Publications
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21.
Pradhan, Prabhakar; Pance, Kristi; Rose, Michael; Sridhar, S
From Localization to Chaos in experimental eigenfunctions of disordered microwave cavities Proceedings Article
In: APS Meeting Abstracts, 2000.
@inproceedings{pradhan2000localization,
title = {From Localization to Chaos in experimental eigenfunctions of disordered microwave cavities},
author = {Prabhakar Pradhan and Kristi Pance and Michael Rose and S Sridhar},
year = {2000},
date = {2000-01-01},
booktitle = {APS Meeting Abstracts},
abstract = {We analyze eigenfunctions of disordered billiards obtained experimentally using microwave cavities, in terms of density correlations and moment distributions. Deviations from universal distributions are observed due to disorder induced localization. Level-to-level Inverse Participation Ratio (IPR I_2) fluctuations are observed and analyzed. Varying frequency (f) enables us to experimentally tune from localized to delocalized states, and this path for I_2 (f) follows a power law decay with exponent 1/2 above the cutoff frequency. In chaotic billiards, I 2 has a mean value close to that of the universal 2-dimensional (2D) limiting value of 3.0, with small level-to-level fluctuations resulting in a symmetric distribution about< I_2>. In disordered billiards not only is the mean value of I_2>> 3.0, but the fluctuations are also much greater. The IPR distribution for the disordered billiards is asymmetric about< I_2>, and is quantitatively …},
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pubstate = {published},
tppubtype = {inproceedings}
}
We analyze eigenfunctions of disordered billiards obtained experimentally using microwave cavities, in terms of density correlations and moment distributions. Deviations from universal distributions are observed due to disorder induced localization. Level-to-level Inverse Participation Ratio (IPR I_2) fluctuations are observed and analyzed. Varying frequency (f) enables us to experimentally tune from localized to delocalized states, and this path for I_2 (f) follows a power law decay with exponent 1/2 above the cutoff frequency. In chaotic billiards, I 2 has a mean value close to that of the universal 2-dimensional (2D) limiting value of 3.0, with small level-to-level fluctuations resulting in a symmetric distribution about< I_2>. In disordered billiards not only is the mean value of I_2>> 3.0, but the fluctuations are also much greater. The IPR distribution for the disordered billiards is asymmetric about< I_2>, and is quantitatively …
22.
Lu, Wentao; Viola, Lorenza; Pance, Kristi; Rose, Michael; Sridhar, S
Microwave study of quantum n-disk scattering Journal Article
In: Physical Review E, vol. 61, no. 4, pp. 3652, 2000.
@article{lu2000microwave,
title = {Microwave study of quantum n-disk scattering},
author = {Wentao Lu and Lorenza Viola and Kristi Pance and Michael Rose and S Sridhar},
year = {2000},
date = {2000-01-01},
journal = {Physical Review E},
volume = {61},
number = {4},
pages = {3652},
publisher = {APS},
abstract = {We describe a wave-mechanical implementation of classically chaotic n-disk scattering based on thin two-dimensional microwave cavities. Two-, three-, and four-disk scatterings are investigated in detail. The experiments, which are able to probe the stationary Green’s function of the system, yield both frequencies and widths of the low-lying quantum resonances. The observed spectra are found to be in good agreement with calculations based on semiclassical periodic orbit theory. Wave-vector autocorrelation functions are analyzed for various scattering geometries, the small wave-vector behavior allowing one to extract the escape rate from the quantum repeller. Quantitative agreement is found with the value predicted from classical scattering theory. For intermediate energies, nonuniversal oscillations are detected in the autocorrelation function, reflecting the presence of periodic orbits.},
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We describe a wave-mechanical implementation of classically chaotic n-disk scattering based on thin two-dimensional microwave cavities. Two-, three-, and four-disk scatterings are investigated in detail. The experiments, which are able to probe the stationary Green’s function of the system, yield both frequencies and widths of the low-lying quantum resonances. The observed spectra are found to be in good agreement with calculations based on semiclassical periodic orbit theory. Wave-vector autocorrelation functions are analyzed for various scattering geometries, the small wave-vector behavior allowing one to extract the escape rate from the quantum repeller. Quantitative agreement is found with the value predicted from classical scattering theory. For intermediate energies, nonuniversal oscillations are detected in the autocorrelation function, reflecting the presence of periodic orbits.
23.
Pance, Kristi; Viola, Lorenza; Sridhar, S
Tunneling proximity resonances: interplay between symmetry and dissipation Journal Article
In: Physics Letters A, vol. 268, no. 4-6, pp. 399–405, 2000.
@article{pance2000tunneling,
title = {Tunneling proximity resonances: interplay between symmetry and dissipation},
author = {Kristi Pance and Lorenza Viola and S Sridhar},
year = {2000},
date = {2000-01-01},
journal = {Physics Letters A},
volume = {268},
number = {4-6},
pages = {399--405},
publisher = {North-Holland},
abstract = {We report the first observation of bound-state proximity resonances in coupled dielectric resonators. The proximity resonances arise from the combined action of symmetry and dissipation. We argue that the large ratio between the widths is a distinctive signature of the multidimensional nature of the system. Our experiments shed light on the properties of 2D tunneling in the presence of a dissipative environment.},
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We report the first observation of bound-state proximity resonances in coupled dielectric resonators. The proximity resonances arise from the combined action of symmetry and dissipation. We argue that the large ratio between the widths is a distinctive signature of the multidimensional nature of the system. Our experiments shed light on the properties of 2D tunneling in the presence of a dissipative environment.
24.
Lu, Wentao; Viola, Lorenza; Pance, Kristi; Rose, Michael; Sridhar, S
Erratum: Microwave study of quantum n-disk scattering [Phys. Rev. E 61, 3652 (2000)] Journal Article
In: Physical Review E, vol. 62, no. 3, pp. 4478, 2000.
@article{lu2000erratum,
title = {Erratum: Microwave study of quantum n-disk scattering [Phys. Rev. E 61, 3652 (2000)]},
author = {Wentao Lu and Lorenza Viola and Kristi Pance and Michael Rose and S Sridhar},
year = {2000},
date = {2000-01-01},
journal = {Physical Review E},
volume = {62},
number = {3},
pages = {4478},
publisher = {APS},
abstract = {ISSN 2470-0053 (online), 2470-0045 (print). ©2019 American Physical Society. All rights reserved. Physical Review E™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. The APS Physics logo and Physics logo are trademarks of the American Physical Society. Information about registration may be found here. Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement.},
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ISSN 2470-0053 (online), 2470-0045 (print). ©2019 American Physical Society. All rights reserved. Physical Review E™ is a trademark of the American Physical Society, registered in the United States, Canada, European Union, and Japan. The APS Physics logo and Physics logo are trademarks of the American Physical Society. Information about registration may be found here. Use of the American Physical Society websites and journals implies that the user has read and agrees to our Terms and Conditions and any applicable Subscription Agreement.
25.
Lu, Wentao; Rose, M; Pance, K; Sridhar, S
Quantum resonances and decay of a chaotic fractal repeller observed using microwaves Journal Article
In: Physical review letters, vol. 82, no. 26, pp. 5233, 1999.
@article{lu1999quantum,
title = {Quantum resonances and decay of a chaotic fractal repeller observed using microwaves},
author = {Wentao Lu and M Rose and K Pance and S Sridhar},
year = {1999},
date = {1999-01-01},
journal = {Physical review letters},
volume = {82},
number = {26},
pages = {5233},
publisher = {APS},
abstract = {The quantum resonances of classically chaotic n-disk geometries were studied experimentally utilizing thin 2D microwave geometries. The experiments yield the frequencies and widths of low-lying resonances, which are compared with semiclassical calculations. The long time or small energy behavior of the wave-vector autocorrelation gives information about the quantum decay rate, which is in good agreement with that obtained from classical scattering theory. The intermediate energy behavior shows nonuniversal oscillations determined by periodic orbits.},
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pubstate = {published},
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The quantum resonances of classically chaotic n-disk geometries were studied experimentally utilizing thin 2D microwave geometries. The experiments yield the frequencies and widths of low-lying resonances, which are compared with semiclassical calculations. The long time or small energy behavior of the wave-vector autocorrelation gives information about the quantum decay rate, which is in good agreement with that obtained from classical scattering theory. The intermediate energy behavior shows nonuniversal oscillations determined by periodic orbits.
26.
Sridhar, S
Wave Chaos and Localization in Closed Billiards and Open Scattering Systems: Microwave Experiments Proceedings Article
In: APS March Meeting Abstracts, 1998.
@inproceedings{sridhar1998wave,
title = {Wave Chaos and Localization in Closed Billiards and Open Scattering Systems: Microwave Experiments},
author = {S Sridhar},
year = {1998},
date = {1998-01-01},
booktitle = {APS March Meeting Abstracts},
abstract = {Microwave experiments are described, which are designed to study the signatures of chaos and localization on the quantum properties of model 2-D closed (billiard) and open scattering geometries. A special advantage of the experiments is the ability to directly measure eigenfunctions. In chaotic billiards, the eigenfunctions display universal density distributions and density autocorrelations, in agreement with expressions derived from random matrix theory and from a 0D nonlinear sigma model of supersymmetry. In contrast, wavefunctions in disordered billiards show deviations from universality due to Anderson localization. The systematics of the distribution functions and inverse participation ratios are studied as a function of frequency and localization length. While results in the regime of incipient localization appear to be successfully described by leading expansions of nonlinear sigma models of supersymmetry …},
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Microwave experiments are described, which are designed to study the signatures of chaos and localization on the quantum properties of model 2-D closed (billiard) and open scattering geometries. A special advantage of the experiments is the ability to directly measure eigenfunctions. In chaotic billiards, the eigenfunctions display universal density distributions and density autocorrelations, in agreement with expressions derived from random matrix theory and from a 0D nonlinear sigma model of supersymmetry. In contrast, wavefunctions in disordered billiards show deviations from universality due to Anderson localization. The systematics of the distribution functions and inverse participation ratios are studied as a function of frequency and localization length. While results in the regime of incipient localization appear to be successfully described by leading expansions of nonlinear sigma models of supersymmetry …
27.
Kudrolli, A; Sridhar, S
Experiments on quantum chaos using microwave cavities: Results for the pseudo-integrable L-billiard Journal Article
In: Pramana, vol. 48, no. 2, pp. 459–467, 1997.
@article{kudrolli1997experiments,
title = {Experiments on quantum chaos using microwave cavities: Results for the pseudo-integrable L-billiard},
author = {A Kudrolli and S Sridhar},
year = {1997},
date = {1997-01-01},
journal = {Pramana},
volume = {48},
number = {2},
pages = {459--467},
publisher = {Springer India},
abstract = {We describe microwave experiments used to study billiard geometries as model problems of non-integrability in quantum or wave mechanics. The experiments can study arbitrary 2-D geometries, including chaotic and even disordered billiards. Detailed results on an L-shaped pseudo-integrable billiard are discussed as an example. The eigenvalue statistics are well-described by empirical formulae incorporating the fraction of phase space that is non-integrable. The eigenfunctions are directly measured, and their statistical properties are shown to be influenced by non-isolated periodic orbits, similar to that for the chaotic Sinai billiard. These periodic orbits are directly observed in the Fourier transform of the eigenvalue spectrum.},
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We describe microwave experiments used to study billiard geometries as model problems of non-integrability in quantum or wave mechanics. The experiments can study arbitrary 2-D geometries, including chaotic and even disordered billiards. Detailed results on an L-shaped pseudo-integrable billiard are discussed as an example. The eigenvalue statistics are well-described by empirical formulae incorporating the fraction of phase space that is non-integrable. The eigenfunctions are directly measured, and their statistical properties are shown to be influenced by non-isolated periodic orbits, similar to that for the chaotic Sinai billiard. These periodic orbits are directly observed in the Fourier transform of the eigenvalue spectrum.
28.
Jacobs, T; Willemsen, Balam A; Sridhar, S
Quantitative analysis of nonlinear microwave surface impedance from non-Lorentzian resonances of high Q resonators Journal Article
In: Review of scientific instruments, vol. 67, no. 10, pp. 3757–3758, 1996.
@article{jacobs1996quantitative,
title = {Quantitative analysis of nonlinear microwave surface impedance from non-Lorentzian resonances of high Q resonators},
author = {T Jacobs and Balam A Willemsen and S Sridhar},
year = {1996},
date = {1996-01-01},
journal = {Review of scientific instruments},
volume = {67},
number = {10},
pages = {3757--3758},
publisher = {American Institute of Physics},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
29.
Kudrolli, A; Sridhar, S
Comment on “Gaussian Orthogonal Ensemble Statistics in a Microwave Stadium Billiard with Chaotic Dynamics: Porter-Thomas Distribution and Algebraic Decay of Time Correlations” Journal Article
In: Physical review letters, vol. 76, no. 16, pp. 3036, 1996.
@article{kudrolli1996comment,
title = {Comment on “Gaussian Orthogonal Ensemble Statistics in a Microwave Stadium Billiard with Chaotic Dynamics: Porter-Thomas Distribution and Algebraic Decay of Time Correlations”},
author = {A Kudrolli and S Sridhar},
year = {1996},
date = {1996-01-01},
journal = {Physical review letters},
volume = {76},
number = {16},
pages = {3036},
publisher = {American Physical Society},
abstract = {A Comment on the Letter by H. Alt et al., Phys. Rev. Lett. 74, 62 (1995).
Received 2 March 1995
DOI:https://doi.org/10.1103/PhysRevLett.76.3036
©1996 American Physical Society},
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A Comment on the Letter by H. Alt et al., Phys. Rev. Lett. 74, 62 (1995).
Received 2 March 1995
DOI:https://doi.org/10.1103/PhysRevLett.76.3036
©1996 American Physical Society
Received 2 March 1995
DOI:https://doi.org/10.1103/PhysRevLett.76.3036
©1996 American Physical Society
30.
Kudrolli, A; Kidambi, V; Sridhar, S
Experimental studies of chaos and localization in quantum wave functions Journal Article
In: Physical review letters, vol. 75, no. 5, pp. 822, 1995.
@article{kudrolli1995experimental,
title = {Experimental studies of chaos and localization in quantum wave functions},
author = {A Kudrolli and V Kidambi and S Sridhar},
year = {1995},
date = {1995-01-01},
journal = {Physical review letters},
volume = {75},
number = {5},
pages = {822},
publisher = {APS},
abstract = {Wave functions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wave functions display universal density distributions and density autocorrelations in agreement with expressions derived from a 0D nonlinear σ model of supersymmetry, which coincides with random matrix theory. In contrast, disordered wave functions show deviations from this universal behavior due to Anderson localization. A systematic behavior of the distribution function is studied as a function of the localization length, and can be understood in the framework of a 1D version of the nonlinear σ model.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Wave functions in chaotic and disordered quantum billiards are studied experimentally using thin microwave cavities. The chaotic wave functions display universal density distributions and density autocorrelations in agreement with expressions derived from a 0D nonlinear σ model of supersymmetry, which coincides with random matrix theory. In contrast, disordered wave functions show deviations from this universal behavior due to Anderson localization. A systematic behavior of the distribution function is studied as a function of the localization length, and can be understood in the framework of a 1D version of the nonlinear σ model.
31.
Prigodin, VN; Taniguchi, Nobuhiko; Kudrolli, A; Kidambi, V; Sridhar, S
Spatial correlation in quantum chaotic systems with time-reversal symmetry: Theory and experiment Journal Article
In: Physical review letters, vol. 75, no. 12, pp. 2392, 1995.
@article{prigodin1995spatial,
title = {Spatial correlation in quantum chaotic systems with time-reversal symmetry: Theory and experiment},
author = {VN Prigodin and Nobuhiko Taniguchi and A Kudrolli and V Kidambi and S Sridhar},
year = {1995},
date = {1995-01-01},
journal = {Physical review letters},
volume = {75},
number = {12},
pages = {2392},
publisher = {American Physical Society},
abstract = {The correlation between the values of wave functions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the wave function density for a given eigenstate, although the background wave function density fluctuates strongly. We show that for large fluctuations, once the value of the wave function at one point is known, its spatial dependence becomes highly predictable for increasingly large space around this point. These results are compared with the experimental wave functions obtained from billiard-shaped microwave cavities, and very good agreement is demonstrated.},
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The correlation between the values of wave functions at two different spatial points is examined for chaotic systems with time-reversal symmetry. Employing a supermatrix method, we find that there exist long-range Friedel oscillations of the wave function density for a given eigenstate, although the background wave function density fluctuates strongly. We show that for large fluctuations, once the value of the wave function at one point is known, its spatial dependence becomes highly predictable for increasingly large space around this point. These results are compared with the experimental wave functions obtained from billiard-shaped microwave cavities, and very good agreement is demonstrated.
32.
Kudrolli, A; Sridhar, S
QUANTUM CHAOS EXPERIMENTS USING MICROWAVE CAVITIES Proceedings Article
In: Proceedings Of The 2nd Experimental Chaos Conference, pp. 184, World Scientific 1995.
@inproceedings{kudrolli1995quantum,
title = {QUANTUM CHAOS EXPERIMENTS USING MICROWAVE CAVITIES},
author = {A Kudrolli and S Sridhar},
year = {1995},
date = {1995-01-01},
booktitle = {Proceedings Of The 2nd Experimental Chaos Conference},
pages = {184},
organization = {World Scientific},
abstract = {We describe experiments using thin microwave cavities to test issues in Quantum Chaos. The experiments exploit the correspondence of the scalar Helmholtz-Maxwell and the time-independent Schrodinger equations. The eigenvalues and eigenfunctions of cavities with cross-sections in the form of chaotic billiards are obtained experimentally. In certain geometries the eigenvalue statistics are in complete agreement with Random Matrix theory. Scars are visible in some eigenfunctions, although a general rule for their obseiVation is not yet available.},
keywords = {},
pubstate = {published},
tppubtype = {inproceedings}
}
We describe experiments using thin microwave cavities to test issues in Quantum Chaos. The experiments exploit the correspondence of the scalar Helmholtz-Maxwell and the time-independent Schrodinger equations. The eigenvalues and eigenfunctions of cavities with cross-sections in the form of chaotic billiards are obtained experimentally. In certain geometries the eigenvalue statistics are in complete agreement with Random Matrix theory. Scars are visible in some eigenfunctions, although a general rule for their obseiVation is not yet available.
33.
Sridhar, S
Cavities of Chaos Journal Article
In: SCIENCE NEWS-WASHINGTON-, vol. 147, pp. 264–264, 1995.
@article{sridhar1995cavities,
title = {Cavities of Chaos},
author = {S Sridhar},
year = {1995},
date = {1995-01-01},
journal = {SCIENCE NEWS-WASHINGTON-},
volume = {147},
pages = {264--264},
publisher = {SCIENCE NEWS},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
34.
Kudrolli, A; Sridhar, S; Pandey, Akhilesh; Ramaswamy, Ramakrishna
Signatures of chaos in quantum billiards: Microwave experiments Journal Article
In: Physical Review E, vol. 49, no. 1, pp. R11, 1994.
@article{kudrolli1994signatures,
title = {Signatures of chaos in quantum billiards: Microwave experiments},
author = {A Kudrolli and S Sridhar and Akhilesh Pandey and Ramakrishna Ramaswamy},
year = {1994},
date = {1994-01-01},
journal = {Physical Review E},
volume = {49},
number = {1},
pages = {R11},
publisher = {APS},
abstract = {The signatures of classical chaos and the role of periodic orbits in the wave-mechanical eigenvalue spectra of two-dimensional billiards are studied experimentally in microwave cavities. The survival probability for all the chaotic cavity data shows a ‘‘correlation hole,’’in agreement with theory, that is absent for the integrable cavity. The spectral rigidity Δ 3 (L), which is a measure of long-range correlation, is shown to be particularly sensitive to the presence of marginally stable periodic orbits. Agreement with random-matrix theory is achieved only after excluding such orbits, which we do by constructing a special geometry, the Sinai stadium. Pseudointegrable geometries are also studied, and are found to display intermediate behavior.},
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The signatures of classical chaos and the role of periodic orbits in the wave-mechanical eigenvalue spectra of two-dimensional billiards are studied experimentally in microwave cavities. The survival probability for all the chaotic cavity data shows a ‘‘correlation hole,’’in agreement with theory, that is absent for the integrable cavity. The spectral rigidity Δ 3 (L), which is a measure of long-range correlation, is shown to be particularly sensitive to the presence of marginally stable periodic orbits. Agreement with random-matrix theory is achieved only after excluding such orbits, which we do by constructing a special geometry, the Sinai stadium. Pseudointegrable geometries are also studied, and are found to display intermediate behavior.
35.
Sridhar, S
Quantum Dynamics of Chaotic Systems Journal Article
In: 1993.
@article{sridhar1993quantum,
title = {Quantum Dynamics of Chaotic Systems},
author = {S Sridhar},
year = {1993},
date = {1993-01-01},
publisher = {Gordon and Breach, Amsterdam},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
36.
Sridhar, S; Hogenboom, D; Kudrolli, A
Exper-imental eigenvalue spectra of “rough” and multiplyconnected billiards,” Journal Article
In: Quantum Dynamics of Chaotic Systems, eds. Yuan, JM, Feng, DH & Zaslavsky, GM (Gordon and Breach, Amsterdam), pp. 297–304, 1993.
@article{sridhar1993exper,
title = {Exper-imental eigenvalue spectra of “rough” and multiplyconnected billiards,”},
author = {S Sridhar and D Hogenboom and A Kudrolli},
year = {1993},
date = {1993-01-01},
journal = {Quantum Dynamics of Chaotic Systems, eds. Yuan, JM, Feng, DH & Zaslavsky, GM (Gordon and Breach, Amsterdam)},
pages = {297--304},
abstract = {We use microwave cavities to study the spectra of billiards with" rough" perimeters, or which ara multiply connected-While simple boundaries show cumulative level densities N (E) which are in good agreement with the Weyl formula, qualitative departures are observed at low energies-when the perimeter is" roughened" by increasing the ratio of perimeter L to area A, and when obstacles are introduced to make the billiard multiply connected. Thus the Weyl formula even including perimeter corrections is not a good yardstick at low energies which probe internal length scales, interestingly, in the case of a multiply-connected billiard with a periodic array of obstacles, large" gaps" are observed in the discrete spectrum, somewhat like a solid-state lattice of finite size. The gaps persist when disorder¿ î introduced, Le. in the analog of a solid-state glass.
The influence of the shape of a planar domain on the eigenvalue …},
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}
We use microwave cavities to study the spectra of billiards with" rough" perimeters, or which ara multiply connected-While simple boundaries show cumulative level densities N (E) which are in good agreement with the Weyl formula, qualitative departures are observed at low energies-when the perimeter is" roughened" by increasing the ratio of perimeter L to area A, and when obstacles are introduced to make the billiard multiply connected. Thus the Weyl formula even including perimeter corrections is not a good yardstick at low energies which probe internal length scales, interestingly, in the case of a multiply-connected billiard with a periodic array of obstacles, large" gaps" are observed in the discrete spectrum, somewhat like a solid-state lattice of finite size. The gaps persist when disorder¿ î introduced, Le. in the analog of a solid-state glass.
The influence of the shape of a planar domain on the eigenvalue …
The influence of the shape of a planar domain on the eigenvalue …
37.
Sridhar, S; Heller, EJ
Physical and numerical experiments on the wave mechanics of classically chaotic systems Journal Article
In: Physical Review A, vol. 46, no. 4, pp. R1728, 1992.
@article{sridhar1992physical,
title = {Physical and numerical experiments on the wave mechanics of classically chaotic systems},
author = {S Sridhar and EJ Heller},
year = {1992},
date = {1992-01-01},
journal = {Physical Review A},
volume = {46},
number = {4},
pages = {R1728},
publisher = {American Physical Society},
abstract = {We study chaotic quantum billiards using both microwave cavities and numerical simulations. For the same geometry, viz., a Sinai billiard, agreement to remarkable precision is found for both the eigenvalue magnitudes and the spatial detail of the eigenfunctions. The association of the eigenfunctions with classical periodic orbits is demonstrated, and scarred states are identified. Desymmetrizing the Sinai billiard by slightly moving the central disk is shown to lead to strong localization of the eigenfunction. The calculated eigenstates of the symmetric billiard show an even-and odd-parity pair whose linear combination gives the localized state.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We study chaotic quantum billiards using both microwave cavities and numerical simulations. For the same geometry, viz., a Sinai billiard, agreement to remarkable precision is found for both the eigenvalue magnitudes and the spatial detail of the eigenfunctions. The association of the eigenfunctions with classical periodic orbits is demonstrated, and scarred states are identified. Desymmetrizing the Sinai billiard by slightly moving the central disk is shown to lead to strong localization of the eigenfunction. The calculated eigenstates of the symmetric billiard show an even-and odd-parity pair whose linear combination gives the localized state.
38.
Sridhar, S; Hogenboom, DO; Willemsen, Balam A
Microwave experiments on chaotic billiards Journal Article
In: Journal of statistical physics, vol. 68, no. 1-2, pp. 239–258, 1992.
@article{sridhar1992microwave,
title = {Microwave experiments on chaotic billiards},
author = {S Sridhar and DO Hogenboom and Balam A Willemsen},
year = {1992},
date = {1992-01-01},
journal = {Journal of statistical physics},
volume = {68},
number = {1-2},
pages = {239--258},
publisher = {Kluwer Academic Publishers-Plenum Publishers},
abstract = {We describe experiments using billiard-shaped microwave cavities, to test ideas in quantum chaos. The experimental method for observing cavity resonances to obtain the eigenvalues, and the advantages and limitations of the techniques, including the influence of absorption, are discussed. An experimental technique to obtain a 2D mapping of the wavefunction is described. Results are displayed for 36 of the low-lying wavefunctions of a Sinai billiard cavity consisting of a central disc in a rectangular enclosure. The wavefunctions demonstrate the influence of classical periodic orbits (PO), of which there are two types: non-isolated PO, which avoid the central disc, and isolated PO, which hit the central disc. Scarred states, including those associated with isolated PO, are directly observed.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
We describe experiments using billiard-shaped microwave cavities, to test ideas in quantum chaos. The experimental method for observing cavity resonances to obtain the eigenvalues, and the advantages and limitations of the techniques, including the influence of absorption, are discussed. An experimental technique to obtain a 2D mapping of the wavefunction is described. Results are displayed for 36 of the low-lying wavefunctions of a Sinai billiard cavity consisting of a central disc in a rectangular enclosure. The wavefunctions demonstrate the influence of classical periodic orbits (PO), of which there are two types: non-isolated PO, which avoid the central disc, and isolated PO, which hit the central disc. Scarred states, including those associated with isolated PO, are directly observed.
39.
Sridhar, S; Parimi, PV; Lu, WT; Vodo, P; Derov, John S; Hanscom, AFRL; Bedford, MA
Negative Refraction and Imaging in Photonic Crystals Journal Article
In: 0000.
@article{sridharnegative,
title = {Negative Refraction and Imaging in Photonic Crystals},
author = {S Sridhar and PV Parimi and WT Lu and P Vodo and John S Derov and AFRL Hanscom and MA Bedford},
abstract = {Negative refraction and left-handed electromagnetism in a photonic crystal are demonstrated in waveguide and free space experiments at microwave frequencies. Precision control to achieve tailor-made refractive indices has been achieved. The negative refraction in these photonic crystals is shown to lead to imaging by a flat lens. We have also developed a generalized theory of flat lens imaging. These results promise potential applications in a variety of optical and microwave systems for communications and imaging.},
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pubstate = {published},
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Negative refraction and left-handed electromagnetism in a photonic crystal are demonstrated in waveguide and free space experiments at microwave frequencies. Precision control to achieve tailor-made refractive indices has been achieved. The negative refraction in these photonic crystals is shown to lead to imaging by a flat lens. We have also developed a generalized theory of flat lens imaging. These results promise potential applications in a variety of optical and microwave systems for communications and imaging.
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