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The semiclassical propagator in fermionic Fock space | | Thomas Engl
; Peter Plößl
; Juan Diego Urbina
; Klaus Richter
; | | Date: |
15 Sep 2014 | | Abstract: | We present a rigorous derivation of a semiclassical propagator for
anticommuting (fermionic) degrees of freedom, starting from an exact
representation in terms of Grassmann variables. As a key feature of our
approach the anticommuting variables are integrated out exactly, and an exact
path integral representation of the fermionic propagator in terms of commuting
variables is constructed. Since our approach is not based on auxiliary
(Hubbard-Stratonovich) fields, it surpasses the calculation of fermionic
determinants yielding a standard form $int {cal D}[psi,psi^{*}] {
m e}^{i
R[psi,psi^{*}]}$ with real actions for the propagator. These two features
allow us to provide a rigorous definition of the classical limit of interacting
fermionic fields and therefore to achieve the long-standing goal of a
theoretically sound construction of a semiclassical van Vleck-Gutzwiller
propagator in fermionic Fock space. As an application, we use our propagator to
investigate how the different universality classes (orthogonal, unitary and
symplectic) affect generic many-body interference effects in the transition
probabilities between Fock states of interacting fermionic systems. | | Source: | arXiv, 1409.4196 | | Services: | Forum | Review | PDF | Favorites | |
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