Quantum Kinetic Equations: Correlation Dynamics and Selfenergy

Abstract

The derivation of non-Markovian quantum kinetic equations is reconsidered in the framework of density operators. Conventional-derivations use for the decoupling of the BBGKY-hierarchy the assumption of vanishing thretpartide correlations ~1 2 3 e 0. This yields non-Markovian kinetic equations with infinite memory depth. We discuss a different closure. relation to the hierarchy, which overcomes this difficulty without sasumptions on weakening of initial correlations and in fact corresponds to the indurion of selfenergy effects (beyond HartretFock).

Non-Markovian Boltzmann Equation

“…of Eq. (15) we have to replace (for details see [50]) (33) and similarly for the terms with 1 W 2. This gives rise to Pauli-blocking and exchange contributions in the retarded self-energy 7 + and to an additional contribution (due to the second term on the r.h.s.…”

“…are included to achieve a consistent treatment of the collision integral and self-energy [38,48]. The simpler case of self-energy in the second Born approximation has been developed in [27,26,49] and is studied in detail in [50]. Damping effects have also been derived for the electron phonon problem in [22].…”

Spectral function and kinetic equation for a normal Fermi liquid

“…The last equality in Eq. ( 28) follows with the help of the expressions (2), (7), and (22). Now taking into account the renormalizing factors standing with the second terms in Eqs.…”

Correlations in many-body systems with two-time Green’s functions

“…Since the first numerical applications of the KBequations by Danielewicz [2] several contributions to this evolving new field have been published with applications to nuclear matter [5,3,6,7], to one-and two-band semiconductors [8,9],to phonon-production in e-e collisions in plasmas [10] as well as to electron plasmas in general [11,12]. Details of the computational methods is published in Computer Physics Communications [13].…”