Chaotic scattering on individual quantum graphs

Pluhař, Z.; Weidenmüller, Hans A.

doi:10.1103/physreve.88.022902

Cited by 20 publications

(44 citation statements)

References 46 publications

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“…However, the BALDA runs into convergence problems on small lattices whenever any of the site occupations approaches 1 [16]. Alternatively, correlation can be treated via orbital functionals, as discussed elsewhere [16,20]. In this paper, however, correlation effects are not included to keep things simple.…”

Section: A Modelmentioning

confidence: 99%

(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer

Ullrich

2019

Phys. Rev. A

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According to the Hohenberg-Kohn theorem of density-functional theory (DFT), all observable quantities of systems of interacting electrons can be expressed as functionals of the ground-state density. This includes, in principle, the spin polarization (magnetization) of open-shell systems; the explicit form of the magnetization as a functional of the total density is, however, unknown. In practice, open-shell systems are always treated with spin-DFT, where the basic variables are the spin densities. Here, the relation between DFT and spin-DFT for open-shell systems is illustrated and the exact magnetization density functional is obtained for the half-filled Hubbard trimer. Errors arising from spin-restricted and -unrestricted exact-exchange Kohn-Sham calculations are analyzed and partially cured via the exact magnetization functional. I. INTRODUCTION: DFT VERSUS SDFTFor the z-components, only the diagonal matrix elements are nonzero, and we get immediatelyB z 7,7 = B z 12,12 = −B z2 B z 8,8 = B z 10,10 = −B z3 B z 9,9 = B z 11,11 = −B z1 B z 13,13 = B z 18,18 = B z2 B z 14,14 = B z 16,16 = B z3 B z 15,15 = B z 17,17 = B z1 B z 19,19 = −B z1 − B z2 − B z3

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Section: A Modelmentioning

confidence: 99%

(Spin-)density-functional theory for open-shell systems: Exact magnetization density functional for the half-filled Hubbard trimer

Ullrich

2019

Phys. Rev. A

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“…According to the last member of Eq. (7) we can set a = b = c = d in the cofactor of (a − c)(b − d) in the Grassmann integral G given in (36). To do the thus simplified Grassmann integral we simply decompose the matrix m as m = (a − c)m + + (b − d)m − + (a − c)(b − d)m +− , reading the summands from the definition (33).…”

Section: B Generating Functionmentioning

confidence: 99%

“…This derivation was based on the supersymmetry method using the color-flavor transformation. The approach was later generalized to universal wave function statistics [33,34], chaotic scattering [35,36], and spectral correlators of all orders [37]. We here focus on directed graphs where the method finds its clearest and simplest realization.…”

Section: A Preliminary Remarksmentioning

confidence: 99%

“…Appendix G: Evaluation of the Grassmann integral (36) An economic way of doing the Grassmann integral G is by differentiation, dη * dηdτ * dτ (·) = ∂ η * ∂ η ∂ τ * ∂ τ (·), since the chain and product rules prove helpful. It is worthwhile to spell out the product rule since a peculiarity of Grassmann calculus must be pointed at.…”

Section: Appendix F: Derivation Of Eq 19mentioning

confidence: 99%

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A review of sigma models for quantum chaotic dynamics

et al. 2015

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We review the construction of the supersymmetric sigma model for unitary maps, using the colorflavor transformation. We then illustrate applications by three case studies in quantum chaos. In two of these cases, general Floquet maps and quantum graphs, we show that universal spectral fluctuations arise provided the pertinent classical dynamics are fully chaotic (ergodic and with decay rates sufficiently gapped away from zero). In the third case, the kicked rotor, we show how the existence of arbitrarily long-lived modes of excitation (diffusion) precludes universal fluctuations and entails quantum localization.2

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“…General analytical results exist only for the correlation function involving a pair of S-matrix elements [23], for select values of the correlation function involving three or four S-matrix elements [24,25], and for the probability distribution of single S-matrix elements [26,27,28,29]. The complete joint probability distribution of all S-matrix elements is known [30,31,32] only in the Ericson regime (strongly overlapping resonances). From a practical point of view, results beyond average cross sections and beyond the Ericson regime, especially for cross-section correlation functions, would be of considerable interest.…”

Section: Implementation Of the Goe For Nuclear Reactionsmentioning

confidence: 99%