Finite size effects on the transport coefficients of strongly interacting QCD matter

The role of finite volume effects on the various transport coefficients of strongly interacting quark matter is analyzed in the Polyakov chiral SU(3) quark mean-field model at finite temperatures and chemical potentials incorporating the fermionic vacuum term. Using a nonzero lower momentum cutoff and two different forms of the Polyakov loop potentials with quark backreaction, we study the following viscous properties: specific shear viscosity (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mi>η</a:mi><a:mo>/</a:mo><a:mi>s</a:mi></a:mrow></a:math>), normalized bulk viscosity (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>ζ</c:mi><c:mi>b</c:mi></c:msub><c:mo>/</c:mo><c:mi>s</c:mi></c:math>), and conductivity properties: electrical conductivity (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>σ</e:mi><e:mrow><e:mi>el</e:mi></e:mrow></e:msub><e:mo>/</e:mo><e:mi>T</e:mi></e:math>) and thermal conductivity (<g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>κ</g:mi><g:mo>/</g:mo><g:msup><g:mi>T</g:mi><g:mn>2</g:mn></g:msup></g:math>). Along with this, some essential thermodynamic quantities in the context of transport properties, such as the square of the speed of sound (<i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msubsup><i:mi>c</i:mi><i:mi>s</i:mi><i:mn>2</i:mn></i:msubsup></i:math>) and the specific heat (<k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:msub><k:mi>c</k:mi><k:mi>v</k:mi></k:msub></k:math>) at a constant volume, are computed. Finite size effects are applied to the vacuum term and its influence on the effective quark masses, thermodynamic quantities, and transport coefficients is studied. The temperature dependence of the transport coefficients is obtained through the kinetic theory approach with the relaxation time approximation. The size of the system has been found to have significant effects on all transport coefficients. We find that all the transport coefficients increase as the size of the system is reduced. We have also studied the specific sound channel <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mo stretchy="false">(</m:mo><m:mi>η</m:mi><m:mo>+</m:mo><m:mn>3</m:mn><m:msub><m:mi>ζ</m:mi><m:mi>b</m:mi></m:msub><m:mo>/</m:mo><m:mn>4</m:mn><m:mo stretchy="false">)</m:mo><m:mo>/</m:mo><m:mi>s</m:mi></m:math> and the bulk-to-shear viscosity ratio <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:msub><q:mi>ζ</q:mi><q:mi>b</q:mi></q:msub><q:mo>/</q:mo><q:mi>η</q:mi></q:math>. The effect of finite size is found to be more prominent in the transition region and vanishes at high <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>T</s:mi></s:math>. The transition temperature <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:msub><u:mi>T</u:mi><u:mi>χ</u:mi></u:msub></u:math> is found to decrease as the system size (characterized by <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mi>R</w:mi></w:math>) decreases. At finite chemical potentials, <y:math xmlns:y="http://www.w3.org/1998/Math/MathML" display="inline"><y:msub><y:mi>T</y:mi><y:mi>χ</y:mi></y:msub></y:math> is shifted to lower values compared to the case of the vanishing chemical potential.