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arXiv · 2010.07296

$C^*$-fermi systems and detailed balance

Vitonofrio Crismale·Rocco Duvenhage·Francesco Fidaleo
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Abstract

A systematic theory of product and diagonal states is developed for tensor products of $\mathbb Z_2$-graded $*$-algebras, as well as $\mathbb Z_2$-graded $C^*$-algebras. As a preliminary step to achieve this goal, we provide the construction of a {\it fermionic $C^*$-tensor product} of $\mathbb Z_2$-graded $C^*$-algebras. Twisted duals of positive linear maps between von Neumann algebras are then studied, and applied to solve a positivity problem on the infinite Fermi lattice. Lastly, these results are used to define fermionic detailed balance (which includes the definition for the usual tensor product as a particular case) in general $C^*$-systems with gradation of type $\mathbb Z_2$, by viewing such a system as part of a compound system and making use of a diagonal state.

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Vitonofrio Crismale, Rocco Duvenhage, Francesco Fidaleo. 2020-10-14. $C^*$-fermi systems and detailed balance. https://doi.org/10.1007/s13324-020-00412-0

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