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Ge Z, Wong D, Lee J, Joucken F, Quezada-Lopez EA, Kahn S, Tsai HZ, Taniguchi T, Watanabe K, Wang F, Zettl A, Crommie MF, Velasco J. Imaging Quantum Interference in Stadium-Shaped Monolayer and Bilayer Graphene Quantum Dots. NANO LETTERS 2021; 21:8993-8998. [PMID: 34699239 DOI: 10.1021/acs.nanolett.1c02271] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Experimental realizations of graphene-based stadium-shaped quantum dots (QDs) have been few and have been incompatible with scanned probe microscopy. Yet, the direct visualization of electronic states within these QDs is crucial for determining the existence of quantum chaos in these systems. We report the fabrication and characterization of electrostatically defined stadium-shaped QDs in heterostructure devices composed of monolayer graphene (MLG) and bilayer graphene (BLG). To realize a stadium-shaped QD, we utilized the tip of a scanning tunneling microscope to charge defects in a supporting hexagonal boron nitride flake. The stadium states visualized are consistent with tight-binding-based simulations but lack clear quantum chaos signatures. The absence of quantum chaos features in MLG-based stadium QDs is attributed to the leaky nature of the confinement potential due to Klein tunneling. In contrast, for BLG-based stadium QDs (which have stronger confinement) quantum chaos is precluded by the smooth confinement potential which reduces interference and mixing between states.
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Affiliation(s)
- Zhehao Ge
- Department of Physics, University of California, Santa Cruz, California 95064, United States
| | - Dillon Wong
- Department of Physics, University of California, Berkeley, California 94720, United States
| | - Juwon Lee
- Department of Physics, University of California, Berkeley, California 94720, United States
| | - Frederic Joucken
- Department of Physics, University of California, Santa Cruz, California 95064, United States
| | - Eberth A Quezada-Lopez
- Department of Physics, University of California, Santa Cruz, California 95064, United States
| | - Salman Kahn
- Department of Physics, University of California, Berkeley, California 94720, United States
| | - Hsin-Zon Tsai
- Department of Physics, University of California, Berkeley, California 94720, United States
| | - Takashi Taniguchi
- International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Kenji Watanabe
- Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
| | - Feng Wang
- Department of Physics, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Kavli Energy NanoSciences Institute at the University of California, Berkeley, and the Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Alex Zettl
- Department of Physics, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Kavli Energy NanoSciences Institute at the University of California, Berkeley, and the Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Michael F Crommie
- Department of Physics, University of California, Berkeley, California 94720, United States
- Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Kavli Energy NanoSciences Institute at the University of California, Berkeley, and the Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Jairo Velasco
- Department of Physics, University of California, Santa Cruz, California 95064, United States
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Seim E, Kohler A, Lukacs R, Brandsrud MA, Marstein ES, Olsen E, Blümel R. Wave chaos enhanced light trapping in optically thin solar cells. CHAOS (WOODBURY, N.Y.) 2021; 31:063136. [PMID: 34241303 DOI: 10.1063/5.0049330] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/03/2021] [Accepted: 06/02/2021] [Indexed: 06/13/2023]
Abstract
Enhancing the energy output of solar cells increases their competitiveness as a source of energy. Producing thinner solar cells is attractive, but a thin absorbing layer demands excellent light management in order to keep transmission- and reflection-related losses of incident photons at a minimum. We maximize absorption by trapping light rays to make the mean average path length in the absorber as long as possible. In chaotic scattering systems, there are ray trajectories with very long lifetimes. In this paper, we investigate the scattering dynamics of waves in a model system using principles from the field of quantum chaotic scattering. We quantitatively find that the transition from regular to chaotic scattering dynamics correlates with the enhancement of the absorption cross section and propose the use of an autocorrelation function to assess the average path length of rays as a possible way to verify the light-trapping efficiency experimentally.
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Affiliation(s)
- E Seim
- RealTek, Norwegian University of Life Sciences, Ås 1430, Norway
| | - A Kohler
- RealTek, Norwegian University of Life Sciences, Ås 1430, Norway
| | - R Lukacs
- The Norwegian Public Service Pension Fund, Oslo 0212, Norway
| | - M A Brandsrud
- RealTek, Norwegian University of Life Sciences, Ås 1430, Norway
| | - E S Marstein
- Department of Solar Energy, Institute of Energy Technology, Kjeller 2007, Norway
| | - E Olsen
- RealTek, Norwegian University of Life Sciences, Ås 1430, Norway
| | - R Blümel
- Department of Physics, Wesleyan University, Middletown, Connecticut 06459-0155, USA
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The effect of deformation of absorbing scatterers on Mie-type signatures in infrared microspectroscopy. Sci Rep 2021; 11:4675. [PMID: 33633244 PMCID: PMC7907113 DOI: 10.1038/s41598-021-84064-5] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2020] [Accepted: 01/18/2021] [Indexed: 11/28/2022] Open
Abstract
Mie-type scattering features such as ripples (i.e., sharp shape-resonance peaks) and wiggles (i.e., broad oscillations), are frequently-observed scattering phenomena in infrared microspectroscopy of cells and tissues. They appear in general when the wavelength of electromagnetic radiation is of the same order as the size of the scatterer. By use of approximations to the Mie solutions for spheres, iterative algorithms have been developed to retrieve pure absorbance spectra. However, the question remains to what extent the Mie solutions, and approximations thereof, describe the extinction efficiency in practical situations where the shapes of scatterers deviate considerably from spheres. The aim of the current study is to investigate how deviations from a spherical scatterer can change the extinction properties of the scatterer in the context of chaos in wave systems. For this purpose, we investigate a chaotic scatterer and compare it with an elliptically shaped scatterer, which exhibits only regular scattering. We find that chaotic scattering has an accelerating effect on the disappearance of Mie ripples. We further show that the presence of absorption and the high numerical aperture of infrared microscopes does not explain the absence of ripples in most measurements of biological samples.
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Bush JWM, Oza AU. Hydrodynamic quantum analogs. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2020; 84:017001. [PMID: 33065567 DOI: 10.1088/1361-6633/abc22c] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Accepted: 10/16/2020] [Indexed: 06/11/2023]
Abstract
The walking droplet system discovered by Yves Couder and Emmanuel Fort presents an example of a vibrating particle self-propelling through a resonant interaction with its own wave field. It provides a means of visualizing a particle as an excitation of a field, a common notion in quantum field theory. Moreover, it represents the first macroscopic realization of a form of dynamics proposed for quantum particles by Louis de Broglie in the 1920s. The fact that this hydrodynamic pilot-wave system exhibits many features typically associated with the microscopic, quantum realm raises a number of intriguing questions. At a minimum, it extends the range of classical systems to include quantum-like statistics in a number of settings. A more optimistic stance is that it suggests the manner in which quantum mechanics might be completed through a theoretical description of particle trajectories. We here review the experimental studies of the walker system, and the hierarchy of theoretical models developed to rationalize its behavior. Particular attention is given to enumerating the dynamical mechanisms responsible for the emergence of robust, structured statistical behavior. Another focus is demonstrating how the temporal nonlocality of the droplet dynamics, as results from the persistence of its pilot wave field, may give rise to behavior that appears to be spatially nonlocal. Finally, we describe recent explorations of a generalized theoretical framework that provides a mathematical bridge between the hydrodynamic pilot-wave system and various realist models of quantum dynamics.
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Affiliation(s)
- John W M Bush
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States of America
| | - Anand U Oza
- Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ, United States of America
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Lai YC, Xu HY, Huang L, Grebogi C. Relativistic quantum chaos-An emergent interdisciplinary field. CHAOS (WOODBURY, N.Y.) 2018; 28:052101. [PMID: 29857689 DOI: 10.1063/1.5026904] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.
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Affiliation(s)
- Ying-Cheng Lai
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Hong-Ya Xu
- School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA
| | - Liang Huang
- School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
| | - Celso Grebogi
- Institute for Complex Systems and Mathematical Biology, King's College, University of Aberdeen, Aberdeen AB24 3UE, United Kingdom
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Xu H, Huang L, Lai YC, Grebogi C. Chiral scars in chaotic Dirac fermion systems. PHYSICAL REVIEW LETTERS 2013; 110:064102. [PMID: 23432246 DOI: 10.1103/physrevlett.110.064102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/28/2012] [Indexed: 06/01/2023]
Abstract
Do relativistic quantum scars in classically chaotic systems possess unique features that are not shared by nonrelativistic quantum scars? We report a class of relativistic quantum scars in massless Dirac fermion systems whose phases return to the original values or acquire a 2π change only after circulating twice about some classical unstable periodic orbits. We name such scars chiral scars, the successful identification of which has been facilitated tremendously by our development of an analytic, conformal-mapping-based method to calculate an unprecedentedly large number of eigenstates with high accuracy. Our semiclassical theory indicates that the physical origin of chiral scars can be attributed to a combined effect of chirality intrinsic to massless Dirac fermions and the geometry of the underlying classical orbit.
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Affiliation(s)
- Hongya Xu
- Institute of Computational Physics and Complex Systems and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
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Hart JA, Antonsen TM, Ott E. Scattering a pulse from a chaotic cavity: transitioning from algebraic to exponential decay. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2009; 79:016208. [PMID: 19257123 DOI: 10.1103/physreve.79.016208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/16/2008] [Indexed: 05/27/2023]
Abstract
The ensemble averaged power scattered in and out of lossless chaotic cavities decays as a power law in time for large times. In the case of a pulse with a finite duration, the power scattered from a single realization of a cavity closely tracks the power-law ensemble decay initially, but eventually transitions to an exponential decay. In this paper, we explore the nature of this transition in the case of coupling to a single port. We find that for a given pulse shape, the properties of the transition are universal if time is properly normalized. We define the crossover time to be the time at which the deviations from the mean of the reflected power in individual realizations become comparable to the mean reflected power. We demonstrate numerically that, for randomly chosen cavity realizations and given pulse shapes, the probability distribution function of reflected power depends only on time, normalized to this crossover time.
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Affiliation(s)
- James A Hart
- Institute for Research in Electronics and Applied Physics, University of Maryland, College Park, Maryland 20740, USA
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8
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Tang Y, Shen Y, Yang J, Liu X, Zi J, Li B. Experimental evidence of wave chaos from a double slit experiment with water surface waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:047201. [PMID: 18999571 DOI: 10.1103/physreve.78.047201] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2008] [Revised: 07/29/2008] [Indexed: 05/27/2023]
Abstract
In this paper, we report experimental evidence of wave chaos using the double slit water surface wave experiment. We demonstrate that classical dynamics of a domain manifests itself in the interference patterns after the diffraction behind the double slit. For a domain whose classical dynamics is integrable clear interference fringes can be observed behind the double slits; for a domain whose classical dynamics is chaotic, however, interference fringes can totally disappear. Our experimental results clearly demonstrate that the centuries-old double slit experiment can render an excellent tool to observe the manifestations of wave chaos.
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Affiliation(s)
- Yunfei Tang
- Surface Physics Laboratory and Department of Physics, Fudan University, Shanghai 200433, People's Republic of China
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9
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Báez G, Martínez-Mares M, Méndez-Sánchez RA. Absorption strength in absorbing chaotic cavities. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:036208. [PMID: 18851122 DOI: 10.1103/physreve.78.036208] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/01/2007] [Revised: 03/14/2008] [Indexed: 05/26/2023]
Abstract
We derive an exact formula to calculate the absorption strength in absorbing chaotic systems such as microwave cavities or acoustic resonators. The formula allows us to estimate the absorption strength as a function of the averaged reflection coefficient and the real coupling parameter. We also define the weak and strong absorption regimes in terms of the coupling parameter and the absorption strength.
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Affiliation(s)
- G Báez
- Area de Física Teórica y Materia Condensada, Universidad Autónoma Metropolitana-Azcapotzalco, Apartado Postal 21-267, 04000 Distrito Federal, Mexico
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10
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Michel C, Doya V, Legrand O, Mortessagne F. Selective amplification of scars in a chaotic optical fiber. PHYSICAL REVIEW LETTERS 2007; 99:224101. [PMID: 18233289 DOI: 10.1103/physrevlett.99.224101] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2007] [Indexed: 05/14/2023]
Abstract
In this Letter we propose an original mechanism to select scar modes through coherent gain amplification in a multimode D-shaped fiber. More precisely, we demonstrate the selective amplification of scar modes by positioning a gain region in the vicinity of the self-focal point of the shortest periodic orbit in the transverse motion.
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Affiliation(s)
- Claire Michel
- Laboratoire de Physique de la Matière Condensée Université de Nice Sophia-Antipolis & CNRS, UMR 6622 06108 Nice cedex 2, France
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de Menezes DD, Jar e Silva M, de Aguiar FM. Numerical experiments on quantum chaotic billiards. CHAOS (WOODBURY, N.Y.) 2007; 17:023116. [PMID: 17614670 DOI: 10.1063/1.2731307] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/16/2023]
Abstract
A recently proposed numerical technique for generation of high-quality unstructured meshes is combined with a finite-element method to solve the Helmholtz equation that describes the quantum mechanics of a particle confined in two-dimensional cavities. Different shapes are treated on equal footing, including Sinai, stadium, annular, threefold symmetric, mushroom, cardioid, triangle, and coupled billiards. The results are shown to be in excellent agreement with available measurements in flat microwave resonator counterparts with nonintegrable geometries.
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Affiliation(s)
- D D de Menezes
- Departamento de Física, Universidade Federal de Pernambuco, Recife, PE 50670-901, Brazil
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12
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13
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Driscoll TA, Gottlieb HPW. Isospectral shapes with Neumann and alternating boundary conditions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:016702. [PMID: 12935282 DOI: 10.1103/physreve.68.016702] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/01/2002] [Indexed: 05/24/2023]
Abstract
The isospectrality of a well-known pair of shapes constructed from two arrangements of seven congruent right isosceles triangles with the Neumann boundary condition is verified numerically to high precision. Equally strong numerical evidence for isospectrality is presented for the eigenvalues of this standard pair in new boundary configurations with alternating Dirichlet and Neumann boundary conditions along successive edges. Good agreement with theory is obtained for the corresponding spectral staircase functions. Strong numerical evidence is also presented for isospectrality in an example of a different pair of shapes whose basic building-block triangle is not isosceles. Some possible confirmatory experiments involving fluids are suggested.
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Affiliation(s)
- T A Driscoll
- Department of Mathematical Sciences, University of Delaware, Newark, Delaware 19716, USA.
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Doya V, Legrand O, Mortessagne F, Miniatura C. Light scarring in an optical fiber. PHYSICAL REVIEW LETTERS 2002; 88:014102. [PMID: 11800948 DOI: 10.1103/physrevlett.88.014102] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/31/2001] [Indexed: 05/23/2023]
Abstract
We report the first experimental study of wave scarring in an optical fiber with a noncircular cross section. This optical multimode fiber serves as a powerful tool to image waves in a system where light rays exhibit a chaotic dynamics. Far-field intensity measurements are used to provide a better identification of scars in the Fourier domain. This first experimental characterization of scarring effect in optics demonstrates the relevance of such an optical waveguide for novel experiments in wave chaos.
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Affiliation(s)
- Valérie Doya
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 6622, Université de Nice Sophia-Antipolis, 06108 Nice, France
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Saichev AI, Berggren KF, Sadreev AF. Distribution of nearest distances between nodal points for the Berry function in two dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 64:036222. [PMID: 11580437 DOI: 10.1103/physreve.64.036222] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2000] [Revised: 04/11/2001] [Indexed: 05/23/2023]
Abstract
According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that both the real and imaginary parts of the wave function are random Gaussian fields we analyze the correlation function and densities of the nodal points. Using two approaches (the Poisson and Bernoulli) we derive the distribution of nearest neighbor separations. Furthermore the distribution functions for nodal points with specific chirality are found. Comparison is made with results from numerical calculations for the Berry wave function.
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Affiliation(s)
- A I Saichev
- Department of Radiophysics, Nizhny Novgorod University, Gagarin prospekt 23, 603600 Nizhny Novgorod, Russia
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Kudrolli A, Abraham MC, Gollub JP. Scarred patterns in surface waves. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2001; 63:026208. [PMID: 11308559 DOI: 10.1103/physreve.63.026208] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2000] [Revised: 06/16/2000] [Indexed: 05/23/2023]
Abstract
Surface wave patterns are investigated experimentally in a system geometry that has become a paradigm of quantum chaos: the stadium billiard. Linear waves in bounded geometries for which classical ray trajectories are chaotic are known to give rise to scarred patterns. Here, we utilize parametrically forced surface waves (Faraday waves), which become progressively nonlinear beyond the wave instability threshold, to investigate the subtle interplay between boundaries and nonlinearity. Only a subset (three main types) of the computed linear modes of the stadium are observed in a systematic scan. These correspond to modes in which the wave amplitudes are strongly enhanced along paths corresponding to certain periodic ray orbits. Many other modes are found to be suppressed, in general agreement with a prediction by Agam and Altshuler based on boundary dissipation and the Lyapunov exponent of the associated orbit. Spatially asymmetric or disordered (but time-independent) patterns are also found even near onset. As the driving acceleration is increased, the time-independent scarred patterns persist, but in some cases transitions between modes are noted. The onset of spatiotemporal chaos at higher forcing amplitude often involves a nonperiodic oscillation between spatially ordered and disordered states. We characterize this phenomenon using the concept of pattern entropy. The rate of change of the patterns is found to be reduced as the state passes temporarily near the ordered configurations of lower entropy. We also report complex but highly symmetric (time-independent) patterns far above onset in the regime that is normally chaotic.
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Affiliation(s)
- A Kudrolli
- Department of Physics, Haverford College, Haverford, Pennsylvania 19041, USA.
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Berggren KF, Ji ZL. Quantum chaos in nano-sized billiards in layered two-dimensional semiconductor structures. CHAOS (WOODBURY, N.Y.) 1996; 6:543-553. [PMID: 12780285 DOI: 10.1063/1.166202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We consider two-dimensional, electron-rich cavities that can be created at a (AlGa)As-GaAs interface. In the modelling of such cavities we include features that are typical for small semiconductor structures or devices, i.e., soft walls representing electrostatic confinement and disorder due to ionized impurities. The introduction of soft walls is found to have a profound effect on the dynamic behaviour. There are situations in which there is a crossover from a Wigner distribution for the nearest level spacing to an effectively Poisson-like one as the confining walls are softened. The crossover occurs in a region which is accessible experimentally. A mechanism for the crossover is discussed in terms of groups of energy levels being separated from each other as walls become soft. The effects of disorder are found to be negligible for high-mobility samples, i.e., the motion of the particles is ballistic. These findings are of a general nature. Chaotic Robnik dots, circular dots with a special "dent," are also investigated. In this case there is no crossover from Wigner to Poisson distributions. An explanation for this difference is proposed. Finally, the effects of leads are investigated in an elementary way by simply attaching two stubs to a circular dot. For wide stubs, which in our simple model would correspond to open leads, we obtain Wigner statistics indicating a transition to irregular behaviour. A lead-induced transition of this kind appears consistent with recent measurements of the line-shape of the weak localization peak, observed in the low-temperature magnetoresistance of square semiconductor billiards. Finally, implications for conductance fluctuations are briefly commented on. (c) 1996 American Institute of Physics.
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Affiliation(s)
- Karl-Fredrik Berggren
- Department of Physics and Measurement Technology, Linkoping University, S-581 83 Linkoping, Sweden
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18
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Wright WB, Budakian R, Putterman SJ. Diffusing light photography of fully developed isotropic ripple turbulence. PHYSICAL REVIEW LETTERS 1996; 76:4528-4531. [PMID: 10061314 DOI: 10.1103/physrevlett.76.4528] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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19
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Chinnery PA, Humphrey VF. Experimental visualization of acoustic resonances within a stadium-shaped cavity. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1996; 53:272-276. [PMID: 9964256 DOI: 10.1103/physreve.53.272] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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20
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Sirko L, Bellermann MR, Haffmans A, Koch PM, Richards D. Probing quantal dynamics of mixed phase space systems with noise. PHYSICAL REVIEW LETTERS 1993; 71:2895-2898. [PMID: 10054806 DOI: 10.1103/physrevlett.71.2895] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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21
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Lan BL, Wardlaw DM. Signatures of chaos in the modulus and phase of time-dependent wave functions. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:2176-2179. [PMID: 9960238 DOI: 10.1103/physreve.47.2176] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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22
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Tomsovic S, Heller EJ. Long-time semiclassical dynamics of chaos: The stadium billiard. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1993; 47:282-299. [PMID: 9960002 DOI: 10.1103/physreve.47.282] [Citation(s) in RCA: 47] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/22/2023]
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23
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Experimente zum Quantenchaos. Naturwissenschaften 1992. [DOI: 10.1007/bf01139195] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Stein J, Stöckmann H. Experimental determination of billiard wave functions. PHYSICAL REVIEW LETTERS 1992; 68:2867-2870. [PMID: 10045515 DOI: 10.1103/physrevlett.68.2867] [Citation(s) in RCA: 95] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
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