scholarly journals Ruelle and Quantum Resonances for Open Hyperbolic Manifolds

2018 ◽  
Vol 2020 (5) ◽  
pp. 1445-1480
Author(s):  
Charles Hadfield
Keyword(s):  
Geodesic Flow ◽  
Hyperbolic Manifolds ◽  
Quantum Resonances ◽  
Classical Quantum ◽  
Convex Cocompact ◽  
Quantum Correspondence

Abstract We establish a direct classical-quantum correspondence on convex cocompact hyperbolic manifolds between the spectra of the geodesic flow and the Laplacian acting on natural tensor bundles. This extends previous work detailing the correspondence for cocompact quotients.

Classical-Quantum Correspondence for Above-Threshold Ionization

2014 ◽  
Vol 112 (11) ◽  
Author(s):  
Min Li ◽  
Ji-Wei Geng ◽  
Hong Liu ◽  
Yongkai Deng ◽  
Chengyin Wu ◽  
...  
Keyword(s):  
Threshold Ionization ◽  
Above Threshold Ionization ◽  
Classical Quantum ◽  
Quantum Correspondence

Quantum Spectra and Classical Orbits in Nano-Microstructure

2010 ◽  
Vol 160-162 ◽  
pp. 625-629 ◽  
Author(s):  
Jun Lu ◽  
Xue Mei Wang
Keyword(s):  
Closed Orbit ◽  
Three Dimensional ◽  
Spectrum Function ◽  
Molecular Reaction ◽  
Classical Quantum ◽  
Orbit Theory ◽  
Quantum Correspondence ◽  
New Evidence ◽  
Quantum Spectrum ◽  
Classical Orbits

A kind of new classical-quantum correspondence principle is proposed using the idea of closed-orbit theory. The quantum spectrum function is introduced by means of the eigenvalues and the eigenfunctions in the system of one-dimensional nano-microstructure. The Fourier transformation of the quantum spectrum function is found corresponding with the classical orbits in the system. These results give new evidence about the classical-quantum correspondence. All the methods and results can be used in a lot of other systems, including some two-dimensional and three-dimensional systems. The researches about these systems are very important in the field of applied science, for example, molecular reaction dynamics and quantum information.

A variation formula for the topological entropy of convex-cocompact manifolds

2010 ◽  
Vol 31 (6) ◽  
pp. 1849-1864 ◽  
Author(s):  
SAMUEL TAPIE
Keyword(s):  
Hausdorff Dimension ◽  
Explicit Formula ◽  
Topological Entropy ◽  
Geodesic Flow ◽  
Kleinian Group ◽  
Limit Set ◽  
Analytic Family ◽  
Variation Formula ◽  
Sectional Curvatures ◽  
Convex Cocompact

AbstractLet (M,gλ) be a 𝒞2-family of complete convex-cocompact metrics with pinched negative sectional curvatures on a fixed manifold. We show that the topological entropy htop(gλ) of the geodesic flow is a 𝒞1 function of λ and we give an explicit formula for its derivative. We apply this to show that if ρλ(Γ)⊂PSL2(ℂ) is an analytic family of convex-cocompact faithful representations of a Kleinian group Γ, then the Hausdorff dimension of the limit set Λρλ(Γ) is a 𝒞1 function of λ. Finally, we give a variation formula for Λρλ (Γ).

Classical-Quantum Correspondence in the Presence of Global Chaos

1988 ◽  
Vol 61 (24) ◽  
pp. 2733-2736 ◽  
Author(s):  
Robert L. Waterland ◽  
Jian-Min Yuan ◽  
Craig C. Martens ◽  
Richard E. Gillilan ◽  
William P. Reinhardt
Keyword(s):  
Classical Quantum ◽  
Quantum Correspondence
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