Isolated resonances in conductance fluctuations and hierarchical states

Bäcker, Arnd; Manze, Achim; Huckestein, Bodo; Ketzmerick, Roland

doi:10.1103/physreve.66.016211

Cited by 36 publications

(48 citation statements)

References 35 publications

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“…05.45.Mt, 32.80.Rm Understanding the properties of long-lived, quasi-bound states in open mesoscopic systems is of central importance for many research subjects, e.g. semiconductor ballistic quantum dots [1,2,3,4], photoionization of Rydberg atoms [5], microwave systems [6,7], quantum chaos [8], and optical microcavities [9,10,11,12,13,14,15]. In several of these studies the long-lived states are scarred.…”

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confidence: 99%

Formation of Long-Lived, Scarlike Modes near Avoided Resonance Crossings in Optical Microcavities

2006

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We study the formation of long-lived states near avoided resonance crossings in open systems. For three different optical microcavities (rectangle, ellipse, and semi-stadium) we provide numerical evidence that these states are localized along periodic rays, resembling scarred states in closed systems. Our results shed light on the morphology of long-lived states in open mesoscopic systems. 05.45.Mt, 32.80.Rm Understanding the properties of long-lived, quasi-bound states in open mesoscopic systems is of central importance for many research subjects, e.g. semiconductor ballistic quantum dots [1,2,3,4], photoionization of Rydberg atoms [5], microwave systems [6,7], quantum chaos [8], and optical microcavities [9,10,11,12,13,14,15]. In several of these studies the long-lived states are scarred. The original scarring phenomenon has been discovered for closed systems in the field of quantum chaos [16]. It refers to the existence of a small fraction of eigenstates with strong localization along unstable periodic orbits of the underlying classical system. In open systems, however, scarred states seem to be the rule rather than the exception. The nature of the mechanism behind this scarlike phenomenon is not yet understood.Avoided level crossings in closed or conservative systems are discussed in textbooks on quantum mechanics. They occur when the curves of two energy eigenvalues, as function of a real parameter ∆, come near to crossing but then repel each other [17]. This behaviour can be understood in terms of a 2 × 2 Hamiltonian matrixFor a closed system this matrix is Hermitian, thus the energies E j are real and the complex off-diagonal elements are related by W = V * . The eigenvalues of the coupled system,differ from the energies of the uncoupled system E j only in a narrow parameter region where the detuning from resonance, |E 1 (∆) − E 2 (∆)|, is smaller or of the size of the coupling strength √ V W . The parameter dependence of V and W can often be safely ignored.The matrix (1) also captures features of avoided resonance crossings (ARCs) in open or dissipative systems if one allows for complex-valued energies E j . The imaginary part determines the lifetime τ j ∝ 1/Im(E j ) of the quasi-bound state far away from the avoided crossing |E 1 −E 2 | 2 ≫ V W , where the off-diagonal coupling can be neglected. Keeping the restriction W = V * allows for two different kinds of ARCs [18]. For 2|V | > |Im(E 1 ) − Im(E 2 )|, there is an avoided crossing in the real part of the energy and a crossing in the imaginary part. At resonance Re(E 1 ) = Re(E 2 ) the eigenvectors of the matrix (1) are symmetric and antisymmetric superpositions of the eigenvectors of the uncoupled system. If one of the latter corresponds to a localized state then such an ARC leads to delocalization and lifetime shortening [19]. For 2|V | < |Im(E 1 ) − Im(E 2 )|, there is a crossing in the real part and an avoided crossing in the imaginary part. This kind of ARC has been exploited to design optical microcavities with unidirectional light emission ...

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confidence: 99%

Formation of Long-Lived, Scarlike Modes near Avoided Resonance Crossings in Optical Microcavities

2006

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“…These isolated resonances were later shown to be associated with the eigenstates of a closed system [24].…”

Section: Introductionmentioning

confidence: 93%

Fractal dynamics in chaotic quantum transport

et al. 2013

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Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

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“…35 Since the hierarchical region couples only very weakly to the leads, quasi-bound states residing in this part of phase space give rise to sharp resonances in transmission. 5,6,7 Classically, an island of regular motion in phase space consists of a set of concentric invariant curves, each of them forming a complete barrier. Accordingly, long-lived quasi-bound states reside also in islands of regular motion and account for additional narrow resonances in transmission.…”

Section: Isolated Resonancesmentioning

confidence: 99%

“…In those hard-wall billiards with shapes that allow for a mixed phase space, it was shown that trapped trajectories lead to quasi-bound states in the corresponding quantum transport problem and appear as isolated resonances in the conductance. 5,6,7 In the chaotic-to-regular crossover regime also so-called "Andreev-billiards" 8,9 and the effect of shot noise suppression 10,11,12 have recently been discussed. Furthermore, mixed classical dynamics was proposed as a mechanism giving rise to fractal conductance fluctuations (FCF).…”

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confidence: 99%

Simulation of electron transport through a quantum dot with soft walls

2005

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We numerically investigate classical and quantum transport through a soft-wall cavity with mixed dynamics. Remarkable differences to hard-wall quantum dots are found which are, in part, related to the influence of the hierarchical structure of classical phase space on features of quantum scattering through the device. We find narrow isolated transmission resonances which display asymmetric Fano line shapes. The dependence of the resonance parameters on the lead mode numbers and on the properties of scattering eigenstates are analyzed. Their interpretation is aided by a remarkably close classical-quantum correspondence. We also searched for fractal conductance fluctuations. For the range of wave numbers kF accessible by our simulation we can rule out their existence.

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Isolated resonances in conductance fluctuations and hierarchical states

Cited by 36 publications

References 35 publications

Formation of Long-Lived, Scarlike Modes near Avoided Resonance Crossings in Optical Microcavities

Formation of Long-Lived, Scarlike Modes near Avoided Resonance Crossings in Optical Microcavities

Fractal dynamics in chaotic quantum transport

Simulation of electron transport through a quantum dot with soft walls

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