Controllable quantum scars in semiconductor quantum dots

Keski-Rahkonen, Joonas; Luukko, Perttu; Kaplan, L.; Heller, E. J.; Räsänen, E.

doi:10.1103/physrevb.96.094204

Cited by 22 publications

(26 citation statements)

References 17 publications

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“…Later, similar scars were observed in a perturbed 2D harmonic oscillator exposed to an external magnetic field. 9 Some of the high-energy eigenstates are scarred exceptionally strongly by short POs of the corresponding unperturbed system. These scars have a similar appearance to the conventional scars, but a fundamentally different origin: they stem from the classical resonances in the unperturbed system resulting in semiclassical near-degeneracies (resonant sets) in the unperturbed quantum system.…”

Section: Introductionmentioning

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: Introductionmentioning

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.…”

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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.…”

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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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“…Over the years, the investigation of scars has further developed into experimental observations for example at microwave frequencies [2], as well as generalizations to pseudointegrable systems [20][21][22], and effects on trace formulae [23][24][25]. More recently, 'strong' quantum scars have been detected and described in integrable systems with impurities [26,27]. Open systems generate a wide class of problems that has greatly concerned the quantum chaos community in the last two decades [28][29][30].…”

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confidence: 99%

Scarring in open chaotic systems: The local density of states

Lippolis¹

2019

EPL

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Chaotic Hamiltonians are known to follow Random Matrix Theory (RMT) ensembles in the apparent randomness of their spectra and wavefunction statistics. Deviations from RMT also do occur, however, due to system-specific properties, or as quantum signatures of classical chaos. Scarring, for instance, is the enhancement of wavefunction intensity near classical periodic orbits, and it can be characterized by a local density of states (or local spectrum) that clearly deviates from RMT expectations, by exhibiting a peaked envelope, which has been described semiclassically. Here, the system is connected to an opening, the local density of states is introduced for the resulting non-Hermitian chaotic Hamiltonian, and estimated a priori in terms of the Green's function of the closed system and the open channels. The predictions obtained are tested on quantum maps coupled both to a single-channel opening and to a Fresnel-type continuous opening. The main outcome is that strong coupling to the opening gradually suppresses the energy dependence of the local density of states due to scarring, and restores RMT behavior.

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Controllable quantum scars in semiconductor quantum dots

Cited by 22 publications

References 17 publications

Effects of scarring on quantum chaos in disordered quantum wells

Effects of scarring on quantum chaos in disordered quantum wells

Quantum Lissajous Scars

Scarring in open chaotic systems: The local density of states

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