Abstract
As in the previous chapter, we consider the fermionic mean-field regime. At positive temperature the state of the system is not described by a vector in the Hilbert space anymore. However, the Araki-Wyss representation allows us to describe it by a vector in a ‘doubled’ Hilbert space. We use the Araki-Wyss method to derive the time-dependent Hartree-Fock equation for mixed states.
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J. Dereziński, C. Gérard, Mathematics of Quantization and Quantum Fields (Cambridge University Press, Cambridge, 2013)
H. Araki, W. Wyss, Representations of canonical anticommutation relations. Helv. Phys. Acta 37, 136 (1964)
N. Benedikter, V. Jaksic, M. Porta, C. Saffirio, B. Schlein, Mean-field Evolution of Fermionic Mixed States. Preprint arXiv:1411.0843
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Benedikter, N., Porta, M., Schlein, B. (2016). Dynamics of Fermionic Quasi-Free Mixed States. In: Effective Evolution Equations from Quantum Dynamics. SpringerBriefs in Mathematical Physics, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-319-24898-1_7
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DOI: https://doi.org/10.1007/978-3-319-24898-1_7
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