Quantum Kinetic Evolution of Marginal Observables
arXiv:1009.1814 · doi:10.3934/krm.2011.4.385
Abstract
We develop a rigorous formalism for the description of the evolution of observables of quantum systems of particles in the mean-field scaling limit. The corresponding asymptotics of a solution of the initial-value problem of the dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution of marginal observables and the evolution of quantum states described in terms of a one-particle marginal density operator are established. Such approach gives the alternative description of the kinetic evolution of quantum many-particle systems to generally accepted approach on basis of kinetic equations.
18 pages
References in corpus (7)
- On the quantum Boltzmann equation
- Mean-Field- and Classical Limit of Many-Body Schrödinger Dynamics for Bosons
- Mean-field limit and Semiclassical Expansion of a Quantum Particle System
- Dynamics of Correlations of Bose and Fermi Particles
- Towards Rigorous Derivation of Quantum Kinetic Equations
- The von Neumann Hierarchy for Correlation Operators of Quantum Many-Particle Systems
- Groups of Operators for Evolution Equations of Quantum Many-Particle Systems
Cited by in corpus (13)
- Quantum Kinetic Equations of Many-Particle Systems in Condensed States
- The Boltzmann-Grad asymptotic behavior of collisional dynamics: a brief survey
- Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations
- On Semigroups of Large Particle Systems and their Scaling Asymptotic Behavior
- Approaches to Derivation of the Boltzmann Equation with Hard Sphere Collisions
- On Kinetic Equations Modeling Evolution of Systems in Mathematical Biology
- Kinetic equations and hierarchies of evolution equations of quantum systems
- On Evolution Equations for Marginal Correlation Operators
- Mean Field Asymptotics of Generalized Quantum Kinetic Equation
- Non-perturbative solutions of hierarchies of evolution equations for colliding particles
- Introduction to the Theory of Evolution Equations of Quantum Many-Particle Systems
- On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate
- Cumulant expansions of operator groups of quantum many-particle systems