介观电路量子力学性质的研究
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摘要
本文是在电荷离散化的基础上，运用已有的量子化理论，对不同介观电路模型的量子力学效应进行了相应的理论推导和数值分析，并做出进一步的研究。
全文的主要内容共分为三章：
第一章是引言部分，介绍了介观系统的相关知识和介观电路的研究进展。
在第二章，首先，简述了非耗散介观电路的量子化方法，为本文后面的工作提供了所需的计算方法。然后，考虑到实际工作中总是存在着耗散，计算了相应的Fock态下、(?)的本征态下耗散介观电路的量子涨落，研究了影响量子涨落的因素。结果表明：量子涨落与介观系统固有参数、电荷量子化密切相关。
第三章研究了介观金属双环互感耦合系统的库仑阻塞效应及量子涨落问题。库仑阻塞的条件与回路电参数有关，并且两回路中磁通的时间变化率同驱动源的取值存在一定的约束关系。在Fock态下外磁场对介观金属双环系统的量子涨落并不产生影响。
我们认为，上述这些量子力学效应在其他的电路模型中也存在，值得我们深入研究。这对于设计微小电路、提高电路集成度、降低单片功耗、压低量子噪声具有一定的现实指导意义。
In this paper, the theory deductions and numerical analysis on the quantummechanics effects for different models of mesoscopic circuits are studieddeeply under some special quantum states by using quantum theory and takingaccount of the charge discreteness.
The thesis is divided into three chapters which are discribed as follows.
Chapter 1 is the introduction of mesoscopic system which illustrates thefundamental concepts and recent development.
In Chpater 2, Firstly, we summarized the method of quantization formesoscopic circuits which relevants to our later work. Secondly, cosideringthe resistance always exists in mesoscopic system actually, the quantumfluctuations in the mesoscopic circuits with dissipation are caculatedrespectively under Fock state and eigen state of ladder functor, and the effectsof the parameters on the quantum fluctuations are also investigated. Theresults show that the quantum fluctuations are related to the parameters of thecircuits and charge quantization closely.
In Chapter 3, the effects of Coulomb blockade and quantum fluctuationsare investigated for the mutual inductances coupled mesoscopic system.Further, the relationships of quantum current and the conditions of Coulombblockade in this system are given here. The outcome indicates that theconditions of the Coulomb blockade are related to electric parameters of the loops, and the time variety frequency of the magnetic flux in two loops hassome connections with the value of the drive source expressly, The externalflux didn't take any effects on quantum fluctuations in Fock state.
These quantum mechanics effects will exist in other models, and we cantake more attentions onit. These work will bring some guiding significances ondesigning micro-circuit, improving circuit integration level, reducing themonolithic power dissipation and lowering quantum noise.
全文的主要内容共分为三章：
第一章是引言部分，介绍了介观系统的相关知识和介观电路的研究进展。
在第二章，首先，简述了非耗散介观电路的量子化方法，为本文后面的工作提供了所需的计算方法。然后，考虑到实际工作中总是存在着耗散，计算了相应的Fock态下、(?)的本征态下耗散介观电路的量子涨落，研究了影响量子涨落的因素。结果表明：量子涨落与介观系统固有参数、电荷量子化密切相关。
第三章研究了介观金属双环互感耦合系统的库仑阻塞效应及量子涨落问题。库仑阻塞的条件与回路电参数有关，并且两回路中磁通的时间变化率同驱动源的取值存在一定的约束关系。在Fock态下外磁场对介观金属双环系统的量子涨落并不产生影响。
我们认为，上述这些量子力学效应在其他的电路模型中也存在，值得我们深入研究。这对于设计微小电路、提高电路集成度、降低单片功耗、压低量子噪声具有一定的现实指导意义。
In this paper, the theory deductions and numerical analysis on the quantummechanics effects for different models of mesoscopic circuits are studieddeeply under some special quantum states by using quantum theory and takingaccount of the charge discreteness.
The thesis is divided into three chapters which are discribed as follows.
Chapter 1 is the introduction of mesoscopic system which illustrates thefundamental concepts and recent development.
In Chpater 2, Firstly, we summarized the method of quantization formesoscopic circuits which relevants to our later work. Secondly, cosideringthe resistance always exists in mesoscopic system actually, the quantumfluctuations in the mesoscopic circuits with dissipation are caculatedrespectively under Fock state and eigen state of ladder functor, and the effectsof the parameters on the quantum fluctuations are also investigated. Theresults show that the quantum fluctuations are related to the parameters of thecircuits and charge quantization closely.
In Chapter 3, the effects of Coulomb blockade and quantum fluctuationsare investigated for the mutual inductances coupled mesoscopic system.Further, the relationships of quantum current and the conditions of Coulombblockade in this system are given here. The outcome indicates that theconditions of the Coulomb blockade are related to electric parameters of the loops, and the time variety frequency of the magnetic flux in two loops hassome connections with the value of the drive source expressly, The externalflux didn't take any effects on quantum fluctuations in Fock state.
These quantum mechanics effects will exist in other models, and we cantake more attentions onit. These work will bring some guiding significances ondesigning micro-circuit, improving circuit integration level, reducing themonolithic power dissipation and lowering quantum noise.
引文
[1] 冯瑞，金国钧．凝聚态物理学的新进展．物理学进展，1991，11(4)：373-386
[2] 魏环，莫文玲，张占新等．介观体系的物理特性．河北理工学院学报，2004，26(2)：108-113
[3] 阎守胜，甘子钊，介观物理．北京：北京大学出版社，1995
[4] 阎守胜．介观体系和介观物理．物理，2001，30(3)：180-181
[5] 李前树，邵彬，邹健，场与介观约瑟夫森结的相互作用．北京：科学出版社，2002
[6] 陈明玉．介观电路的压缩效应与库仑阻塞效应：[硕士学位论文]．江西：江西师范大学物理与通信电子学院，2004
[7] 王继锁．介观电路和非简谐振子势场的量子效应：[博士学位论文]．安徽：中国科学院安徽光学精密机械研究所，2001
[8] 陈斌，李有泉，沙健等．介观耦合电路的量子压缩效应．科学通报．1996，41(14)：1275-1277
[9] Chen B, Li Y Q, Fang H, et al. Quantum effects in a mesoscopic circuit. Phy. Letters. A, 1995, 205(1): 121-124
[10] 王继锁，韩宝存，孙长勇．介观电容耦合电路的量子涨落．物理学报，1998，47(7)：1187-1197
[11] 梁麦林，袁兵．分回路中有电阻时电容耦合电路的量子涨落．物理学报，2003，52(4)：978-983
[12] 崔元顺．耗散介观电路的量子波函数及零点起伏．量子电子学报，1998， 15(6)：542-548
[13] Garcia N. Self-persistent currents in coherent magnetic rings. Phys. Letters. A, 2004, 321(1): 366-368
[14] 龙超云．耗散介观电容耦合电路的量子涨落．物理学报，2002，51(1)：159-162
[15] 嵇英华，谢芳森，雷敏生．介观耗散耦合电感电路的量子涨落．量子电子学报，2000，17(4)：339-344
[16] 崔元顺，胡洁，周淮玲．压缩真空态的激发态下介观耦合电路的量子效应．光子学报，2001，30(2)：1500-1503
[17] 崔元顺．压缩真空态下介观耦合电路的量子涨落及电源对量子涨落的影响．计算物理，1999，16(3)：521-527
[18] Cheung H F, Yuval G, Eberhard K R, et al. Persistent currents in small one-dimensional metal rings. Phys. Rev. B, 1988, 37(11): 6050-6062
[19] Chandrasekhar V, Webb R A, Brady M J, et al. Magnetic response of a single, isolated gold loop. Phys. Rev. Lett., 1991, 67(25): 3578-3581
[20] Orellana P A, Pacheco M. Persistent current magnification in a double quantum ring system. Phys. Rev. B, 2005, 71: 235330
[21] Wang J S, Liu T K, Zhan M S. Quantum wavefunctions and fluctuations of mesoscopic RLC circuit. Chin. Phys. Lett., 2000, 17(7): 528-529
[22] Liang X T, Fan H Y. Quantum fluctuations in mesoscopic resistance- inductance-capacitance electric circuits at finite temperature. Chinese Physics., 2001, 10(6): 486-489
[23] 崔元顺．介观LC电路中电压、电流的量子涨落．光子学报，1998，27(6)：517-520
[24] Cedraschi P, Ponomarenko V, Buttiker M. Zero-point fluctuations and the quenching of the persistent current in normal metal rings. Phys. Rev. Lett., 2000, 84(2): 346-349
[25] Zhang S, Choi J R, Um C I, et al. Quantum uncertainties of mesoscopic inductance-resistance coupled circuit. Korean Phys. Soc., 2002, 40(2): 325
[26] Zhang S, Choi J R, Um C I, et al. Quantum uncertainties of mesoscopic capacitance coupled circuit. Phys. Lett. A, 2001, 289: 257
[27] Zhang S, Choi J R, Um C I, et al. Quantum squeezing effect of mesoscopic capacitance-inductance-resistance coupled circuit. Phys. Lett. A, 2002, 294: 319
[28] Zhang S, Zhao Y F, Jing X G, et al. Quantum fluctuations of a mesoscopic capacitance coupled circuit with power source. Chin. Phys. Lett., 2003, 20(4): 561-563
[29] Li Y Q, Chen B. Quantum theory of mesoscopic electrical circuits. Phys. Rev. B, 1996, 53(16): 4027-4032
[30] Flores J C. Mesoscopic circuits with charge discreteness: Quantum transmission lines. Phys. Rev. B, 2001, 64(23): 235309
[31] Lu T, Li Y Q. Mesoscopic circuit with linear dissipation. Modern Physics Latters B, 2002, 16(26): 1-5
[32] Flores J C, Utreras Diaz C A. Faraday' s effect for N-mesoscopic rings charge discreteness. Phys. Lett. A, 2004, 332(15): 194-196
[33] 崔元顺，周淮玲．电荷不连续时电容耦合介观电路的量子回路方程及其能谱．量子光学学报，2005，11(1)：1-5
[34] 崔元顺．无耗散耦合介观电路的能谱及量子电流．光电子·激光，2005，16(6)：678-681
[35] 崔元顺，周淮玲．电感耦合介观电路的量子回路方程及其能谱．量子电子学报，2006，23(1)：77-82
[36] 崔元顺．介观金属双环系统中的持续电流和量子能谱．原子与分子物理学报，2006，23(3)：527-531
[37] 宋同强．耗散介观电路电容耦合电路的量子化．物理学报，2004，53(5)：1352-1356
[38] 嵇英华，刘咏梅，辛建之等．磁场对介观耦合金属环中持续电流的影响．物理学报，2004，53(4)：1207-1210
[39] 陈明玉，吴云翼，雷敏生，嵇英华．介观耗散电容耦合电路的库仑阻塞效应．江西师范大学学报，2004，28(3)：252-253
[40] 李洪奇．有限温度下生物细胞中电流电压的量子涨落．光电子·激光，2005，16(6)：757-760
[41] 陈斌，李有泉，沙健等．介观电路中电荷的量子效应．物理学报，1997，46(1)：129
[42] 蔡绍洪，邱深玉．介观物质系统的统计性质及量子涨落．贵州学报，2006，24(2)：1-4
[43] 嵇英华，饶建平，雷敏生．介观LC电路中的量子隧道效应．物理学报，2002，51(2)：395-398
[44] 王继锁，冯健，詹明生．无耗散介观电感耦合电路的库仑阻塞和电荷的量子效应．物理学报，2001，50(2)：299-303
[45] Flores J C, Utreras Diaz C A. Mesoscopic circuits with charge discreteness: Quantum current magnification for mutual inductances. Phys. Rev. B, 2002, 66(15): 153410
[46] 崔元顺．介观多环耦合系统中的量子电流增强效应．物理学报，2005，54(4)：1799-1803
[47] Duncan D S, Topinka M A, Westervelt R M, et al. Aharonov-Bohm phase shift in an open electron resonator. Phys Rev., 2001, B64 (3): 033310
[48] Constantino A, Utreras Diaz C A, Flores J C, et al. Simple approach to the mesoscopic open electron resonator: Quantum current oscillations. Solid state commu., 2005(2): 93-96
[49] Spector J, Stormer H L, Baldwin K W , et al. Control of ballistic electrons in macroscopic two-dimensional electron systems. Appl Phys Lett.,1990, 56(10): 967-969
[50] Katine J A, Eriksson M A, Adourian A S, et al. Point contact conductance of an open resonator. Phys Rev Lett., 1997, 79(24): 4806-4809
[2] 魏环，莫文玲，张占新等．介观体系的物理特性．河北理工学院学报，2004，26(2)：108-113
[3] 阎守胜，甘子钊，介观物理．北京：北京大学出版社，1995
[4] 阎守胜．介观体系和介观物理．物理，2001，30(3)：180-181
[5] 李前树，邵彬，邹健，场与介观约瑟夫森结的相互作用．北京：科学出版社，2002
[6] 陈明玉．介观电路的压缩效应与库仑阻塞效应：[硕士学位论文]．江西：江西师范大学物理与通信电子学院，2004
[7] 王继锁．介观电路和非简谐振子势场的量子效应：[博士学位论文]．安徽：中国科学院安徽光学精密机械研究所，2001
[8] 陈斌，李有泉，沙健等．介观耦合电路的量子压缩效应．科学通报．1996，41(14)：1275-1277
[9] Chen B, Li Y Q, Fang H, et al. Quantum effects in a mesoscopic circuit. Phy. Letters. A, 1995, 205(1): 121-124
[10] 王继锁，韩宝存，孙长勇．介观电容耦合电路的量子涨落．物理学报，1998，47(7)：1187-1197
[11] 梁麦林，袁兵．分回路中有电阻时电容耦合电路的量子涨落．物理学报，2003，52(4)：978-983
[12] 崔元顺．耗散介观电路的量子波函数及零点起伏．量子电子学报，1998， 15(6)：542-548
[13] Garcia N. Self-persistent currents in coherent magnetic rings. Phys. Letters. A, 2004, 321(1): 366-368
[14] 龙超云．耗散介观电容耦合电路的量子涨落．物理学报，2002，51(1)：159-162
[15] 嵇英华，谢芳森，雷敏生．介观耗散耦合电感电路的量子涨落．量子电子学报，2000，17(4)：339-344
[16] 崔元顺，胡洁，周淮玲．压缩真空态的激发态下介观耦合电路的量子效应．光子学报，2001，30(2)：1500-1503
[17] 崔元顺．压缩真空态下介观耦合电路的量子涨落及电源对量子涨落的影响．计算物理，1999，16(3)：521-527
[18] Cheung H F, Yuval G, Eberhard K R, et al. Persistent currents in small one-dimensional metal rings. Phys. Rev. B, 1988, 37(11): 6050-6062
[19] Chandrasekhar V, Webb R A, Brady M J, et al. Magnetic response of a single, isolated gold loop. Phys. Rev. Lett., 1991, 67(25): 3578-3581
[20] Orellana P A, Pacheco M. Persistent current magnification in a double quantum ring system. Phys. Rev. B, 2005, 71: 235330
[21] Wang J S, Liu T K, Zhan M S. Quantum wavefunctions and fluctuations of mesoscopic RLC circuit. Chin. Phys. Lett., 2000, 17(7): 528-529
[22] Liang X T, Fan H Y. Quantum fluctuations in mesoscopic resistance- inductance-capacitance electric circuits at finite temperature. Chinese Physics., 2001, 10(6): 486-489
[23] 崔元顺．介观LC电路中电压、电流的量子涨落．光子学报，1998，27(6)：517-520
[24] Cedraschi P, Ponomarenko V, Buttiker M. Zero-point fluctuations and the quenching of the persistent current in normal metal rings. Phys. Rev. Lett., 2000, 84(2): 346-349
[25] Zhang S, Choi J R, Um C I, et al. Quantum uncertainties of mesoscopic inductance-resistance coupled circuit. Korean Phys. Soc., 2002, 40(2): 325
[26] Zhang S, Choi J R, Um C I, et al. Quantum uncertainties of mesoscopic capacitance coupled circuit. Phys. Lett. A, 2001, 289: 257
[27] Zhang S, Choi J R, Um C I, et al. Quantum squeezing effect of mesoscopic capacitance-inductance-resistance coupled circuit. Phys. Lett. A, 2002, 294: 319
[28] Zhang S, Zhao Y F, Jing X G, et al. Quantum fluctuations of a mesoscopic capacitance coupled circuit with power source. Chin. Phys. Lett., 2003, 20(4): 561-563
[29] Li Y Q, Chen B. Quantum theory of mesoscopic electrical circuits. Phys. Rev. B, 1996, 53(16): 4027-4032
[30] Flores J C. Mesoscopic circuits with charge discreteness: Quantum transmission lines. Phys. Rev. B, 2001, 64(23): 235309
[31] Lu T, Li Y Q. Mesoscopic circuit with linear dissipation. Modern Physics Latters B, 2002, 16(26): 1-5
[32] Flores J C, Utreras Diaz C A. Faraday' s effect for N-mesoscopic rings charge discreteness. Phys. Lett. A, 2004, 332(15): 194-196
[33] 崔元顺，周淮玲．电荷不连续时电容耦合介观电路的量子回路方程及其能谱．量子光学学报，2005，11(1)：1-5
[34] 崔元顺．无耗散耦合介观电路的能谱及量子电流．光电子·激光，2005，16(6)：678-681
[35] 崔元顺，周淮玲．电感耦合介观电路的量子回路方程及其能谱．量子电子学报，2006，23(1)：77-82
[36] 崔元顺．介观金属双环系统中的持续电流和量子能谱．原子与分子物理学报，2006，23(3)：527-531
[37] 宋同强．耗散介观电路电容耦合电路的量子化．物理学报，2004，53(5)：1352-1356
[38] 嵇英华，刘咏梅，辛建之等．磁场对介观耦合金属环中持续电流的影响．物理学报，2004，53(4)：1207-1210
[39] 陈明玉，吴云翼，雷敏生，嵇英华．介观耗散电容耦合电路的库仑阻塞效应．江西师范大学学报，2004，28(3)：252-253
[40] 李洪奇．有限温度下生物细胞中电流电压的量子涨落．光电子·激光，2005，16(6)：757-760
[41] 陈斌，李有泉，沙健等．介观电路中电荷的量子效应．物理学报，1997，46(1)：129
[42] 蔡绍洪，邱深玉．介观物质系统的统计性质及量子涨落．贵州学报，2006，24(2)：1-4
[43] 嵇英华，饶建平，雷敏生．介观LC电路中的量子隧道效应．物理学报，2002，51(2)：395-398
[44] 王继锁，冯健，詹明生．无耗散介观电感耦合电路的库仑阻塞和电荷的量子效应．物理学报，2001，50(2)：299-303
[45] Flores J C, Utreras Diaz C A. Mesoscopic circuits with charge discreteness: Quantum current magnification for mutual inductances. Phys. Rev. B, 2002, 66(15): 153410
[46] 崔元顺．介观多环耦合系统中的量子电流增强效应．物理学报，2005，54(4)：1799-1803
[47] Duncan D S, Topinka M A, Westervelt R M, et al. Aharonov-Bohm phase shift in an open electron resonator. Phys Rev., 2001, B64 (3): 033310
[48] Constantino A, Utreras Diaz C A, Flores J C, et al. Simple approach to the mesoscopic open electron resonator: Quantum current oscillations. Solid state commu., 2005(2): 93-96
[49] Spector J, Stormer H L, Baldwin K W , et al. Control of ballistic electrons in macroscopic two-dimensional electron systems. Appl Phys Lett.,1990, 56(10): 967-969
[50] Katine J A, Eriksson M A, Adourian A S, et al. Point contact conductance of an open resonator. Phys Rev Lett., 1997, 79(24): 4806-4809