# The Dirac spectrum in Complex Langevin Simulations of QCD

Source: [The Dirac spectrum in Complex Langevin Simulations of QCD](<https://www.sota2.com/research/paper/68fa2e7a1e209131ce863160>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-27T03:27:04.337Z

Authors: K. Splittorff

Published: 2014-12-01T15:07:50.000Z

## Abstract

We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one in simulations with ordinary non-complexified gauge fields: At low temperatures the small eigenvalues of the Dirac operator must be inside the quark mass for chemical potentials as large as a third of the nucleon mass. In particular, in the chiral limit the Dirac eigenvalues of complex Langevin simulations must accumulate at the origin.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1412.0502>)

[PDF](<https://arxiv.org/pdf/1412.0502.pdf>)