Gaussian phase-space representations for fermions

Details Gaussian phase-space representations for fermions Gaussian phase-space representations for fermions

2004-11-29

arxiv.org/abs/cond-mat/0411712v3

Phys. Rev. B 73, 125112 (2006).

Physics

Condensed Matter

Other Condensed Matter

More references and examples. Much less mathematical material

Scientific paper

10.1103/PhysRevB.73.125112

We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behaviour in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.

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