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**1 - 7**of**7**### unknown title

, 2013

"... Taylor coefficients of the thermodynamic potential to sixth order in the vector interaction extended NJL model Taylor-Koeffizienten des thermodynamischen Potenzials bis zur sechsten Ordnung im mit Vektor-Wechselwirkung erweiterten NJL-Modell ..."

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Taylor coefficients of the thermodynamic potential to sixth order in the vector interaction extended NJL model Taylor-Koeffizienten des thermodynamischen Potenzials bis zur sechsten Ordnung im mit Vektor-Wechselwirkung erweiterten NJL-Modell

### Mesonic Excitations in an Inhomogeneous Phase of the Nambu–Jona-Lasinio Model Mesonische Anregungen in einer Inhomogenen Phase des Nambu–Jona-Lasinio–Modells

, 2013

"... We study the inhomogeneous phase with chiral density wave modulation within the framework of the two-flavor Nambu–Jona-Lasinio model. Using mean-field methods we determine the dressed quark propagator for the inhomogeneous phase and calculate constituent quark masses. The polarization loop of the Be ..."

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We study the inhomogeneous phase with chiral density wave modulation within the framework of the two-flavor Nambu–Jona-Lasinio model. Using mean-field methods we determine the dressed quark propagator for the inhomogeneous phase and calculate constituent quark masses. The polarization loop of the Bethe-Salpeter equation playing a crucial role in acquiring mesonic propagators and masses is investigated. Numerically evaluable expressions for the polarization loop are derived and results of calculations for simple scenarios are shown.

### Large-Nc equivalence and the sign problem at finite baryon density

"... QCD with a finite baryon chemical potential, despite its importance, is not well understood because the standard lattice QCD simulation is not applicable due to the sign problem. Although QCD-like theories which do not suffer from the sign problem have been studied intensively, relation to QCD with ..."

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QCD with a finite baryon chemical potential, despite its importance, is not well understood because the standard lattice QCD simulation is not applicable due to the sign problem. Although QCD-like theories which do not suffer from the sign problem have been studied intensively, relation to QCD with a finite baryon chemical potential was not clear. This paper introduces large-Nc equivalences between QCD and various QCD-like theories. These equivalences lead us to a unified viewpoint for QCD with baryon and isospin chemical potentials, SO(2Nc) and Sp(2Nc) gauge theories, QCD with adjoint matters and two-color QCD. In particular QCD with the baryon chemical potential is equivalent to its phase quenched version in a certain parameter region, which is relevant for heavy ion collision experiments. This result is useful especially for finding or excluding a possible QCD critical point, through the phase quenched simulation of the SU(3) QCD. 1 ar

### Taming the pion condensation in QCD at finite baryon density

, 2014

"... In the Monte Carlo study of QCD at finite baryon density based upon the phase reweighting method, the pion condensation in the phase-quenched theory and associated zero-mode prevent us to go to the low-temperature high-density region. We propose a method to circumvent them by a simple modification o ..."

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In the Monte Carlo study of QCD at finite baryon density based upon the phase reweighting method, the pion condensation in the phase-quenched theory and associated zero-mode prevent us to go to the low-temperature high-density region. We propose a method to circumvent them by a simple modification of the density of state method. We first argue that the standard version of the density of state method, which is invented to solve the overlapping problem, is effective only for a certain ‘good ’ class of observables. We then modify it so as to solve the overlap problem for ‘bad ’ observables as well. While, in the standard version of the density of state method, we usually constrain an observable we are interested in, we fix a different observable in our new method which has a sharp peak at some particular value characterizing the correct vacuum of the target theory. In the finite-density QCD, such an observable is the pion condensate. The average phase becomes vanishingly small as the value of the pion condensate becomes large, hence it is enough to consider configurations with pi+ ' 0, where the zero mode does not appear. We demonstrate an effectiveness of our method by using a toy model (the chiral random matrix theory) which captures the properties of finite-density QCD qualitatively. We also argue how to apply our method to other theories including finite-density QCD. Although the example we study numerically is based on the phase reweighting method, the same idea can be applied to more general reweighting methods and we show how this idea can be applied to find a possible QCD critical point.