Four-fermion interactions and the chiral symmetry breaking in an external magnetic field

We investigate the chiral symmetry and its spontaneous breaking at finite temperature and in an external magnetic field with four-fermion interactions of different channels. Quantum and thermal fluctuations are included within the functional renormalization group approach, and properties of the set of flow equations for different couplings, such as its fixed points, are discussed. It is found that external parameters, e.g. the temperature and the external magnetic field and so on, do not change the structure of the renormalization group flows for the couplings. The flow strength is found to be significantly dependent on the route and direction in the plane of couplings of different channels. Therefore, the critical temperature for the chiral phase transition shows a pronounced dependence on the direction as well. Given fixed initial ultraviolet couplings, the critical temperature increases with the increasing magnetic field, viz., the magnetic catalysis is observed with initial couplings fixed.Comment: 8 pages, 4 figure

Mesonic excitations and pi--pi scattering lengths at finite temperature in the two-flavor Polyakov--Nambu--Jona-Lasinio model

The mesonic excitations and s-wave pi--pi scattering lengths at finite temperature are studied in the two-flavor Polyakov--Nambu--Jona-Lasinio (PNJL) model. The masses of pi-meson and sigma-meson, pion-decay constant, the pion-quark coupling strength, and the scattering lengths $a_{0}$ and $a_{2}$ at finite temperature are calculated in the PNJL model with two forms of Polyakov-loop effective potential. The obtained results are almost independent of the choice of the effective potentials. The calculated results in the PNJL model are also compared with those in the conventional Nambu--Jona-Lasinio model and indicate that the effect of color confinement screens the effect of temperature below the critical one in the PNJL model. Furthermore, the Goldberger-Treiman relation and the Gell-Mann--Oakes--Renner relation are extended to the case at finite temperature in the PNJL model.Comment: 25 pages, 8 figure

Effect of chain stiffness on ion distributions around a polyelectrolyte in multivalent salt solutions

Ion distributions in dilute polyelectrolyte solutions are studied by means of Langevin dynamics simulations. We show that the distributions depend on the conformation of a chain while the conformation is determined by the chain stiffness and the salt concentration. We observe that the monovalent counterions originally condensed on a chain can be replaced by the multivalent ones dissociated from the added salt due to strong electrostatic interaction. These newly condensed ions give an important impact on the chain structure. At low and at high salt concentrations, the conformation of a semiflexible chain is rodlike. The ion distributions show similarity to those for a rigid chain, but difference to those for a flexible chain whose conformation is a coil. In the mid-salt region, the flexible chain and the semiflexible chain collapse but the collapsed chain structures are, respectively, disordered and ordered structures. The ion distributions hence show different profiles for these three chain stiffness with the curves for the semiflexible chain lying between those for the flexible and the rigid chains. The number of the condensed multivalent counterions, as well as the effective chain charge, also shows similar behavior, demonstrating a direct connection with the chain morphology. Moreover, we find that the condensed multivalent counterions form triplets with two adjacent monomers and are localized on the chain axis at intermediate salt concentration when the chain stiffness is semiflexible or rigid. The microscopic information obtained here provides valuable insight to the phenomena of DNA condensation and is very useful for researchers to develop new models.Comment: 28 pages, 10 figures, accepted for publication in JC

Unfolding Polyelectrolytes in Trivalent Salt Solutions Using DC Electric Fields: A Study by Langevin Dynamics Simulations

We study the behavior of single linear polyelectrolytes condensed by trivalent salt under the action of electric fields through computer simulations. The chain is unfolded when the strength of the electric field is stronger than a critical value. This critical electric field follows a scaling law against chain length and the exponent of the scaling law is $-0.77(1)$, smaller than the theoretical prediction, $-3\nu/2$ [Netz, Phys. Rev. Lett. 90 (2003) 128104], and the one obtained by simulations in tetravalent salt solutions, $-0.453(3)$ [Hsiao and Wu, J. Phys. Chem. B 112 (2008) 13179]. It demonstrates that the scaling exponent depends sensitively on the salt valence. Hence, it is easier to unfold chains condensed by multivalent salt of smaller valence. Moreover, the absolute value of chain electrophoretic mobility increases drastically when the chain is unfolded in an electric field. The dependence of the mobility on electric field and chain length provides a plausible way to impart chain-length dependence in free-solution electrophoresis via chain unfolding transition induced by electric fields. Finally, we show that, in addition to an elongated structure, a condensed chain can be unfolded into an U-shaped structure. The formation of this structure in our study is purely a result of the electric polarization, but not of the elasto-hydrodynamics dominated in sedimentation of polymers.Comment: 15 pages, 7 figures, accepted for publication in Biomicrofluidic