Towards Rigorous Derivation of Quantum Kinetic Equations
arXiv:1008.2100 · doi:10.1088/1751-8113/43/48/485203
Abstract
We develop a rigorous formalism for the description of the evolution of states of quantum many-particle systems in terms of a one-particle density operator. For initial states which are specified in terms of a one-particle density operator the equivalence of the description of the evolution of quantum many-particle states by the Cauchy problem of the quantum BBGKY hierarchy and by the Cauchy problem of the generalized quantum kinetic equation together with a sequence of explicitly defined functionals of a solution of stated kinetic equation is established in the space of trace class operators. The links of the specific quantum kinetic equations with the generalized quantum kinetic equation are discussed.
25 pages
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Cited by in corpus (12)
- On Rigorous Derivation of the Enskog Kinetic Equation
- Quantum Kinetic Evolution of Marginal Observables
- Quantum Kinetic Equations of Many-Particle Systems in Condensed States
- Mean Field Asymptotic Behavior of Quantum Particles with Initial Correlations
- On Evolution Equations for Marginal Correlation Operators
- Kinetic equations and hierarchies of evolution equations of quantum systems
- Introduction to the Theory of Evolution Equations of Quantum Many-Particle Systems
- Mean Field Asymptotics of Generalized Quantum Kinetic Equation
- On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate
- On Dynamics of Correlations in Quantum Many-Particle Systems
- Cumulant expansions of operator groups of quantum many-particle systems
- On Operators Generated by Density Matrix