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The Solutions of Bbgky Hierarchy of Quantum Kinetic Equations for Dense Systems

M. Yu. Rasulova, Muzaffar Muhammadjanovich Rahmatullaev, Abul Hasan Siddiqi +1 more

Lecture notes in pure and applied mathematicsJul 19, 20051 citation

Cauchy problem for the BBGKY hierarchy. One-dimensional quantum lattice systems

Alexander K. Vidybida

Theoretical and Mathematical PhysicsJun 1, 19792 citations

Quantum Kinetic Equations and Evolution of Many-Particle Systems

V. I. Gerasimenko

In the paper we discuss possible approaches to the problem of the rigorous derivation of quantum kinetic equations from underlying many-particle dynamics. For the description of a many-particle evolution we construct solutions of the Cauchy problems of the BBGKY hierarchy and the dual BBGKY hierarchy in suitable Banach spaces. In the framework of the conventional approach to the description of kinetic evolution the mean-field asymptotics of the quantum BBGKY hierarchy solution is constructed. We develop also alternative approaches. One method is based on the construction of the solution asymptotics of the initial-value problem of the quantum dual BBGKY hierarchy. One more approach is based on the generalized quantum kinetic equation that is a consequence of the equivalence of the Cauchy problems of such evolution equation and the BBGKY hierarchy with initial data determined by the one-particle density operator.In the paper we discuss possible approaches to the problem of the rigorous derivation of quantum kinetic equations from underlying many-particle dynamics. For the description of a many-particle evolution we construct solutions of the Cauchy problems of the BBGKY hierarchy and the dual BBGKY hierarchy in suitable Banach spaces. In the framework of the conventional approach to the description of kinetic evolution the mean-field asymptotics of the quantum BBGKY hierarchy solution is constructed. We develop also alternative approaches. One method is based on the construction of the solution asymptotics of the initial-value problem of the quantum dual BBGKY hierarchy. One more approach is based on the generalized quantum kinetic equation that is a consequence of the equivalence of the Cauchy problems of such evolution equation and the BBGKY hierarchy with initial data determined by the one-particle density operator.

arXiv:0908.2797Aug 19, 20090 citations

Nonlinear Amplitude Equations and Soliton Excitations in Bose-Einstein Condensates

Guoxiang Huang

Springer eBooksFeb 18, 20074 citations

THE RELATION BETWEEN SOLUTION OF BBGKY HIERARCHY OF KINETIC EQUATIONS AND THE SOLUTION OF WIGNER EQUATION

M. Yu. Rasulova

The solution of BBGKY hierarchy of quantum kinetic equations is defined through the solution of the Wigner equation.

Jan 1, 20060 citations

Higher Dimensional Nonlinear Schrödinger Equations of Bose–Einstein Condensates

Wu‐Ming Liu, Emmanuel Kengne

Springer eBooksJan 1, 20190 citations