| Summary: | Within the ultrarelativistic quantum molecular dynamics (UrQMD) model, the effect of initial density fluctuations on cumulants of the net-proton multiplicity distribution in Au + Au Collisions at <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msqrt><msub><mi>s</mi><mrow><mi>N</mi><mi>N</mi></mrow></msub></msqrt></semantics></math></inline-formula> = 7.7 GeV was investigated by varying the minimum distance <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>min</mi></msub></semantics></math></inline-formula> between two nucleons in the initialization. It was found that the initial density fluctuations increased with the decrease of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>min</mi></msub></semantics></math></inline-formula> from 1.6 fm to 1.0 fm, and the influence of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>min</mi></msub></semantics></math></inline-formula> on the magnitude of the net-proton number fluctuation in a narrow pseudorapidity window (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>η</mi><mo>≤</mo></mrow></semantics></math></inline-formula> 4) was negligible even if it indeed affected the density evolution during the collision. At a broad pseudorapidity window (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>η</mi><mo>≥</mo></mrow></semantics></math></inline-formula> 4), the cumulant ratios were enlarged when the initial density fluctuations were increased with the smaller value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>d</mi><mi>min</mi></msub></semantics></math></inline-formula>, and this enhancement was comparable to that observed in the presence of the nuclear mean-field potential. Moreover, the enhanced cumulants were more evident in collisions with a larger impact parameter. The present work demonstrates that the fingerprint of the initial density fluctuations on the cumulants in a broad pseudorapidity window is clearly visible, while it is not obvious as the pseudorapidity window becomes narrow.
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