Microscopic theory for the quantum to classical crossover in chaotic transport

We present a semiclassical theory for the scattering matrix S of a chaotic ballistic cavity at finite Ehrenfest time. Using a phase-space representation coupled with a multibounce expansion, we show how the Liouville conservation of phase-space volume decomposes S as S=S(cl) plus sign in circle S(qm). The short-time, classical contribution S(cl) generates deterministic transmission eigenvalues T=0 or 1, while quantum ergodicity is recovered within the subspace corresponding to the long-time, stochastic contribution S(qm). This provides a microscopic foundation for the two-phase fluid model, in which the cavity acts like a classical and a quantum cavity in parallel, and explains recent numerical data showing the breakdown of universality in quantum chaotic transport in the deep semiclassical limit. We show that the Fano factor of the shot-noise power vanishes in this limit, while weak localization remains universal.     

Role of orbital dynamics in spin relaxation and weak antilocalization in quantum dots

We develop a semiclassical theory for spin-dependent quantum transport to describe weak (anti)localization in quantum dots with spin-orbit coupling. This allows us to distinguish different types of spin relaxation in systems with chaotic, regular, and diffusive orbital classical dynamics. We find, in particular, that for typical Rashba spin-orbit coupling strengths, integrable ballistic systems can exhibit weak localization, while corresponding chaotic systems show weak antilocalization. We further calculate the magnetoconductance and analyze how the weak antilocalization is suppressed with decreasing quantum dot size and increasing additional in-plane magnetic field.     

Ehrenfest time and the coherent backscattering off ballistic cavities

If the Ehrenfest time tau(E) of a ballistic cavity is not negligible in comparison to its dwell time tau(D), the weak localization correction to the cavity's transmission is suppressed proportional to exp(-tau(E/tau(D). At the same time, quantum interference enhances the probability of reflection into the mode of incidence by a factor two. This "enhanced backscattering" does not depend on the Ehrenfest time. We show that, in addition to the diagonal enhanced backscattering, there are off-diagonal contributions to coherent backscattering that become relevant if tau(E) > or = tau(D).     

Geometric correlations and breakdown of mesoscopic universality in spin transport

We construct a unified semiclassical theory of charge and spin transport in chaotic ballistic and disordered diffusive mesoscopic systems with spin-orbit interaction. Neglecting dynamic effects of spin-orbit interaction, we reproduce the random matrix theory results that the spin conductance fluctuates universally around zero average. Incorporating these effects into the theory, we show that geometric correlations generate finite average spin conductances, but that they do not affect the charge conductance to leading order. The theory, which is confirmed by numerical transport calculations, allows us to investigate the entire range from the weak to the previously unexplored strong spin-orbit regime, where the spin rotation time is shorter than the momentum relaxation time.     

Anomalous magnetoresistance of two-dimensional systems in the presence of spin-orbit scattering

A theory of weak localization in two-dimensional semiconductor structures and metal films is developed for spin relaxation by the Elliott-Yafet mechanism. The theory is valid in the entire range of classically weak magnetic fields. It is shown that effects due to spin-orbit interaction substantially modify magnetoresistance in both diffusive and ballistic regimes.     

Ehrenfest-time-dependent excitation gap in a chaotic Andreev billiard

A semiclassical theory is developed for the appearance of an excitation gap in a ballistic chaotic cavity connected by a point contact to a superconductor. Diffraction at the point contact is a singular perturbation in the limit variant Planck's over 2pi -->0, which opens up a gap E(gap) in the excitation spectrum. The time scale variant Planck's over 2pi /E(gap) proportional, variant alpha(-1)ln( variant Planck's over 2pi (with alpha the Lyapunov exponent) is the Ehrenfest time, the characteristic time scale of quantum chaos.     

Experimental verification of fidelity decay: from perturbative to fermi golden rule regime

The scattering matrix was measured for a flat microwave cavity with classically chaotic dynamics. The system can be perturbed by small changes of the geometry. We define the "scattering fidelity" in terms of parametric correlation functions of scattering matrix elements. In chaotic systems and for weak coupling, the scattering fidelity approaches the fidelity of the closed system. Without free parameters, the experimental results agree with random matrix theory in a wide range of perturbation strengths, reaching from the perturbative to the Fermi golden rule regime.     

外腔半导体激光器随机数熵源的腔长分析

利用光反馈半导体激光器产生的混沌激光作为随机数熵源,详细研究了混沌源外腔长度对500Mbit/s随机数特性的影响.研究表明:在单路混沌源情况下,外腔反馈引起的谐振会使产生的随机序列具有弱周期性,且当外腔反馈时间与采样时间的比值为整数时,产生序列的随机性最差,仅能通过NIST统计测试2,3项;在两路混沌源情况下,当混沌源的外腔长不相等且不成比例时,通过两路异或处理可消除由外腔反馈引起的弱周期性,产生的随机序列能够通过NIST的全部统计测试项.     

Frequency-modulated ratchet with autoresonance

Motion of an ensemble of non-interacting classical particles in a space-periodic potential subjected to a weak external wave-like perturbation is considered. With large values of the wavenumber, the perturbation causes a resonance-induced chaotic layer in a certain area of phase space. Different scenarios of the emergence of chaos are considered. Adiabatic space or time modulation of the phase of the perturbation changes the location of the chaotic layer. A significant number of particles trapped within the chaotic layer is retained inside in course of the adiabatic modulation, revealing autoresonant behavior. We show that this phenomenon can be used to generate a directed ballistic current using a weak perturbation, even if particle’s energies are initially close to the minimal value.     

From chaos to disorder: Statistics of the eigenfunctions of microwave cavities

We study the statistics of the experimental eigenfunctions of chaotic and disordered microwave billiards in terms of the moments of their spatial distributions, such as the inverse participation ratio (IPR) and density-density auto-correlation. A path from chaos to disorder is described in terms of increasing IPR. In the chaotic, ballistic limit, the data correspond well with universal results from random matrix theory. Deviations from universal distributions are observed due to disorder induced localization, and for the weakly disordered case the data are well-described by including finite conductance and mean free path contributions in the framework of nonlinear sigma models of supersymmetry.     

Quantum transport in lattices of coupled electronic billiards

A new system with dynamic chaos—2D lattice of single Sinai billiards coupled through quantum dots—is studied experimentally. Localization in such a system was found to be substantially suppressed, because the characteristic size of the billiard for g≤1 (g is conductance measured in e ₂/h units) is the localization length rather than the de Broglie wavelength of an electron, as in the usual 2D electron system. Lattice ballistic effects (commensurate peaks in the magnetoresistance) for g?1, as well as extremely large magnetoresistance caused by the interference in chaotic electron trajectories, were found. Thus, this system is shown to be characterized by simultaneous existence of effects that are inherent in order (commensurate peaks of magnetoresistance), disorder (percolation charge transport), and chaos (weak localization in chaotic electron trajectories).     

Electron-electron interaction in the magnetoresistance of graphene

We investigate the magnetotransport in large area graphene Hall bars epitaxially grown on silicon carbide. In the intermediate field regime between weak localization and Landau quantization, the observed temperature-dependent parabolic magnetoresistivity is a manifestation of the electron-electron interaction. We can consistently describe the data with a model for diffusive (magneto)transport that also includes magnetic-field-dependent effects originating from ballistic time scales. We find an excellent agreement between the experimentally observed temperature dependence of magnetoresistivity and the theory of electron-electron interaction in the diffusive regime. We can further assign a temperature-driven crossover to the reduction of the multiplet modes contributing to electron-electron interaction from 7 to 3 due to intervalley scattering. In addition, we find a temperature-independent ballistic contribution to the magnetoresistivity in classically strong magnetic fields.     

Spin-orbit coupling,antilocalization, and parallel magnetic fields in quantum dots

We investigate antilocalization due to spin-orbit coupling in ballistic GaAs quantum dots. Antilocalization that is prominent in large dots is suppressed in small dots, as anticipated theoretically. Parallel magnetic fields suppress both antilocalization and also, at larger fields, weak localization, consistent with random matrix theory results once orbital coupling of the parallel field is included. In situ control of spin-orbit coupling in dots is demonstrated as a gate-controlled crossover from weak localization to antilocalization.     

Semiclassical theory of chaotic conductors

We calculate the Landauer conductance through chaotic ballistic devices in the semiclassical limit, to all orders in the inverse number of scattering channels without and with a magnetic field. Families of pairs of entrance-to-exit trajectories contribute, similarly to the pairs of periodic orbits making up the small-time expansion of the spectral form factor of chaotic dynamics. As a clue to the exact result we find that close self-encounters slightly hinder the escape of trajectories into leads. Our result explains why the energy-averaged conductance of individual chaotic cavities, with disorder or "clean," agrees with predictions of random-matrix theory.     

Monte Carlo simulation of the coherent backscattering of electrons in a ballistic system

We study weak localization effects in the ballistic regime as induced by man-made scatterers. Specular reflection of the electrons off these scatterers causes backscattered trajectories to occur, which interfere with their time-reversed path resulting in weak localization corrections to the resistance. Using a semi-classical theory, we calculate the change in resistance due to these backscattered trajectories. We found that the inclusion of the exact shape of the scatterers is very important in order to explain the experimental results of Katine et al.[Superlattices and Microstructures 20 , 337 (1996)].     

Interaction correction to the conductance of a ballistic conductor

In disordered metals, electron-electron interactions are the origin of a small correction to the conductivity, the "Altshuler-Aronov correction." Here we investigate the Altshuler-Aronov correction deltaG{AA} of a conductor in which the electron motion is ballistic and chaotic. We consider the case of a double quantum dot, which is the simplest example of a ballistic conductor in which deltaG{AA} is nonzero. The fact that the electron motion is ballistic leads to an exponential suppression of deltaG{AA} if the Ehrenfest time is larger than the mean dwell time tau{D} or the inverse temperature h/T.     

金属互连电迁移噪声的相关维数研究

针对金属铝互连中噪声信号随电迁移过程变化规律及其所反映的内部失效机理问题，提出将相关维数用于对电迁移噪声时间序列的分析.通过对互连电迁移噪声实验数据的相关维数计算，发现随着电迁移的进行，金属铝互连噪声由随机性成分占主导变为确定性成分占主导，反映出噪声由随机信号转变为混沌动力学信号.应用散射理论解释上述现象，在金属互连电迁移中，空位扩散阶段噪声主要产生机制是空位随机散射；在空位聚集到空洞成核这一过程中，噪声产生机制逐渐从随机散射转变到弹道混沌腔输运机制为主.通过与传统表征参量的对比，证明相关维数可用于预测金 关键词： 电迁移 噪声 相关维数 混沌     

Adiabatic quantization of Andreev quantum billiard levels

We identify the time T between Andreev reflections as a classical adiabatic invariant in a ballistic chaotic cavity (Lyapunov exponent lambda), coupled to a superconductor by an N-mode constriction. Quantization of the adiabatically invariant torus in phase space gives a discrete set of periods T(n), which in turn generate a ladder of excited states epsilon (nm)=(m+1/2)pi(h) /T(n). The largest quantized period is the Ehrenfest time T(0)=lambda(-1)ln(N). Projection of the invariant torus onto the coordinate plane shows that the wave functions inside the cavity are squeezed to a transverse dimension W/sqrt[N], much below the width W of the constriction.     

Quantum corrections to the conductance of a square quantum dot with soft confinement

We study the conductance of a square quantum dot, modeling the potential with a self-consistent Thomas-Fermi approximation. The resulting potential is characterized by level statistics indicative of mixed chaotic and regular electron dynamics within the dot in spite of the regular geometry of the gates defining the dot. We calculate numerically, for the case of a quantum dot with soft confinement, the weak localization (WL) correction. We demonstrate that this confining potential may generate either Lorentzian or linear lineshapes depending on the number of modes in the leads. Finally, we present experimental WL data for a lithographically square dot and compare the results with numerical calculations. We analyze the experimental results and numerical simulations in terms of semiclassical and random matrix theory (RMT) predictions and discuss their limitations as far as real experimental structures are concerned. Our results indicate that direct application of the above predictions to distinguish between chaotic and regular dynamics in a particular cavity can not always lead to reliable conclusions as the shape and magnitude of the WL correction can be strongly sensitive to the geometry-specific, non-universal features of the system. Received 13 May 1998     

Spatiotemporal dynamics in the coherence collapsed regime of semiconductor lasers with optical feedback

This paper presents a spatiotemporal characterization of the dynamics of a single-mode semiconductor laser with optical feedback. I use the two-dimensional representation of a time-delayed system (where the delay time plays the role of a space variable) to represent the time evolution of the output intensity and the phase delay in the external cavity. For low feedback levels the laser output is generally periodic or quasiperiodic and with the 2D representation I obtain quasiperiodic patterns. For higher feedback levels the coherence collapsed regime arises, and in the 2D patterns the quasiperiodic structures break and "defects" appear. In this regime the patterns present features that resemble those of an extended spatiotemporally chaotic system. The 2D representation allows the recognition of two distinct types of transition to coherence collapse. As the feedback intensity grows the number of defects increases and the patterns become increasingly chaotic. As the delay time increases the number of defects in the patterns do not increase and there is a signature of the previous quasiperiodic structure that remains. The nature of the two transitions is understood by examining the behavior of various chaotic indicators (the field autocorrelation function, the Lyapunov spectrum, the fractal dimension, and the metric entropy) when the feedback intensity and the delay time vary. (c) 1997 American Institute of Physics.