Knowledge Control Model of Distance Learning System on IMS Standard

Kravtsov, Hennadiy; Kravtsov, D.

doi:10.1007/978-1-4020-8739-4_35

Cited by 16 publications

(20 citation statements)

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“…1 we exhibit the decay rate κ(a) ≡ R a (s = ∞) for 0 < a < 4 computed numerically from Eq. (43). At present we could not find an analytic form of κ(a).…”

Section: Level Spacing Distributions Of the Deformed Kernelmentioning

confidence: 54%

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Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles

Nishigaki

1999

Phys. Rev. E

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We consider orthogonal, unitary, and symplectic ensembles of random matrices with (1/a)(ln x) 2 potentials, which obey spectral statistics different from the Wigner-Dyson and are argued to have multifractal eigenstates. If the coefficient a is small, spectral correlations in the bulk are universally governed by a translationally invariant, one-parameter generalization of the sine kernel. We provide analytic expressions for the level spacing distribution functions of this kernel, which are hybrids of the Wigner-Dyson and Poisson distributions. By tuning the single parameter, our results can be excellently fitted to the numerical data for three symmetry classes of the three-dimensional Anderson Hamiltonians at the metal-insulator transition, previously measured by several groups using exact diagonalization. PACS number(s): 71.30.+h, 72.15.Rn

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“…1 we exhibit the decay rate κ(a) ≡ R a (s = ∞) for 0 < a < 4 computed numerically from Eq. (43). At present we could not find an analytic form of κ(a).…”

Section: Level Spacing Distributions Of the Deformed Kernelmentioning

confidence: 54%

“…Our main result consists of Eqs. (43), (45), and (47). For s ≪ 1/a, we can Taylor-expand hyperbolic functions, to obtain a perturbative solution to Eq.…”

Section: Level Spacing Distributions Of the Deformed Kernelmentioning

confidence: 99%

Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles

Nishigaki

1999

Phys. Rev. E

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“…16 Thus, since the width of the distribution of the Kondo temperature is enhanced by wave function correlations, one can expect a widening of the Kondo distribution in the GOE-GUE crossover regime due to the presence of a weak magnetic field or a small amount of spin scattering. 49 The wave function correlation function is then given by…”

Section: Dependence Of P (Tk) On the Concentration Of Magnetic Imentioning

confidence: 99%

Disorder-quenched Kondo effect in mesoscopic electronic systems

Kettemann

Mucciolo

2007

Phys. Rev. B

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Nonmagnetic disorder is shown to quench the screening of magnetic moments in metals, the Kondo effect. The probability that a magnetic moment remains free down to zero temperature is found to increase with disorder strength. Experimental consequences for disordered metals are studied. In particular, it is shown that the presence of magnetic impurities with a small Kondo temperature enhances the electron's dephasing rate at low temperatures in comparison to the clean metal case. It is furthermore proven that the width of the distribution of Kondo temperatures remains finite in the thermodynamic (infinite volume) limit due to wave function correlations within an energy interval of order 1/τ , where τ is the elastic scattering time. When time-reversal symmetry is broken either by applying a magnetic field or by increasing the concentration of magnetic impurities, the distribution of Kondo temperatures becomes narrower.

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“…For ␤ϭ2, the MC result coincides with the value obtained by the method of orthogonal polynomials. 44 The first hundred of these for the power-law potential can be easily generated numerically 44 and the density at ⑀ϭ0 obtained from them converges very fast. This fast N independence of the center of the spectrum is also seen very well with the simulations and it is an important property of the particle density for weak confinement.…”

Section: A the Density Of Statesmentioning

confidence: 99%

“…Since the cluster function must satisfy the normalization sum rule, this implies a faster decay of R 2 (0,s) at large s. Using the method of orthogonal polynomials, one can show that this decay goes like 1/s (1ϩ1/␣) . 44 We now discuss the bulk properties of R 2 (s,sЈ) for the logarithmic potential. As shown in Fig.…”

Section: B the Two-level Correlation Functionmentioning

confidence: 99%

Model for a random-matrix description of the energy-level statistics of disordered systems at the Anderson transition

1996

Phys. Rev. B

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We consider a family of random-matrix ensembles ͑RME's͒ invariant under similarity transformations and described by the probability density P(H)ϭexp͓ϪTrV(H)͔. Dyson's mean-field theory ͑MFT͒ of the corresponding plasma model of eigenvalues is generalized to the case of weak confining potential, V(⑀)ϳ(A/2)ln 2 (⑀). The eigenvalue statistics derived from MFT are shown to deviate substantially from the classical Wigner-Dyson statistics when AϽ1. By performing systematic Monte Carlo simulations on the plasma model, we compute all the relevant statistical properties of the RME's with weak confinement. For A c Ϸ0.4 the distribution function of the energy-level spacings ͑LSDF͒ of this RME coincides in a large energy window with the LSDF of the three-dimensional Anderson model at the metal-insulator transition. For the same A c , the variance of the number of levels, ͗n 2 ͘Ϫ͗n͘ 2 , in an interval containing ͗n͘ levels on average, grows linearly with ͗n͘, and its slope is equal to 0.32Ϯ0.02, which is consistent with the value found for the Anderson model at the critical point.

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Knowledge Control Model of Distance Learning System on IMS Standard

Cited by 16 publications

References 0 publications

Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles

Level spacings at the metal-insulator transition in the Anderson Hamiltonians and multifractal random matrix ensembles

Disorder-quenched Kondo effect in mesoscopic electronic systems

Model for a random-matrix description of the energy-level statistics of disordered systems at the Anderson transition

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