纠缠态表象求出了系统在恒稳电路状态下的能量量子化公式以及特征频率,发现互感越大,特征频率越高。文中同时也得到了系统的波函数和零点能,这在经典框架中是无从顾及的。By discussing quantization of a two-loop quantum mesoscopic circuit in which a capacitance is sharingand mutual inductance exists between two inductances, we propose the conception of characteristic frequencyfor complex electric circuit in the context of quantum mechanics. In the steady case of the circuit, after thequantum Hamilton operator is correctly deduced, and by using the entangled state representation we derive theenergy quantization formula and the characteristic frequency of the system. It shows that the greater the mutualinductance, the higher the characteristic frequency. At the same time, the wave function and zero point energy arealso obtained, which are impossible to be taken into account in the classical framework of the system.

关 键 词：纠缠态表象 介观电路 正则变换 特征频率 

分 类 号：O413.1[理学—理论物理]