节点文献
介观体系中的量子效应
【作者】 张玉强；
【导师】 蔡绍洪；
【作者基本信息】 贵州大学 ， 理论物理， 2008， 硕士
【摘要】 介观物理是当今凝聚态物理发展的一个研究热点,是物理学中的一个新的分支。它主要是随着20世纪70年代和80年代人们对固体中载流子运动的深入研究特别是无序体系电子的运动规律的研究迅速发展起来的。文献上把尺度相当或小于单粒子波函数相位相干长度的微小尺度的体系称为介观体系。由于介观体系的尺度和电子波函数的相位相干长度相当,量子的波动性凸现,随着科技特别是半导体行业的发展,电路的尺寸进入介观领域已是大势所趋,此时就必须考虑电路及器件的量子效应。作为微电子技术发展的原理性基础,电路及器件中的量子效应已成为当今社会人们所研究的主要课题。本文在前人研究的几个介观电路模型在不同情况下(电路的元件、耦合的方式等)的量子效应的基础上,从介观电路中经典运动方程出发,运用量子力学理论,借助于正则变换及幺正变换的方法分析了介观领域中更具有普适性的耗散介观电容电阻电感耦合电路的量子效应问题,结果表明其哈密顿量等价于两个独立的谐振子的哈密顿量之和,耗散介观电容电阻电感耦合电路中的两个回路中的量子效应是相互关联的,电荷和电流的量子效应不仅与其组成的元件有关,还与其耦合的回路有关,还可以看出此介观电路的量子效应与回路中的电源无关。这对降低为电路中噪声对信号稳定性的影响、提高电路的集成度和降低电器元件的量子涨落提供了可行性的研究思路。本文主要有以下几个创新之处:(1)建立了耗散介观电容电阻电感耦合电路的模型,比单一元件或两元件介观耦合电路更具有普适性;(2)用量子力学理论,通过正则变换及幺正变换等方法研究了耗散介观电容电阻电感耦合电路的量子效应,结果表明该电路哈密顿量等效于两个独立的谐振子的哈密顿量之和,从而进一步探究了影响此介观电路量子效应的相关因素;(3)提出了用量子理论来探讨不同结构及不同元件的介观电路的量子效应的路径及方法,从而更进一步研究介观领域的相关特征,使理论更好的服务于实际。本文对两网孔耗散介观电容电阻电感耦合电路的量子效应的研究结果表明与人们用所研究的两网孔单元件(如只有电容耦合或只有电感耦合),以及两网孔的两元件耦合(如电阻与电感的耦合或电容与电感的耦合)得到有类似的结论,当把本文研究的三元件的耦合退化到两元件或一元件的耦合时,就会得到与他人研究的一致的结论。通过本文的研究分析,能够对介观电路模型及其研究的路径和方法有进一步的理解,对介观体系中所呈现的特有的现象有更加深刻的认识。这对人们进一步设计微电路在实际生活及生产中的应用在理论上具有重要的参考和指导意义。
【Abstract】 Mesoscopic physics is a hotspot in Condensed States Physics. It’s a rather young branch of science, which started about 25 years old ago. It developed with the being researched of the current carrier in solid and the movement law of the electrons in disordered system. The scale less than or equal to the mean free path, which is the distance that an electron travels before its initial momentum is destroyed, called it mesoscopic system. Because of the scale of the mesoscopic system is equivalent to relevant length of the electronic wave function, the fluctuations of the quantum is shown especially. With the rapid development of the semiconductor industry, the circuit components on the field size has entered into mesoscopic system, we should consider the quantum effects of circuit devices. Because of the widespread applications of mesoscopic devices in micro-electronics technology and integrate circuit and so on, more and more attention has been paid to the research of those in today’s word.In this paper, based on the studies of the several circuit models, which are in different structures (circuit components, coupled mode, and so on) on quantum effect in mesoscopic circuits. Beginning from the classic equation, we investigated the quantum fluctuations of a dissipative mesoscopic capacitance- resistance- inductance coupled circuit using canonical transformation unitary transformation. It is found that the quantum fluctuations of charge and current in each component circuit are not related to power source, but influenced by the devices and their magnitudes of the mesoscopic circuits. It’s useful to reduce noise in circuits for the stability of signal and the quantum fluctuations in order to improve the stabilization of the integrated circuits and electrical components, and it can also provide a feasibility study ideas.There are following innovations in this paper:(1) To establish the model of the dissipative mesoscopic capacitance- resistance-inductance coupled circuit model, which is more universal than a single component or two components coupling circuit;(2) Using the quantum theory. We have studied the quantization in mesoscopic capacitance-resistance-inductance coupled circuit of two meshes using canonical transformation. The results reveal that its Hamiltonian is unitary equivalent to that of two independent harmonic oscillators. So we can study the quantum effect of the circuit for more.(3) Some methods and path are put forward to solve the quantum effect of different components and structures of the mesoscopic circuits, so we can investigate the characters of the mesoscopic circuit for the practicalities.There are analogous conclusions between the dissipative mesoscopic capacitance-resistance- inductance coupled circuit of two meshes and the coupled circuit with single component(capacitance or inductance) or two components (resistance-inductance or capacitance -inductance)on quantum effects when we reduce the numbers of the components from three to two or one, the conclusion is accordant. We can have more cognition to the path and methods of studying the mesoscopic circuits. All above is useful for people to design the microcircuit in people’s living and production.