Observation of 'scarred' wavefunctions in a quantum well with chaotic electron dynamics

Wilkinson, Paul; Fromhold, T. M.; Eaves, L.; Sheard, F. W.; Miura, Noriko N.; Takamasu, T.

doi:10.1038/380608a0

Cited by 167 publications

(136 citation statements)

References 17 publications

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“…In the seemingly random density distribution, some clear density maxima emerge, both in momentum as well as in real space. These density accumulations derive from periodic orbitals of the underlying classical model and are termed quantum scars [42,57,58]. The appearance of scars is an example of the classically chaotic model leaving a trace in its quantum counterpart.…”

Section: B Long Time Dynamics; Thermalizationmentioning

confidence: 99%

Chaos-driven dynamics in spin-orbit-coupled atomic gases

2013

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The dynamics, appearing after a quantum quench, of a trapped, spin-orbit coupled, dilute atomic gas is studied. The characteristics of the evolution is greatly influenced by the symmetries of the system, and we especially compare evolution for an isotropic Rashba coupling and for an anisotropic spin-orbit coupling. As we make the spin-orbit coupling anisotropic, we break the rotational symmetry and the underlying classical model becomes chaotic; the quantum dynamics is affected accordingly. Within experimentally relevant time-scales and parameters, the system thermalizes in a quantum sense. The corresponding equilibration time is found to agree with the Ehrenfest time, i.e. we numerically verify a ∼ log(h −1 ) scaling. Upon thermalization, we find the equilibrated distributions show examples of quantum scars distinguished by accumulation of atomic density for certain energies. At shorter time-scales we discuss non-adiabatic effects deriving from the spin-orbit coupled induced Dirac point. In the vicinity of the Dirac point, spin fluctuations are large and, even at short times, a semi-classical analysis fails.

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Section: B Long Time Dynamics; Thermalizationmentioning

confidence: 99%

Chaos-driven dynamics in spin-orbit-coupled atomic gases

2013

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“…Experimentally it has been shown in a quantum well in a high magnetic field [12] and Sinai-billiard-shaped microwave cavities [13]. So far, no experimental evidence exists for the existence of scars in optical microcavities.…”

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confidence: 99%

Observation of Scarred Modes in Asymmetrically Deformed Microcylinder Lasers

et al. 2002

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“…Similar problems of specificity and reliability (7,8) also baffle other approaches to chaos detection that rely on certain topological or information measures of attractors reconstructed from the data (9,10). The lack of a definitive test of chaos in experimental time series has thwarted the application of nonlinear dynamics theory (4,11) to a variety of physical (6,(12)(13)(14)(15), biomedical (16)(17)(18)(19)(20)(21)(22)(23)(24), and socioeconomic systems (25)(26)(27)(28)(29)(30) where chaos is thought to play a role. Overcoming these hurdles may open exciting possibilities for practical applications such as the improved forecasting of weather (31) and economic (30) patterns, novel strategies for diagnosis and control of pathological states in biomedicine (23,24,(32)(33)(34)(35) or the unmasking of chaotically encrypted electronic or optical communication signals (36)(37)(38)(39).…”

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confidence: 99%

Titration of chaos with added noise

Poon

Barahona

2001

Proc. Natl. Acad. Sci. U.S.A.

135

114

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Deterministic chaos has been implicated in numerous natural and man-made complex phenomena ranging from quantum to astronomical scales and in disciplines as diverse as meteorology, physiology, ecology, and economics. However, the lack of a definitive test of chaos vs. random noise in experimental time series has led to considerable controversy in many fields. Here we propose a numerical titration procedure as a simple ''litmus test'' for highly sensitive, specific, and robust detection of chaos in short noisy data without the need for intensive surrogate data testing. We show that the controlled addition of white or colored noise to a signal with a preexisting noise floor results in a titration index that: (i) faithfully tracks the onset of deterministic chaos in all standard bifurcation routes to chaos; and (ii) gives a relative measure of chaos intensity. Such reliable detection and quantification of chaos under severe conditions of relatively low signal-to-noise ratio is of great interest, as it may open potential practical ways of identifying, forecasting, and controlling complex behaviors in a wide variety of physical, biomedical, and socioeconomic systems.

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Observation of 'scarred' wavefunctions in a quantum well with chaotic electron dynamics

Cited by 167 publications

References 17 publications

Chaos-driven dynamics in spin-orbit-coupled atomic gases

Chaos-driven dynamics in spin-orbit-coupled atomic gases

Observation of Scarred Modes in Asymmetrically Deformed Microcylinder Lasers

Titration of chaos with added noise

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