ISSN:
1572-9613
Keywords:
Van Hove's two-time method
;
Wigner function on energy and time
;
two-time dyad
;
Liouvillian
;
energy superoperator
;
quantum kinetic equation
;
factorization theorem
;
second-order approximation in density expansion
;
three-particle scattering
;
δ shell potential
;
resonance scattering
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract Van Hove's partial density matrix,ρ E (t), in his generalized master equation is interpreted as a Wigner representation of “two-time dyad” for “energy E” and “time t”. This interpretation enables us to integrate the “energy”E in Van Hove's master equation. The resultant equation is of non-Markov type on two time parameters. Starting with this master equation, the derivation of quantum kinetic equations, including the second-order approximation in the density expansion, is discussed. The scaling of the quantum kinetic equation is examined in detail for a system in which particles interact through the delta shell potential. It is shown that the quantum kinetic equation, including three-particle scattering, may exist for the physical situations of low-energy scattering,high-energy scattering, and for resonance scattering for time scales of the system sufficiently separated. In deriving the quantum kinetic equation, a factorization theorem form-particle distribution functions is proved to arbitrary order in perturbation expansion.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01011877
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