*Pier A. Mello and Narendra Kumar*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198525820
- eISBN:
- 9780191712234
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525820.001.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities ...
More

This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities and quantum dots) or possessing quenched randomness (e.g., disordered conductors). The emphasis here is on mesoscopic fluctuations of the sample-specific transport. The universal character of the statistical behaviour of these phenomena is revealed in a natural way through a novel maximum-entropy approach (MEA). The latter leads to the most probable distribution for the set of random matrices that describe the ensemble of disordered/chaotic samples, which are macroscopically identical but differ in microscopic details. Here, the Shannon information entropy associated with these random matrices is maximized subject to the symmetries and the constraints which are physically relevant. This non-perturbative information-theoretic approach is reminiscent of, but distinct from, the standard random-matrix theory, and indeed forms the most distinctive feature of the book.Less

This book presents a statistical theory of complex wave scattering and quantum transport in a class of physical systems of current interest having chaotic classical dynamics (e.g., microwave cavities and quantum dots) or possessing quenched randomness (e.g., disordered conductors). The emphasis here is on mesoscopic fluctuations of the sample-specific transport. The universal character of the statistical behaviour of these phenomena is revealed in a natural way through a novel maximum-entropy approach (MEA). The latter leads to the most probable distribution for the set of random matrices that describe the ensemble of disordered/chaotic samples, which are macroscopically identical but differ in microscopic details. Here, the Shannon information entropy associated with these random matrices is maximized subject to the symmetries and the constraints which are physically relevant. This non-perturbative information-theoretic approach is reminiscent of, but distinct from, the standard random-matrix theory, and indeed forms the most distinctive feature of the book.

*Pier A. Mello and Narendra Kumar*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198525820
- eISBN:
- 9780191712234
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525820.003.0006
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter focuses on scattering from classically chaotic cavities. A maximum-entropy approach is employed to derive the probability distribution for the S matrix, with and without the presence of ...
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This chapter focuses on scattering from classically chaotic cavities. A maximum-entropy approach is employed to derive the probability distribution for the S matrix, with and without the presence of direct processes. The latter (with direct processes) is included as a constraint through the imposition of a given average S matrix, in addition to its analytic properties. Theoretical calculations are compared with the results of computer simulations and experimental data. The contents of this chapter include statistical ensembles of S matrices; invariant measure; distribution of the conductance in the two-equal-lead case; numerical calculations and comparison with theory; dephasing effects; and comparison with experimental data and physical experiments.Less

This chapter focuses on scattering from classically chaotic cavities. A maximum-entropy approach is employed to derive the probability distribution for the *S* matrix, with and without the presence of direct processes. The latter (with direct processes) is included as a constraint through the imposition of a given average *S* matrix, in addition to its analytic properties. Theoretical calculations are compared with the results of computer simulations and experimental data. The contents of this chapter include statistical ensembles of *S* matrices; invariant measure; distribution of the conductance in the two-equal-lead case; numerical calculations and comparison with theory; dephasing effects; and comparison with experimental data and physical experiments.

*Pier A. Mello and Narendra Kumar*

- Published in print:
- 2004
- Published Online:
- September 2007
- ISBN:
- 9780198525820
- eISBN:
- 9780191712234
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780198525820.003.0001
- Subject:
- Physics, Condensed Matter Physics / Materials

This chapter introduces the notion of complex scattering of waves, emphasizes the generality of the ideas involved, and explains its relevance to the field of nuclear physics and microwave cavities. ...
More

This chapter introduces the notion of complex scattering of waves, emphasizes the generality of the ideas involved, and explains its relevance to the field of nuclear physics and microwave cavities. It then introduces the subject of coherent wave transport through mesoscopic systems, e.g., disordered conductors and chaotic cavities, with emphasis on the statistics of fluctuations observed in these systems. These fluctuations, among them the universal conductance fluctuation, arise ultimately from the complex wave interference. Various length- and time-scales defining the mesoscopic system are discussed. The idea of maximum entropy approach (MEA) is introduced as distinct from, but related to, the idea of random-matrix theory (RMT) pioneered by Wigner originally in the context of isolated resonances of complex nuclei. The contents of this chapter include complex atomic nuclei and chaotic microwave cavities; wave localization; statistical fluctuations; mesoscopic conductors: time- and length-scales, ballistic mesoscopic cavities, diffusive mesoscopic conductors, and statistical approach to mesoscopic fluctuations.Less

This chapter introduces the notion of complex scattering of waves, emphasizes the generality of the ideas involved, and explains its relevance to the field of nuclear physics and microwave cavities. It then introduces the subject of coherent wave transport through mesoscopic systems, e.g., disordered conductors and chaotic cavities, with emphasis on the statistics of fluctuations observed in these systems. These fluctuations, among them the universal conductance fluctuation, arise ultimately from the complex wave interference. Various length- and time-scales defining the mesoscopic system are discussed. The idea of maximum entropy approach (MEA) is introduced as distinct from, but related to, the idea of random-matrix theory (RMT) pioneered by Wigner originally in the context of isolated resonances of complex nuclei. The contents of this chapter include complex atomic nuclei and chaotic microwave cavities; wave localization; statistical fluctuations; mesoscopic conductors: time- and length-scales, ballistic mesoscopic cavities, diffusive mesoscopic conductors, and statistical approach to mesoscopic fluctuations.