Strong quantum scarring by local impurities

Luukko, Perttu; Drury, Byron; Klales, Anna; Kaplan, L.; Heller, Eric J.; Räsänen, E.

doi:10.1038/srep37656

Cited by 30 publications

(47 citation statements)

References 32 publications

(43 reference statements)

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“…9, and -in general -PI scars are relatively common. 8 Here we do not quantitatively assess the dependence of the PI scars on the bump locations, i.e., we only consider one realization of random potential showing strong PI scarring. We focus on the general properties of the system, particularly the eigenspectrum and its subsets, as a function of M and σ.…”

Section: Systemmentioning

confidence: 99%

Effects of scarring on quantum chaos in disordered quantum wells

Keski-Rahkonen

Luukko

Åberg

et al. 2019

J. Phys.: Condens. Matter

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The suppression of chaos in quantum reality is evident in quantum scars, i.e., in enhanced probability densities along classical periodic orbits. They provide opportunities in controlling quantum transport in nanoscale quantum systems. Here, we study energy level statistics of perturbed twodimensional quantum systems exhibiting recently discovered, strong perturbation-induced quantum scarring. In particular, we focus on the effect of local perturbations and an external magnetic field on both the eigenvalue statistics and scarring. Energy spectra are analyzed to investigate the chaoticity of the quantum system in the context of the Bohigas-Giannoni-Schmidt conjecture. We find that in systems where strong perturbation-induced scars are present, the eigenvalue statistics are mostly mixed, i.e., between Wigner-Dyson and Poisson pictures in random matrix theory. However, we report interesting sensitivity of both the eigenvalue statistics to the perturbation strength, and analyze the physical mechanisms behind this effect.

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Section: Systemmentioning

confidence: 99%

Effects of scarring on quantum chaos in disordered quantum wells

Keski-Rahkonen

Luukko

Åberg

et al. 2019

J. Phys.: Condens. Matter

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“…In addition, dynamical localization is not able to explain that scars generally orient to coincide with as many bumps as possible (see also Refs. [30,32]). Furthermore, even though similar in appearance, the conventional scar theory [18,19,44,45] cannot describe the Lissajous scarring, as it would require the existence of short, moderately unstable POs in the perturbed system.…”

mentioning

confidence: 99%

“…To explain the Lissajous scarring, we generalize the PI scar theory beyond circularly symmetric potentials [30][31][32]. Recently, PI scars have drawn attention since they have been demonstrated to be highly controllable [32], and can be utilized to propagate quantum wave packets in the system with high fidelity [30]. Combined, this may open a door to coherently modulate quantum transport in nanoscale devices by exploiting the scarring.…”

mentioning

confidence: 99%

“…Note that the scars exist, although the corresponding unperturbed classical PO does not. metry [30][31][32]46], such as an anisotropic oscillator.…”

mentioning

confidence: 99%

“…An important avenue of future research is to analyze the effect of PI scarring on the conductance of the QD in more detail (see Refs. [30,32]) by employing realistic quantum transport calculations. Previous studies (see, e.g., Refs.…”

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confidence: 99%

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Quantum Lissajous Scars

et al. 2019

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A quantum scar -an enhancement of a quantum probability density in the vicinity of a classical periodic orbit -is a fundamental phenomenon connecting quantum and classical mechanics. Here we demonstrate that some of the eigenstates of the perturbed two-dimensional anisotropic (elliptic) harmonic oscillator are strongly scarred by the Lissajous orbits of the unperturbed classical counterpart. In particular, we show that the occurrence and geometry of these quantum Lissajous scars are connected to the anisotropy of the harmonic confinement, but unlike the classical Lissajous orbits the scars survive under a small perturbation of the potential. This Lissajous scarring is caused by the combined effect of the quantum (near) degeneracies in the unperturbed system and the localized character of the perturbation. Furthermore, we discuss experimental schemes to observe this perturbation-induced scarring.

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Controllable Spin‐Split Phantom Scars in Quantum Dots

Berger

Berakdar

2023

Adv Quantum Tech

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Quantum states of systems with an underlying classical chaotic dynamics can be "scarred," meaning that the associated probability density is localized around the short, unstable periodic orbits. Here, it is shown that, via tunneling, the scarred state can be imaged to a region that does not support scarring. This "phantom scar" is also present in the spin channel and has marked influence on the spin-dependent system dynamics, as illustrated by explicit calculations for the fidelity and correlation functions. Numerical simulations and analysis are performed for the spin-dependent electron dynamics in semiconductor-based double quantum dots, including disorder, Rashba-type spin-orbital coupling, exchange fields, and external magnetic fields. The results elucidate the unique feature of scarring as a coherent phenomenon spanning the whole system and affecting its localization properties in a narrow spectral window.

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Strong quantum scarring by local impurities

Cited by 30 publications

References 32 publications

Effects of scarring on quantum chaos in disordered quantum wells

Effects of scarring on quantum chaos in disordered quantum wells

Quantum Lissajous Scars

Controllable Spin‐Split Phantom Scars in Quantum Dots

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