Schedule Aug 25, 2010
Nonequilibrium Green's Functions Approach to Sub-femtosecond Dynamics of Plasmas and Atoms in Intense X-ray Fields
Michael Bonitz, Kiel Univ. & KITP

In this talk I discuss the idea of nonequilibrium Green's functions (NEGF) and recent theoretical and computational results. I will start by introducing the real-time (Keldysh) Green's functions for a many-body system of bosons or fermions and their equations of motion - the Keldysh-Kadanoff-Baym equations (KBE). Their main advantage is that they guarantee the relevant conservation laws, are applicable to fields of arbitrary intensity as well as to arbitrarily short pulses. There are two main lines of research:

1. Use the KBE to derive general quantum kinetic equations for the Wigner function or density matrix. These equations contain collisions including nonlinear field effects, finite collision durations etc. I will illustrate this by examples from dense laser plasmas.

2. Direct solution of the KBE for the two-time NEGF. Here numerical results were obtained for the correlated electron gas and for electron-hole plasmas in semiconductors in excited by optical pulses. These results can directly be extended to small atoms interacting with short x-ray pulses. Here first results have been obtained by our group, in particular by my affiliate Karsten Balzer. I will give a brief overview and discuss the capabilities of this method.

The presentation contains a summary of the talk and a few additional applications with references which were skipped due to time limitations, in particular:
  1. transparancies 21-24 an example how to derive quantum kinetic equations from the two-time NEGF. The example shows a gauge-invariant derivation of the collision integral of an electron-ion plasma in the presence of a monochromotic field (optical to x-ray). The result includes multiphoton absorption and inverse bremsstrahlung heating of electrons.
  2. 25-27: numerical solution of the derived kinetic equation for an electron-ion plasma in a strong field, including harmonics generation.
  3. 28 demonstration of total energy conservation - observed by full solution of the two-time Keldysh-Kadanoff-Baym equations (KBE) for the NEGF. This is in contrast to Boltzmann type (Markovian) kinetic equations which conserve only kinetic energy, transparancy 29.
  4. 30-31 Solution of the KBE for a two band semiconductor under optical excitation.
  5. 32-34 Solution of the KBE for an inhomogeneous electron gas which yields the dynamic structure factor including correlations and vertex corrections in a sum rule preserving fashion.

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(View notes on density operator.)

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