Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization of classical systems to arbitrary Hamiltonian (Lie-Jordan, or Poissonian) algebras, in particular to the algebras of operators in indefinite spaces. A functional calculus is developed for the uniformized observables, which unifies the calculi of generating functionals for classical, Bosonian and Fermionian multiparticle variables. The nonlinear kinetic equation of Vlasov and Hartree type are derived for both classical and quantum multiparticle Hamiltonian systems in the mean field approximation. The possibilities for finding approximate solutions of these equations from the solutions of uniformized linear equations are investigated.Nonlinear Hamiltonian systems describing the abstract Vlasov and Hartree equations are considered in the framework of algebraic Poissonian theory. The concept of uniformization is introduced; it generalizes the method of second quantization of classical systems to arbitrary Hamiltonian (Lie-Jordan, or Poissonian) algebras, in particular to the algebras of operators in indefinite spaces. A functional calculus is developed for the uniformized observables, which unifies the calculi of generating functionals for classical, Bosonian and Fermionian multiparticle variables. The nonlinear kinetic equation of Vlasov and Hartree type are derived for both classical and quantum multiparticle Hamiltonian systems in the mean field approximation. The possibilities for finding approximate solutions of these equations from the solutions of uniformized linear equations are investigated.

arXiv:math-ph/0512051Dec 15, 20050 citations

Multiparticle correlated wave function for Bose systems

Sudip Chakravarty, Chia-Wei Woo

A correlated wave function for interacting Bose systems with correlation factors up to five-particle parts is suggested. The vehicle used is an analysis for the weakly interacting Bose gas by a new method. Terms up to $O({\ensuremath{\lambda}}^{2})$, where $\ensuremath{\lambda}$ measures the strength of the interaction, for the two-particle (Jastrow) factor and the three-particle factor, as well as ground-state energy up to $O({\ensuremath{\lambda}}^{4})$, are shown to agree with exact results obtained previously with other methods. New results include all multiparticle correlation factors up to $O({\ensuremath{\lambda}}^{4})$. The wave function will be most useful for analytically soluble model systems, and more importantly, for Monte Carlo or molecular-dynamics calculations dealing with realistic systems such as superfluid $^{4}\mathrm{He}$ .A correlated wave function for interacting Bose systems with correlation factors up to five-particle parts is suggested. The vehicle used is an analysis for the weakly interacting Bose gas by a new method. Terms up to $O({\ensuremath{\lambda}}^{2})$, where $\ensuremath{\lambda}$ measures the strength of the interaction, for the two-particle (Jastrow) factor and the three-particle factor, as well as ground-state energy up to $O({\ensuremath{\lambda}}^{4})$, are shown to agree with exact results obtained previously with other methods. New results include all multiparticle correlation factors up to $O({\ensuremath{\lambda}}^{4})$. The wave function will be most useful for analytically soluble model systems, and more importantly, for Monte Carlo or molecular-dynamics calculations dealing with realistic systems such as superfluid $^{4}\mathrm{He}$.

Physical review. B, Solid stateJan 1, 19765 citations

Multiparticle correlations of an oscillating scatterer

Michael V. Moskalets, Μ. Büttiker

Using multiparticle distribution functions, we calculate the correlations produced by a periodically driven scatterer in a system of noninteracting electrons at zero temperature. The multiparticle correlations due to a quantum exchange effect are expressed in terms of photon-assisted scattering amplitudes. The results we obtain are valid for slow but arbitrary in strength driving. We show that even for large amplitude pumps the zero-frequency noise power is related to two-particle correlations. In addition to two-particle correlations a large amplitude pump can generate multiparticle correlations.Using multiparticle distribution functions, we calculate the correlations produced by a periodically driven scatterer in a system of noninteracting electrons at zero temperature. The multiparticle correlations due to a quantum exchange effect are expressed in terms of photon-assisted scattering amplitudes. The results we obtain are valid for slow but arbitrary in strength driving. We show that even for large amplitude pumps the zero-frequency noise power is related to two-particle correlations. In addition to two-particle correlations a large amplitude pump can generate multiparticle correlations.

arXiv:cond-mat/0511398Physical Review BMar 15, 200618 citations

^{4}\mathrm{He}