119142727
Approximate Solutions of Functional Equations
Approximate solutions to functional evolution equations are constructed through a combination of series and conjugation methods, and relative errors are estimated. The methods are illustrated, both analytically and numerically, by construction of approximate continuous functional iterates for , sin x, and λx(1 − x). Simple functional conjugation by these functions, and their inverses, substantially improves the numerical accuracy of formal series approximations for their continuous iterates.
115164400
Classical and quantal ternary algebras
We consider several ternary algebras relevant to physics. We compare and contrast the quantal versions of the algebras, as realized through associative products of operators, with their classical counterparts, as realized through classical Nambu brackets. In some cases involving infinite algebras, we show the classical limit may be obtained by a contraction of the quantal algebra, and then explicitly realized through classical brackets. We illustrate this classical-contraction method by the Virasoro-Witt example.
118617324
Zeros of QCD partition function from finite density lattices
Email: xjin@riken.jpPartition function zeros steer the critical behavior of a system. Studying four-ﬂavor lattice QCDat ﬁnite temperature and density with the Wilson-clover fermion action and the Iwasaki gauge ac-tion using a phase-quenched fermion determinant, we combine statistics from multiple chemicalpotentials to improve sampling of the conﬁguration space, and aim at unraveling the movementof zeros in ﬁnite systems. Preparing for further investigations, we discuss methods and criteriaused to sieve through complex parameter space spanned by (Rem;Imm) and (Rem;Imb), andpresent statistically robust zeros of the partition function.31st International Symposium on Lattice Field Theory LATTICE 2013July 29 – August 3, 2013Mainz, Germany
6262185
Lattice QCD with Eight Degenerate Quark Flavors
We report on simulations of QCD with many flavors of degenerate quarks, the DBW2 gauge action and naive staggered fermions, using the rational hybrid Monte Carlo algorithm. We primarily focus on eight degenerate quark flavors where a variety of values of the coupling constant and quark mass have been used in the simulations. The scaling behavior of the hadron spectrum and the string tension of the heavy quark potential is studied, to probe whether the zero temperature, continuum limit of the theory breaks chiral symmetry.
119211023
Critical endpoint of the finite temperature phase transition for three flavor QCD
We investigate the critical endpoint of finite temperature phase transition of $N_f=3$ QCD at zero chemical potential. We employ the renormalization-group improved Iwasaki gauge action and non-perturbatively $O(a)$-improved Wilson-clover fermion action. The critical endpoint is determined by using the intersection point of kurtosis for the temporal size $N_t$=4, 6, 8. Spatial sizes of $N_l$=6-16 ($N_t$=4), 10-24 ($N_t$=6), and 12-24 ($N_t$=8) are employed. We find that $N_t$=4 is out of the scaling region. Using results for $N_t$=6 and 8, and making linear extrapolations in $1/N_t^2$, we obtain $\sqrt{t_0}T_{\rm E}=0.0975(14)(8)$, $\sqrt{t_0}m_{\rm PS,E}=0.2254(52)(105)$ and $m_{\rm PS,E}/T_{\rm E}=2.311(63)(13)$, where the first error is statistical error, the second error is systematic error, and $m_{\rm PS}$ is the pseudo scalar meson mass. If one uses $1/\sqrt{t_0}=1.347(30)$ GeV reported by Borsanyi et al., one finds $T_{\rm E}=131(2)(1)(3)$ MeV, $m_{\rm PS,E}=304(7)(14)(7)$ MeV and $m_{\rm PS,E}/m_{\rm PS,E}^{\rm phys, sym}=0.739(17)(34)(17)$, where the third error comes from error of $\sqrt{t_0}$ and $m_{\rm PS}^{\rm phys, sym}=\sqrt{(m_\pi^2+2m_K^2)/3}$. Our current estimation of $\sqrt{t_0}m_{\rm PS,E}$ in the continuum limit is about 25% smaller than the SU(3) symmetric point.