Number-phase quantization of a mesoscopic RLC circuit

With the help of the time-dependent Lagrangian for a damped harmonic oscillator, the quantization of mesoscopic RLC circuit in the context of a number-phase quantization scheme is realized and the corresponding Hamiltonian operator is obtained. Then the evolution of the charge number and phase difference across the capacity are obtained. It is shown that the number-phase analysis is useful to tackle the quantization of some mesoscopic circuits and dynamical equations of the corresponding operators.     

介观耗散传输线的量子化

从耗散传输线的经典运动方程出发,将传输线中的单模信号进行量子化,研究了传输线在激发相干态下的量子效应.结果表明,传输线的量子涨落不仅与电路参数和电路的状态有关,还与传输线的位置有关. 关键词： 介观传输线 耗散 单模 激发相干态     

Near-perfect correlation of the resistance components of mesoscopic samples at the quantum Hall regime

We study the four-terminal resistance fluctuations of mesoscopic samples near the transition between the nu=2 and the nu=1 quantum Hall states. We observe near-perfect correlations between the fluctuations of the longitudinal and Hall components of the resistance. These correlated fluctuations appear in a magnetic-field range for which the two-terminal resistance of the samples is quantized. We discuss these findings in light of edge-state transport models of the quantum Hall effect. We also show that our results lead to an ambiguity in the determination of the width of quantum Hall transitions.     

Fractional differential kinetics of dispersive transport as the consequence of its self-similarity

Analysis of the experimental data on anomalous transport in disordered semiconductors reveals a universal behavior of the transient photocurrent, which indicates the self-similarity of the transport process. The kinetic equations of the process, which contain a time derivative of a fractional order α ∈ (0, 1), have been derived on the basis of the self-similarity principle. These equations satisfy the “correspondence principle”: in the limit α → 1, they are transformed to the normal-diffusion equations. The solutions of the equations with fractional derivatives are expressed in terms of stable densities and are in good agreement with the experimental data.     

介观耗散电容耦合电路量子化中的正则变换

针对介观耗散电容耦合RLC电路提出一种一般的正则变换, 并证明了其正确性和合理性. 用这种正则变换研究了双回路介观耗散电容耦合电路的量子化问题, 得出的对角化哈密顿量比文献中多出一非线性项. 这种具有普遍性的一般正则变换可能对研究介观多回路耗散系统的量子涨落、量子噪声等性质具有重要的意义. 关键词： RLC电路')" href="#">RLC电路 量子化 正则变换     

Cooper-pair number-phase quantization analysis in double-Josephson-junction mesoscopic circuit coupled by a capacitor

This paper examines the quantization of mesoscopic circuit including Josephson junctions. Following Feynman＇s assumption, via the Hamilton dynamic approach and by virtue of the entangled state representation, it constructs Hamiltonian operator for the double-Josephson-junction mesoscopic circuit coupled by a capacitor. Then it uses the Heisenberg equation of motion to derive the induction voltage across each Josephson junction. The result manifestly shows how the voltage is affected by the capacitance coupling.     

Fractional quantum Hall effect at a suppressed energy gap

In the fractional quantum Hall effect regime, the diagonal (ρ_xx) and Hall (ρ_xy) magnetoresistivity tensor components of the two-dimensional electron system (2DES) in gated GaAs/Al_xGa_1−x As heterojunctions are measured together with the capacitance between 2DES and the gate. The 1/3-and 2/3-fractional quantum Hall effects are observed at rather low magnetic fields where the corresponding fractional minima in the thermodynamic density of the states have already disappeared, thus, implying the suppression of the quasiparticle energy gaps. The text was submitted by the authors in English.     

Fractional quantum Hall regime of a gas of ultracold atoms

We study the physics of a rapidly rotating gas of ultracold bosonic atoms. In the limit of very rapid rotation of the trap the system exhibits a fractional quantum Hall regime analogous to that of electrons in the fractional quantum Hall effect. We show that the ground state of the system is a 1/2-Laughlin liquid, a highly correlated atomic liquid. Exotic excitations consisting of localized quasiholes of 1/2 of an atom can be created by focusing lasers at the desired positions. We show how to manipulate these quasiholes in order to probe directly their 1/2-statistics.     

Fractional quantum Hall effect of composite fermions

In a GaAs/AlGaAs quantum well of density 1 x 10(11) cm(-2) we observed a fractional quantum Hall effect (FQHE) at nu = 4/11 and 5/13, and weaker states at nu = 6/17, 4/13, 5/17, and 7/11. These sequences of fractions do not fit into the standard series of integral quantum Hall effects of composite fermions (CF) at nu = p/(2mp +/- 1). They rather can be regarded as the FQHE of CFs attesting to residual interactions between these composite particles. In tilted magnetic fields the nu = 4/11 state remains unchanged, strongly suggesting it to be spin polarized. The weak nu = 7/11 state vanishes quickly with tilt.     

Unconventional Fractional Quantum Hall States in a Wide Quantum Well

JETP Letters - A bilayer electron system that is formed in a 60-nm-wide GaAs quantum well and has a large difference of the electron densities in the layers has been studied. It has been found...     

Topological invariant and the quantization of the Hall conductance

The topological aspects of wavefunctions for electrons in a two dimensional periodic potential with a magnetic field are discussed. Special attention is paid to the linear response formula for the Hall conductance σ_xy. It is shown that the quantized value of σ_xy is related to the number of zeros of wavefunctions in the magnetic Brillouin zone. A phase of wavefunctions cannot be determined in a unique and smooth way over the entire magnetic Brillouin zone unless the magnetic subband carries no Hall current.     

分数量子霍尔效应的新理论

在经典霍尔效应中 ,霍尔电压ＶＨ 线性正比于垂直方向的外场Ｂ⊥ ,并且沿电流方向的纵向电压Ｖ∥ 也随Ｂ⊥ 的增加而连续上升 .1980年 ,冯·克里青 (ＫｌａｕｓｖｏｎＫｌｉｔｚｉｎｇ)用半导体场效应晶体管进行霍尔测量 ,研究被限制在二维平面内的电子运动 .他发现 ,在极低温和强磁场的条件下 ,霍尔电压ＶＨ 不再随外场的增加而线性增加 ,而是 (在ＶＨ-Ｂ⊥ 图上 )表现为一连串ＶＨ =常数的阶跃平台 .与一个个平台相对应的霍尔电阻ＶＨ Ｉ(Ｉ是纵向电流 )恰好等于物理常数ｈ ｅ2 除以一个整数ｉ(ｉ=1,2 ,3,4 ,… ) .克里青的发现后来被称为…