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arXiv · 1204.4124

The Gaussian entropy of fermionic systems

Tomislav Prokopec·Michael G. Schmidt·Jan Weenink
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Abstract

We consider the entropy and decoherence in fermionic quantum systems. By making a Gaussian Ansatz for the density operator of a collection of fermions we study statistical 2-point correlators and express the entropy of a system fermion in terms of these correlators. In a simple case when a set of N thermalised environmental fermionic oscillators interacts bi-linearly with the system fermion we can study its time dependent entropy, which also represents a quantitative measure for decoherence. We then consider a relativistic fermionic quantum field theory and take a mass mixing term as a simple model for the Yukawa interaction. It turns out that even in this Gaussian approximation, the fermionic system decoheres quite effectively, such that in a large coupling and high temperature regime the system field approaches the temperature of the environmental fields.

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Tomislav Prokopec, Michael G. Schmidt, Jan Weenink. 2012-04-18. The Gaussian entropy of fermionic systems. https://doi.org/10.1016/j.aop.2012.09.003

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