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By Michael Bonitz

This booklet provides quantum kinetic conception in a entire method. the point of interest is on density operator tools and on non-equilibrium eco-friendly services. the speculation permits to carefully deal with nonequilibrium dynamics in quantum many-body platforms. Of specific curiosity are ultrafast tactics in plasmas, condensed topic and trapped atoms which are prompted via quickly constructing experiments with brief pulse lasers and unfastened electron lasers. to explain those experiments theoretically, the main strong procedure is given via non-Markovian quantum kinetic equations which are mentioned intimately, together with computational facets.

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Von Neumann Equation 31 Each of these micro-states will be realized with a certain probability Wk , with Wk ≥ 0 M and Wk = 1. 8) k=1 The main properties of the density operator are 1. N = 1 2. e. ρ is the projection operator onto this state. On the other hand, in a mixed state, ρ has a statistical (probabilistic) meaning, which is introduced by Wk . 3. N 4. i... N = ρ1... N , (identical particles) 5. 9) 6. N contains the full quantum-mechanical information on the N -particle state without any losses.

Bärwinkel and Grossmann were the first to show that total energy conservation in kinetic equations is closely related to the time structure (non-Markovian or retardation effects) of the collision integral [84, 85]. 35 In particular, the kinetic equations derived by Prigogine contain an initial correlation term and a t non-Markovian scattering term d F(t)/dt = I I C (t − t0 ) + t0 dτ K (t − τ )F(τ ). It could be shown in very general form that the initial correlation term is damped. We will recover this general form from the BBGKY-hierarchy in Chap.

The laser area indicates energy versus pulse duration (below one picosecond) of modern lasers ble, where particles emit radiation. There is a large variety of interaction mechanisms, among them are (i) free charge acceleration in the oscillating electric field of the wave: The average oscillation energy of an electron (“quiver” or ponderomotive energy) in the field of amplitude E and frequency ω follows from Newton’s equation17 : Upond = e2 E 2 /(4m e ω). With modern high-intensity lasers electrons are easily accelerated up to relativistic energies18 ; (ii) carrier-photon scattering: In scattering processes with photons electrons may gain (lose) energy, re-emitting a photon of lower (higher) energy (Thomson scattering).

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