On ?Universal? correlations in disordered and chaotic systems

Zakrzewski, Jakub

doi:10.1007/bf01324533

Cited by 12 publications

(14 citation statements)

References 25 publications

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“…The distribution functions (16) and (27) below are equivalent only in the sense that they lead to identical correlation functions in the "thermodynamic" limit N → ∞.…”

Section: Exact ("Micro-canonical") Joint Distribution Functionsmentioning

confidence: 99%

“…The joint distribution function defined by equations (16) and (27) serves as the basis for this calculation which employs a scheme based on the orthogonal polynomial expansion. In accordance with the definition (7), the parametric correlation function is represented as…”

Section: Parametric Correlation Functions In the Energy Representationmentioning

confidence: 99%

“…A related quantity which in the past has been extensively studied in the context of parametric correlations in chaotic and disordered systems using either numerical or approximate analytical techniques [13,7,14,15,16] is the single level velocity correlation function C 0 (x). Within the formalism developed in the present paper, it is convenient to represent it as a special case of the following correlation function:…”

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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“…The distribution functions (16) and (27) below are equivalent only in the sense that they lead to identical correlation functions in the "thermodynamic" limit N → ∞.…”

Section: Exact ("Micro-canonical") Joint Distribution Functionsmentioning

confidence: 99%

Section: Parametric Correlation Functions In the Energy Representationmentioning

confidence: 99%

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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“…Explicit expressions have been obtained [14] for a closely related [but distinct from C v (λ)] autocorrelation functions at fixed energy. A global approximation forC v (X) has been proposed [16]. For the case of a classically chaotic system subject to a Aharonov-Bohm flux Berry and Keating [22] obtained a semiclassical approximation for C v (λ) having the form of an everywhere analytic function of λ.…”

Section: Consider Next the Velocity-velocity Correlation Function A mentioning

confidence: 99%

“…To reveal the universality one has both to unfold the energy levels [3] and appropriately rescale the parameter, λ [8,11,14]. Other statistical measures of parametric dynamics such as the level slopes (velocities) distribution (Gaussian shaped for random systems [8,11,14]), the velocity-velocity correlation function [14,15,16,17] in the bound spectrum or parametric conductance fluctuations [18] and fluctuations in the Wigner time delay [19] for scattering systems have also been discussed.…”

Section: Introductionmentioning

confidence: 99%

Nonuniversality in level dynamics

Kunstman¹,

Życzkowski²,

Zakrzewski³

1997

Phys. Rev. E

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Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime between three universality classes. It is shown that the statistical properties of level dynamics are in general non universal and strongly depend on the way in which the parametric dynamics is introduced.

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Magnetic field control of molecular dissociation energies

Jost

1997

Int. J. Quant. Chem.

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We show that it is possible to control the dissociation energies of molecules with an external magnetic field. We focus our interest on the lowest dissociation channel for which the two atomic andror molecular products are formed in their ground state. The crucial requirement is the paramagnetic character of at least one of the two dissociation products. Then, an external magnetic field lowers the energy of the paramagnetic species in its lowest Zeeman component and, possibly, the corresponding energy of dissociation of the parent molecule. This it true for diatomic molecules when at least one of the atoms has an odd number of electrons. This is also true for oxygen and phosphorus atoms which have a 3 P ground state. The Zeeman energy shift of 2 paramagnetic species is always of the order of 1 cm y1 per tesla. The main theoretical difficulty is to determine the correlation diagram existing between the bound states of the parent molecule and the states of the products, or equivalently, how the energy evolves as a function of the internuclear distance corresponding to the dissociation coordinate. Little is known about this evolution, except for diatomic molecules, because the large internuclear distances are difficult to observe experimentally. The main part of the information come from ab initio calculations. For diatomic molecules, the dissociation coordinate is also the unique internuclear distance while for polyatomic molecules, the potential energy surface has 3N-6 coordinates and multidimensional effects should be Ž . considered. In any case, the singlet᎐triplet᎐quintet, etc . . . or doublet᎐quartet, etc . . . interactions should play an important role in the correlation diagram because crossings Ž are expected between singlet and triplet potential energy curves from short to long . internuclear distances and these interactions transform the crossings into anticrossings.Ž . The specific examples of alkali diatomic molecules Li , Na , etc . . . , of NO and of 2 2 2 Ž . O are analyzed in details.

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On ?Universal? correlations in disordered and chaotic systems

Cited by 12 publications

References 25 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

Nonuniversality in level dynamics

Magnetic field control of molecular dissociation energies

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