Interacting multiple zero mode formulation and its application to a system consisting of a dark soliton in a condensate

To formulate the zero modes in a finite-size system with spontaneous breakdown of symmetries in quantum field theory is not trivial, for in the naive Bogoliubov theory, one encounters difficulties such as phase diffusion, the absence of a definite criterion for determining the ground state, and infrared divergences. A new interacting zero mode formulation that has been proposed for systems with a single zero mode to avoid these difficulties is extended to general systems with multiple zero modes. It naturally and definitely gives the interactions among the quantized zero modes, the consequences of which can be observed experimentally. In this paper, as a typical example, we consider an atomic Bose-Einstein condensed system with a dark soliton that contains two zero modes corresponding to spontaneous breakdown of the U(1) gauge and translational symmetries. Then we evaluate the standard deviations of the zero mode operators and see how the mutual interaction between the two zero modes affects them.

Quark number density at imaginary chemical potential and its extrapolation to large real chemical potential by the effective model

We evaluate quark number densities at imaginary chemical potential by lattice QCD with clover-improved two-flavor Wilson fermion. The quark number densities are extrapolated to the small real chemical potential region by assuming some function forms. The extrapolated quark number densities are consistent with those calculated at real chemical potential with the Taylor expansion method for the reweighting factors. In order to study the large real chemical potential region, we use the two-phase model consisting of the quantum hadrodynamics model for the hadron phase and the entanglement-PNJL model for the quark phase. The quantum hadrodynamics model is constructed to reproduce nuclear saturation properties, while the entanglement-PNJL model reproduces well lattice QCD data for the order parameters such as the Polyakov loop, the thermodynamic quantities and the screening masses. Then, we calculate the mass-radius relation of neutron stars and explore the hadron-quark phase transition with the two-phase model.

Heavy quark potential at finite imaginary chemical potential

We investigate chemical-potential ($mu$) dependence of the static-quark free energies in both the real and imaginary $mu$ regions, using the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potentials are evaluated from Polyakov-loop correlators in the deconfinement phase and the imaginary $mu=imu_{rm I}$ region and extrapolated to the real $mu$ region with analytic continuation. As the analytic continuation, the potential calculated at imaginary $mu=imu_{rm I}$ is expanded into a Taylor-expansion series of $imu_{rm I}/T$ up to 4th order and the pure imaginary variable $imu_{rm I}/T$ is replaced by the real one $mu_{rm R}/T$. At real $mu$, the 4th-order term weakens $mu$ dependence of the potential sizably. Also, the color-Debye screening mass is extracted from the color-singlet potential at imaginary $mu$, and the mass is extrapolated to real $mu$ by analytic continuation. The screening mass thus obtained has stronger $mu$ dependence than the prediction of the leading-order thermal perturbation theory at both real and imaginary $mu$.

Color screening potential at finite density in two-flavor lattice QCD with Wilson fermions

We investigate chemical-potential (mu) dependence of static-quark free energies in both the real and imaginary mu regions, performing lattice QCD simulations at imaginary mu and extrapolating the results to the real mu region with analytic continuation. Lattice QCD calculations are done on a 16^{3}times 4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. Static-quark potential is evaluated from the Polyakov-loop correlation functions in the deconfinement phase. As the analytic continuation, the potential calculated at imaginary mu=imu_{rm I} is expanded into a Taylor-expansion series of imu_{rm I}/T up to 4th order and the pure imaginary variable imu_{rm I}/T is replaced by the real one mu_{rm R}/T. At real mu, the 4th-order term weakens mu dependence of the potential sizably. At long distance, all of the color singlet and non-singlet potentials tend to twice the single-quark free energy, indicating that the interactions between heavy quarks are fully color-screened for finite mu. For both real and imaginary mu, the color-singlet q{bar q} and the color-antitriplet qq interaction are attractive, whereas the color-octet q{bar q} and the color-sextet qq interaction are repulsive. The attractive interactions have stronger mu/T dependence than the repulsive interactions. The color-Debye screening mass is extracted from the color-singlet potential at imaginary mu, and the mass is extrapolated to real mu by analytic continuation. The screening mass thus obtained has stronger mu dependence than the prediction of the leading-order thermal perturbation theory at both real and imaginary mu.