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arXiv · 1802.01154

Full counting statistics in the free Dirac theory

Takato Yoshimura
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Abstract

We study charge transport and fluctuations of the (3+1)-dimensional massive free Dirac theory. In particular, we focus on the steady state that emerges following a local quench whereby two independently thermalized halves of the system are connected and let to evolve unitarily for a long time. Based on the two-time von Neumann measurement statistics and exact computations, the scaled cumulant generating function associated with the charge transport is derived. We find that it can be written as a generalization of Levitov-Lesovik formula to the case in three spatial dimensions. In the massless case, we note that only the first four scaled cumulants are nonzero. Our results provide also a direct confirmation for the validity of the extended fluctuation relation in higher dimensions. An application of our approach to Lifshitz fermions is also briefly discussed.

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Takato Yoshimura. 2018-02-04. Full counting statistics in the free Dirac theory. https://doi.org/10.1088/1751-8121/aae769

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