The semiclassical propagator in fermionic Fock space

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 $\int \mathcal{D}[\psi ,{\psi }^{\ast }]{\mathrm{e}}^{iR[\psi ,{\psi }^{\ast }]}$ 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.

20 pages, 1 figure

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• Semiclassical Lindblad master equation for spin dynamics
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• Complex saddle trajectories for multidimensional quantum wave packet/coherent state propagation: application to a many-body system
• Many-body coherence and entanglement probed by randomized correlation measurements
• Many-Body Spin Echo
• The semiclassical propagator in Fock space: dynamical echo and many-body interference
• Semiclassical Prediction of Large Spectral Fluctuations in Interacting Kicked Spin Chains
• Coherent backscattering in the Fock space of ultracold bosonic atoms
• Aspects of integrability in a classical model for non-interacting fermionic fields
• Towards a semiclassical understanding of chaotic single- and many-particle quantum dynamics at post-Heisenberg time scales
• A Mapping between the Spin and Fermion Algebra