Lyapunov exponent in quantum mechanics. A phase-space approach

DOI10.1016/S0167-2789(00)00117-2zbMath0982.81029arXivquant-ph/0002049OpenAlexW2003766539MaRDI QIDQ1589749

R. Vilela Mendes, Vladimir I. Man'ko

Publication date: 16 April 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/quant-ph/0002049

zbMATH Keywords

probability distributionsWigner functionsquantum tomographysymplectic tomography map

Mathematics Subject Classification ID

Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30)

Related Items (17)

Upper quantum Lyapunov exponent and Anosov relations for quantum systems driven by a classical flow ⋮ On the notion of quantum Lyapunov exponent ⋮ Bifurcation conditions for the solutions of the Lyapunov equation in a Hilbert space ⋮ Quantum Lyapunov spectrum ⋮ Matter-wave chaos with a cold atom in a standing-wave laser field ⋮ Center of mass tomography for reconstructing quantum states of multipartite systems ⋮ Probability description and entropy of classical and quantum systems ⋮ On the tomographic description of classical fields ⋮ Boundary-value problems for the evolutionary Schrödinger equation. I ⋮ One Lyapunov control for quantum systems and its application to entanglement generation ⋮ Star products, duality and double Lie algebras ⋮ Radon transform of the Wheeler-De Witt equation and tomography of quantum states of the universe ⋮ Tomographic representation of minisuperspace quantum cosmology and Noether symmetries ⋮ Photon waiting-time distributions: A keyhole into dissipative quantum chaos ⋮ Quantum Lyapunov exponents beyond continuous measurements ⋮ Tomographic representation of evolution equation for density matrix of open system ⋮ Quantum sensitive dependence

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A proof of Oseledec's multiplicative ergodic theorem
• Dynamical entropy of C *-algebras and von Neumann algebras
• Chaos in classical and quantum mechanics
• Remarks on quantum characteristic exponents
• On the existence of quantum characteristic exponents
• Unified theory of Lyapunov exponents and a positive example of deterministic quantum chaos
• On the computation of quantum characteristic exponents.
• Noncommutative time-frequency tomography.
• Regular and chaotic quantum motions.
• Symplectic tomography as classical approach to quantum systems.
• Non-stochasticity of time-dependent quadratic Hamiltonians and the spectra of canonical transformations
• Statistics and quantum chaos
• Sensitive dependence and entropy for quantum systems
• Quantized Arnold cat maps can be entropic K-systems
• On quantum characteristic exponents
• On the Quantum Correction For Thermodynamic Equilibrium
• Time-dependent invariants for dirac equation and Newton–Wigner position operator
• Quantum chaos
• Chaotic observables for a free quantum particle
• Classical and quantum localization and delocalization in the Fermi accelerator, kicked rotor and two‐sided kicked rotor models

This page was built for publication: Lyapunov exponent in quantum mechanics. A phase-space approach