Tomaschitz, R. (1992). Relativistic quantum chaos in de Sitter cosmologies, in: Quantum Chaos – Quantum Measurement (Copenhagen, May 28 - June 1, 1991, P. Cvitanovic, I. Percival, A. Wirzba, eds.) NATO Science Series C 358, Kluwer, Dordrecht, 1992, pp. 187-197.

 

 

Abstract (SpringerLink, CDS, SAO/NASA ADS)

We consider classical and quantal motion in open de Sitter cosmologies of multiple spatial connectivity. The topological structure of the spacelike slices creates on the one hand chaotic trajectories, on the other hand bound states whose wave fields and energies are intimately connected with the Hausdorff dimension and measure of limit sets of chaotic trajectories in the covering space of the manifold. We discuss the time evolution of the energy of wave fields coupled to the curvature scalar of the 4-manifold in the early and late stages of the cosmic expansion, and its dependence on the spectral variable of the Laplace-Beltrami operator on the space sections. This spectrum is in turn entirely determined by the topological and metrical structure of the sections.

 

 

 

 

Title:

 

Relativistic quantum chaos in de Sitter cosmologies

Authors:

 

Tomaschitz, Roman

Affiliation:

 

AA(Dipartimento di Matematica Pura ed Applicata dell' Università degli Studi di Padova, Via Belzoni 7, I-35131 Padova, Italy)

Publication:

 

Relativistic quantum chaos in de Sitter cosmologies, in: Quantum Chaos - Quantum Measurement (P. Cvitanovic, I. Percival, A. Wirzba, eds.) NATO Science Series C 358, Kluwer, Dordrecht, 1992, pp. 187-197

Publication Date:

 

00/1992

Origin:

 

AUTHOR

Keywords:

 

relativistic chaos, de Sitter universe, multiply connected hyperbolic 3-space

Abstract Copyright:

 

Springer

Bibliographic Code:

 

1992qcqm.book..187T

 

 

 

 

Fig. 1: Tiling induced on the sphere at infinity of the Poincaré ball by the universal cover of the manifold. The quasi self-similar Jordan curve determines the bounded trajectories, and its Hausdorff measure the corresponding chaotic wave fields. g(S) = 19, δ = 1.382.

 

Fig. 1: Tiling induced on the sphere at infinity of the Poincaré ball by the universal cover of the manifold. The quasi self-similar Jordan curve determines the bounded trajectories, and its Hausdorff measure the corresponding chaotic wave fields. g(S) = 19, δ = 1.382. full size image

 

 

 

Fig. 2: As Fig. 1, covering of S∞ stemming from a spacelike section t = const. of the 4-manifold. Figs. 1,2 show tilings of two non-isometric points on a path (F(t),Γ(t)) in the deformation space of the topological manifold I × S. g(S) = 19, δ = 1.424.

 

Fig. 2: As Fig. 1, covering of S stemming from a spacelike section t  = const. of the 4-manifold. Figs. 1,2 show tilings of two non-isometric points on a path (F(t),Γ(t)) in the deformation space of the topological manifold I × S. g(S) = 19, δ = 1.424. full size image

 

 

description: Roman Tomaschitz (1992) Relativistic quantum chaos in de Sitter cosmologies, in: Quantum Chaos – Quantum Measurement (P. Cvitanovic, I. Percival, A. Wirzba, eds.) NATO Science Series C 358, Kluwer, Dordrecht, pp. 187-197.

 

Keywords: relativistic chaos, open de Sitter universe with multiply connected hyperbolic 3-space, constant negative curvature, Klein–Gordon equation, Laplace–Beltrami operator, energy of scalar wave fields on open hyperbolic 3-manifolds, time evolution and positivity of energy, ground state energy, fractal limit sets of Kleinian groups, quasi-Fuchsian covering groups, Hausdorff measure and dimension of a limit set, polyhedral tessellation of hyperbolic space, universal covering projection, localized ground-state wave function on open hyperbolic 3-manifolds, Poisson kernel, chaotic world lines, deformation spaces of fibered hyperbolic 3-manifolds

 

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