scholarly journals Quantum Vlasov equation and its Markov limit

1998 ◽  
Vol 58 (12) ◽  
Author(s):  
Yuval Kluger ◽  
Emil Mottola ◽  
Judah M. Eisenberg
1967 ◽  
Vol 22 (6) ◽  
pp. 869-872 ◽  
Author(s):  
D. BlSkamp

The selfconsistent field equation (VLASOV equation) is derived for the one-particle WIGNER function of a relativistic electron-positron gas. From the linearized form we obtain the dispersion relation for any quasi-equilibrium state, which for the special case of thermal equilibrium has already been derived by TSYTOVICH 1.


Author(s):  
Nathalie Deruelle ◽  
Jean-Philippe Uzan

This chapter covers the equations governing the evolution of particle distribution and relates the macroscopic thermodynamical quantities to the distribution function. The motion of N particles is governed by 6N equations of motion of first order in time, written in either Hamiltonian form or in terms of Poisson brackets. Thus, as this chapter shows, as the number of particles grows it becomes necessary to resort to a statistical description. The chapter first introduces the Liouville equation, which states the conservation of the probability density, before turning to the Boltzmann–Vlasov equation. Finally, it discusses the Jeans equations, which are the equations obtained by taking various averages over velocities.


2001 ◽  
Vol 159 (2) ◽  
pp. 85-108 ◽  
Author(s):  
E. Caglioti ◽  
S. Caprino ◽  
C. Marchioro ◽  
M. Pulvirenti

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