On nonlinear Koopman's construction

DOI10.1016/S0034-4877(97)85899-5zbMath0912.46066OpenAlexW2062033134MaRDI QIDQ1387124

Marcin Marciniak, Wladyslaw Adam Majewski

Publication date: 3 May 1999

Published in: Reports on Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0034-4877(97)85899-5

zbMATH Keywords

quantum dynamical systemsquantum chaosGelfand transformKoopman's constructionabelian unital \(C^*\)-algebraextension of the pure state spaceGelfand-Najmark theoremintroducing nonlinearity

Mathematics Subject Classification ID

Quantum chaos (81Q50) Noncommutative dynamical systems (46L55) Applications of selfadjoint operator algebras to physics (46L60) Applications of functional analysis in statistical physics (46N55)

Related Items (5)

On quantum quadratic operators of \(\mathbb M_2(\mathbb C)\) and their dynamics ⋮ Remarks on quantum characteristic exponents ⋮ QUADRATIC STOCHASTIC OPERATORS AND PROCESSES: RESULTS AND OPEN PROBLEMS ⋮ On Pure Quasi-Quantum Quadratic Operators of 𝕄2(ℂ) II ⋮ On Pure Quasi-Quantum Quadratic Operators of 𝕄₂(ℂ)

Cites Work

• Convergence of the quantum Boltzmann map
• Nonlinear quantum dynamical semigroups for many-body open systems
• Quantum dynamical system with hyperbolic instabilities
• Remarks on quantum characteristic exponents
• Nonlinear Schrödinger-type field equation for the description of dissipative systems. I. Derivation of the nonlinear field equation and one-dimensional example
• On quantum characteristic exponents
• Anosov actions on noncommutative algebras
• Spectral properties of quantumN-body systems versus chaotic properties of their mean-field approximations
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