Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?

Kröger, H.; Laprise, Jean-François; Melkonyan, G.; Zomorrodi, Reza

doi:10.1007/3-540-32023-7_20

Cited by 2 publications

(3 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Section: Introductionmentioning

confidence: 99%

“…Another problem of great theoretical interest is understanding how to compare quantum and classical chaos (temporal complexity) and explaining the reason why the former is weaker than the latter [22][23][24]. Indeed, it is commonly conjectured that the weakness of quantum chaos may be a consequence of the Heisenberg uncertainty relation [22][23][24]. It is also known that a quantum description of chaos is qualitatively different from a classical description and that the later cannot simply be considered an approximation of the former.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Softening the Complexity of Entropic Motion on Curved Statistical Manifolds

Cafaro

Giffin

Lupo

et al. 2012

Open Syst. Inf. Dyn.

View full text Add to dashboard Cite

We study the information geometry and the entropic dynamics of a 3D Gaussian statistical model. We then compare our analysis to that of a 2D Gaussian statistical model obtained from the higher-dimensional model via introduction of an additional information constraint that resembles the quantum mechanical canonical minimum uncertainty relation. We show that the chaoticity (temporal complexity) of the 2D Gaussian statistical model, quantified by means of the Information Geometric Entropy (IGE) and the Jacobi vector field intensity, is softened with respect to the chaoticity of the 3D Gaussian statistical model.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Softening the Complexity of Entropic Motion on Curved Statistical Manifolds

Cafaro

Giffin

Lupo

et al. 2012

Open Syst. Inf. Dyn.

View full text Add to dashboard Cite

show abstract

“…Comparing classical and quantum chaoticity (i.e. temporal complexity) and explaining the reason why the former is stronger than the latter is of great theoretical interest [58][59][60]. It is usually conjectured that the weakness of quantum chaos may be due to the Heisenberg uncertainty relation.…”

Section: G Example 7: Softening Of Classical Chaos By Quantizationmentioning

confidence: 99%

An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information

Ali

Cafaro

Gassner

et al. 2018

Advances in Mathematical Physics

View full text Add to dashboard Cite

Motivated by the presence of deep connections among dynamical equations, experimental data, physical systems, and statistical modeling, we report on a series of findings uncovered by the authors and collaborators during the last decade within the framework of the so-called Information Geometric Approach to Chaos (IGAC). The IGAC is a theoretical modeling scheme that combines methods of information geometry with inductive inference techniques to furnish probabilistic descriptions of complex systems in presence of limited information. In addition to relying on curvature and Jacobi field computations, a suitable indicator of complexity within the IGAC framework is given by the so-called information geometric entropy (IGE). The IGE is an information geometric measure of complexity of geodesic paths on curved statistical manifolds underlying the entropic dynamics of systems specified in terms of probability distributions. In this manuscript, we discuss several illustrative examples wherein our modeling scheme is employed to infer macroscopic predictions when only partial knowledge of the microscopic nature of a given system is available. Finally, we include comments on the strengths and weaknesses of the current version of our proposed theoretical scheme in our concluding remarks.

show abstract

Quantum Chaos Versus Classical Chaos: Why is Quantum Chaos Weaker?

Abstract: We discuss the questions: How to compare quantitatively classical chaos with quantum chaos? Which one is stronger? What are the underlying physical reasons?

Cited by 2 publications

References 27 publications

Softening the Complexity of Entropic Motion on Curved Statistical Manifolds

Softening the Complexity of Entropic Motion on Curved Statistical Manifolds

An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information

Contact Info

Product

Resources

About