含二极管非线性介观电路的量子化求解
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摘要
含有二极管的介观电容电感电路,是典型的非线性电路,非线性项的存在造成薛定谔方程求解困难.本文利用微扰方法,得到了体系能级和波函数,并讨论了体系电荷的量子涨落.所得结果有助于对含有二极管的介观电容电感电路的量子效应的深入研究,也有利于介观电路量子理论应用的推广.
Diodes included mesoscopic inductive-capacitance circuit is a typical nonlinear circuit.It is difficult to solve the Schrodinger equation for the existence of nonlinear term in Hamilton.Based on the perturbative theory,the detailed energy spectrum and wave functions of the system are achieved.As an application,the quantum fluctuation of charge is calculated.The results of the paper are helpful to the further research work about diodes included mesoscopic circuit and the application of quantum theory of mesoscopic circuits.
Diodes included mesoscopic inductive-capacitance circuit is a typical nonlinear circuit.It is difficult to solve the Schrodinger equation for the existence of nonlinear term in Hamilton.Based on the perturbative theory,the detailed energy spectrum and wave functions of the system are achieved.As an application,the quantum fluctuation of charge is calculated.The results of the paper are helpful to the further research work about diodes included mesoscopic circuit and the application of quantum theory of mesoscopic circuits.
引文
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[2]LI Youquan,CHEN Bin.Quantum theory for mesoscopic electric circuits[J].Phys Rev,1996,B(53):4027-4032.
[3]JI Yinghua,LUO haimei,WU Yunyi.Behaviors of mesoscopic LC circuit in the external magnetic field[J].Phys Lett,2003,A(318):141-145.
[4]FAN Hongyi,LIANG Xianting.Quantum fluctuation in thermal vacuum state for mesoscopic LC electric circuit[J].Chin Phys Lett,2000,17(3):174-176.
[5]WANG Jisuo,SUN Changyong.Quantum effects of mesoscopic RLC circuit in squeezed vacuum state[J].Int J Theor Phys,1998,37:1213-1216.
[6]FLERACHERS E L M,JANSSEN H J,BEERDEN L.Piecewise linear anharmonic LRC circuit for demonstrating soft and hardspring nonlinear resonant behavior[J].Am J Phys,1985,53(6):574-577.
[7]ZHANG S,UM C I,YEON K H.Zero-point energy in a mesoscopic nonlinear inductance-capacitance circuit[J].Chin Phys Lett,2002,19(7):985-987.
[8]侯伯元,云国宏,杨战营.路径积分与量子物理导引[M].北京:科学出版社,2008:61-69.