Parametric Spectral Correlations in Disordered and Chaotic Structures

Smolyarenko, Igor; Marchetti, F. M.; Simons, Benjamin D.

doi:10.1103/physrevlett.88.256808

Cited by 8 publications

(26 citation statements)

References 24 publications

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“…In Ref. [17] the distribution p 0 for r = 1 was found using the fact that, as a special property of r = 1, this distribution coincides with the level spacing of the combined ensemble of levels {ǫ α } ∪ {ǫ ′ β }. Using the present formalism, this quantity, as well as the corresponding c 0 can be evaluated in a more direct way.…”

Section: Parametric Correlation Functions In the Number Representationmentioning

confidence: 99%

“…Similarly, to the leading order in the 1/N expansion, the density of states ρ (ǫ) can be approximated by an ǫ-independent inverse mean level spacing 1/∆, thus simplifying (38) to the form quoted in [17]:…”

Section: Parametric Correlation Functions In the Energy Representationmentioning

confidence: 99%

“…Owing to the determinantal structure of R nm [17,7,18] (see also Section 3.1 below), the latter possess representations in terms of Fredholm determinants of certain parameterdependent integral kernels.…”

Section: Introductionmentioning

confidence: 99%

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Parametric spectral statistics in unitary random matrix ensembles: from distribution functions to intra-level correlations

Smolyarenko

Simons

2003

J. Phys. A: Math. Gen.

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Abstract. We establish a general framework to explore parametric statistics of individual energy levels in unitary random matrix ensembles. For a generic confinement potential W (H), we (i) find the joint distribution functions of the eigenvalues of H and H ′ = H + V for an arbitrary fixed V both for finite matrix size N and in the "thermodynamic" N → ∞ limit; (ii) derive manypoint parametric correlation functions of the two sets of eigenvalues and show that they are naturally parametrised by the eigenvalues of the reactance matrix for scattering off the "potential" V ; (iii) prove the universality of the correlation functions in unitary ensembles with non-Gaussian non-invariant confinement potential W (H − V ); (iv) establish a general scheme for exact calculation of level-number-dependent parametric correlation functions and apply the scheme to the calculation of intra-level velocity autocorrelation function and the distribution of parametric level shifts.

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Section: Parametric Correlation Functions In the Number Representationmentioning

confidence: 99%

Section: Parametric Correlation Functions In the Energy Representationmentioning

confidence: 99%

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Parametric spectral statistics in unitary random matrix ensembles: from distribution functions to intra-level correlations

Smolyarenko

Simons

2003

J. Phys. A: Math. Gen.

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“…(12). It is interesting that a joint probability distribution can also be found in the more general, non-rank-one case 26 that we do not consider here. The ground state overlap ∆ is expressed entirely in terms of the unperturbed and perturbed eigenvalues {ǫ} and {λ} [see Eq.…”

Section: B Mesoscopic Systemsmentioning

confidence: 99%

Fermi edge singularities in the mesoscopic regime: Anderson orthogonality catastrophe

2005

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For generic mesoscopic systems like quantum dots or nanoparticles, we study the Anderson orthogonality catastrophe (AOC) and Fermi edge singularities in photoabsorption spectra in a series of two papers. In the present paper we focus on AOC for a finite number of particles in discrete energy levels where, in contrast to the bulk situation, AOC is not complete. Moreover, fluctuations characteristic for mesoscopic systems lead to a broad distribution of AOC ground state overlaps. The fluctuations originate dominantly in the levels around the Fermi energy, and we derive an analytic expression for the probability distribution of AOC overlaps in the limit of strong perturbations. We address the formation of a bound state and its importance for symmetries between the overlap distributions for attractive and repulsive potentials. Our results are based on a random matrix model for the chaotic conduction electrons that are subject to a rank one perturbation corresponding, e.g., to the localized core hole generated in the photoabsorption process.

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“…Under these hypotheses, the joint probability distribution P ({ǫ}, {λ}) was derived by Aleiner and Matveev [9] (see [13] for a generalization to the non-rank-one case):…”

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confidence: 99%

Fermi-Edge Singularities in the Mesoscopic X-Ray Edge Problem

2004

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We study the x-ray edge problem for a chaotic quantum dot or nanoparticle displaying mesoscopic fluctuations. In the bulk, x-ray physics is known to produce Fermi edge singularities -deviations from the naively expected photoabsorption cross section in the form of a peaked or rounded edge. For a coherent system with chaotic dynamics, we find substantial changes; in particular, a photoabsorption cross section showing a rounded edge in the bulk will change to a slightly peaked edge on average as the system size is reduced to a mesoscopic (coherent) scale.

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Parametric Spectral Correlations in Disordered and Chaotic Structures

Cited by 8 publications

References 24 publications

Parametric spectral statistics in unitary random matrix ensembles: from distribution functions to intra-level correlations

Parametric spectral statistics in unitary random matrix ensembles: from distribution functions to intra-level correlations

Fermi edge singularities in the mesoscopic regime: Anderson orthogonality catastrophe

Fermi-Edge Singularities in the Mesoscopic X-Ray Edge Problem

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