Chaos, ergodicity, and equilibria in a quantum Kac model

DOI10.1016/j.aim.2019.106827zbMath1427.35172arXiv1804.10280OpenAlexW2980696070MaRDI QIDQ2335488

Michael Loss, Eric Anders Carlen, Maria Conception Carvalho

Publication date: 14 November 2019

Published in: Advances in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1804.10280

zbMATH Keywords

equilibriumcompletely positivequantum master equation

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Applications of operator algebras to the sciences (47L90) Quantum chaos (81Q50) Derivations, dissipations and positive semigroups in (C^*)-algebras (46L57) Boltzmann equations (35Q20)

Related Items

The Kac model: variations on a theme

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Speed of approach to equilibrium for Kac's caricature of a Maxwellian gas
• On Villani's conjecture concerning entropy production for the Kac master equation
• General state changes in quantum theory
• Entropy and chaos in the Kac model
• A Schwarz inequality for positive linear maps on C\(^*\)-algebras
• Completely positive maps and entropy inequalities
• The eigenvalues of Kac's master equation
• On the rate of entropy production for the Boltzmann equation
• Cercignani's conjecture is sometimes true and always almost true
• Spectral gap for Kac's model of Boltzmann equation.
• Determination of the spectral gap for Kac's master equation and related stochastic evolution.
• A generalized Schwarz inequality and algebraic invariants for operator algebras
• Kinetic Theory and the Kac Master Equation
• Entropy is the only increasing functional of Kac's one-dimensional caricature of a Maxwellian gas
• Positive Functions on C ∗ -Algebras