The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for many-body dissipative randomly driven systems

  title={The Bogolyubov-Born-Green-Kirkwood-Yvon hierarchy and Fokker-Planck equation for many-body dissipative randomly driven systems},
  author={Oleksii Sliusarenko and Alexei Chechkin and Yu. V. Slyusarenko},
  journal={Journal of Mathematical Physics},
By generalizing Bogolyubov’s reduced description method, we suggest a formalism to derive kinetic equations for many-body dissipative systems in external stochastic field. As a starting point, we use a stochastic Liouville equation obtained from Hamilton’s equations taking dissipation and stochastic perturbations into account. The Liouville equation is then averaged over realizations of the stochastic field by an extension of the Furutsu-Novikov formula to the case of a non-Gaussian field. As… 

Corrections to the Landau kinetic equation for a weakly dissipative randomly driven system and the fluctuation-dissipation theorem

This paper is devoted to the derivation of a kinetic equation for many-body one-component dissipative systems in an external random field. The system under consideration was discussed in the recent

Reduced description method in the kinetic theory of Brownian motion with active fluctuations

We develop a microscopic approach to the kinetic theory of many-particle systems with dissipative and potential interactions in the presence of active fluctuations. The approach is based on a

On the kinetics of a many-body dissipative system placed in a random field

  • V. GorevA. Sokolovsky
  • Physics, Mathematics
    2017 XXIInd International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED)
  • 2017
A kinetic equation for a dissipative system is obtained up to the second order in small potential interaction, small dissipative interaction and small correlation functions of an external random

Kinetic theory of weakly ionized dilute gas of hydrogen-like atoms of the first principles of quantum statistics and dispersion laws of eigenwaves

We develop a microscopic approach to the construction of the kinetic theory of dilute weakly ionized gas of hydrogen-like atoms. The approach is based on the statements of the second quantization

Kinetics of low-temperature gas of hydrogen-like atoms in an external electromagnetic field

A microscopic approach for the construction of the kinetic theory of low-temperature hydrogen-like gases in an external electromagnetic field was developed. The approach is based on the formulation

Reticulate collisional structure in boundary-driven granular gases.

A peculiar head-on collision network between two vibrating boundaries is reported, which is due to an orientation correlation between the relative position and velocity of any particle pair, and the molecular chaos assumption is violated in a larger portion of the phase space.

Random First Order Transition from a Supercooled Liquid to an Ideal Glass (Review)

The random first order transition theory (RFOT) describing the transition from a supercooled liquid to an ideal glass has been actively developed over the last twenty years. This theory is formulated

A Complete Bibliography of Publications in the Journal of Mathematical Physics: 2005{2009

(2 < p < 4) [200]. (Uq(∫u(1, 1)), oq1/2(2n)) [92]. 1 [273, 79, 304, 119]. 1 + 1 [252]. 2 [352, 318, 226, 40, 233, 157, 299, 60]. 2× 2 [185]. 3 [456, 363, 58, 18, 351]. ∗ [238]. 2 [277]. 3 [350]. p

Метод колективних змінних в теорії нелінійних флуктуацій з урахуванням кінетичних процесів

Для узгодженого опису кiнетики та гiдродинамiки систем взаємодiючих частинок оптимiзовано набiр параметрiв скороченого опису згiдно з Боголюбовим, що передбачає залучення колективних змiнних. При

Generalization of the Landau-Vlasov kinetic equation for a dissipative randomly driven system

  • V. GorevA. Sokolovsky
  • Physics, Mathematics
    2017 IEEE International Young Scientists Forum on Applied Physics and Engineering (YSF)
  • 2017
The Landau-Vlasov kinetic equation is generalized for dissipative randomly driven systems. The work is a development of the paper by Sliusarenko, Chechkin, and Slyusarenko (J. Math. Phys., 56,



Anomalous transport due to long-lived fluctuations in plasma Part 1. A general formalism for two-time fluctuations

A general formalism for describing two-time fluctuations in magnetized plasma is presented. Two-time expectations of one-body operators (phase functions) are written in terms of the phase space

Perspectives on the mode-coupling approximation for the dynamics of interacting Brownian particles

We analyse the field theory for the dissipative dynamics of interacting inertialess particles, using a dynamic density-wave model (Bagchi 1987Physica A 145 273), including thermal fluctuations (Dean

Self-propelled particles with selective attraction–repulsion interaction: from microscopic dynamics to coarse-grained theories

In this work we derive and analyse coarse-grained descriptions of self-propelled particles with selective attraction–repulsion interaction, where individuals may respond differently to their

Towards a quantitative kinetic theory of polar active matter

A recent kinetic approach for Vicsek-like models of active particles is reviewed. The theory is based on an exact Chapman- Kolmogorov equation in phase space. It can handle discrete time dynamics and

Dissipative dynamics for hard spheres

The dynamics for a system of hard spheres with dissipative collisions is described at the levels of statistical mechanics, kinetic theory, and simulation. The Liouville operator(s) and associated

Transport coefficients for driven granular mixtures at low density.

  • N. KhalilV. Garzó
  • Physics
    Physical review. E, Statistical, nonlinear, and soft matter physics
  • 2013
The transport coefficients of a granular binary mixture driven by a stochastic bath with friction are determined from the inelastic Boltzmann kinetic equation. A normal solution is obtained via the