Non-Markovian Boltzmann Equation

Kremp, D.; Bönitz, M.; Kraeft, W. D.; Schlanges, M.

doi:10.1006/aphy.1997.5703

Cited by 58 publications

(70 citation statements)

References 39 publications

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“…At present, a lot of actual problems still remain in the relativistic kinetic theory, e.g., going beyond the quasiparticle approximation, taking into account nonlocal (and, in particular, non-Markovian) effects in kinetic processes, cluster decomposition, etc. (see, e.g., [1,27,28,36,37,38,43,44,46]). An important feature of the examined approach is a lack of some dynamical constraints into a corresponding quantum field theory (these constraints are introduced in order to eliminate "unnecessary", non-physical degrees of freedom).…”

Section: Discussionmentioning

confidence: 99%

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A Covariant Generalization of the Real-Time Green's Functions Method in the Theory of Kinetic Equations

Smolyansky

Prozorkevich

Maino

et al. 2000

Progress in Nonequilibrium Green's Functions

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A generalized quantum kinetic equation (RKE) of the Kadanoff-Baym type is obtained on the basis of the Heisenberg equations of motion where the time evolution and space translation are separated from each other by means of the covariant method. The same approach is used also for a covariant modification of the real-time Green's functions method based on the Wigner representation. The suggested approach does not contain arbitrariness' elements and uncertainties which often arise from derivation of RKE on the basis of the motion equations of the Kadanoff-Baym type for the correlation functions in the case of systems with inner degrees of freedom.Possibilities of the proposed method are demonstrated by examples of derivation of RKE of the Vlasov type and collision integrals of the Boltzmann-Uehling-Uhlenbeck (BUU) type in the frame of the σω-version of quantum hadrodynamics, for the simplest case of spin saturated nuclear matter without antinuclear component. Here, the quasiparticle approximation in a covariant performance is used. A generalization of the method for the description of strong non-equilibrium states based on the non-equilibrium statistical operator is then proposed as well.

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Section: Discussionmentioning

confidence: 99%

“…RKE (46) converts in RKE of the Vlasov type when conditions of the collision effects are neglected (S(xP ) = 0). The Vlasov RKE in this form was obtained and analyzed for the first time in Refs.…”

Section: Generalized Rkementioning

confidence: 99%

A Covariant Generalization of the Real-Time Green's Functions Method in the Theory of Kinetic Equations

Smolyansky

Prozorkevich

Maino

et al. 2000

Progress in Nonequilibrium Green's Functions

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“…[29,31,32] and, in the weak coupling limit, reduces to the second Born approximation (first term); the "+" ("-") in Eq. (5) refers to bosons (fermions) and summation over l is implied.…”

Section: Nonequilibrium Green Functions T-matrix Approximationmentioning

confidence: 99%

Toward a Nonequilibrium Green Functions Approach to Diffusion in Strongly Coupled Finite Quantum Systems

Bönitz

Schlünzen

Hermanns

2014

Contrib. Plasma Phys.

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Transport properties of strongly correlated quantum systems are of central interest in condensed matter, ultracold atoms and in dense plasmas. There, the proper treatment of strong correlations poses a great challenge to theory. Here, we apply a Nonequilibrium Green Functions approach using a lattice model as a basic system. This allow us to treat a finite spatially inhomogeneous system with an arbitrary nonequilibrium initial state. Placing all particles initially to one side of the system allows for a nonequilibrium study of diffusion. Strong correlation effects are incorporated via T‐matrix selfenergies. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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“…In Ref. [12], this equation has been derived within the density operator technique. The nonequilibrium Green's functions approach, however, opens the possibility to derive two-time quantum kinetic equations with their well-known advantages (e.g.…”

Section: Generalized T-matrix Approximationmentioning

confidence: 99%

Kadanoff–Baym equations and non-Markovian Boltzmann equation in generalized T-matrix approximation

Semkat

Kremp

Bönitz

2000

Journal of Mathematical Physics

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A recently developed method [1,2] for incorporating initial binary correlations into the KadanoffBaym equations (KBE) is used to derive a generalized T-matrix approximation for the self-energies. It is shown that the T-matrix obtains additional contributions arising from initial correlations. Using these results and taking the time-diagonal limit of the KBE, a generalized quantum kinetic equation in binary collision approximation is derived. This equation is a far-reaching generalization of Boltzmann-type kinetic equations: it selfconsistently includes memory effects (retardation, off-shell T-matrices) as well as many-particle effects (damping, in-medium T-matrices) and spin-statistics effects (Pauli-blocking).

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Non-Markovian Boltzmann Equation

Cited by 58 publications

References 39 publications

A Covariant Generalization of the Real-Time Green's Functions Method in the Theory of Kinetic Equations

A Covariant Generalization of the Real-Time Green's Functions Method in the Theory of Kinetic Equations

Toward a Nonequilibrium Green Functions Approach to Diffusion in Strongly Coupled Finite Quantum Systems

Kadanoff–Baym equations and non-Markovian Boltzmann equation in generalized T-matrix approximation

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