Volovik effect in the ±\pms-wave state for the iron-based superconductors

We studied the field dependencies of specific heat coefficient $\gamma(H) = \lim_{T \rightarrow 0} C(T,H)/T$ and thermal conductivity coefficient $\lim_{T \rightarrow 0} \kappa(T ,H)/T$ of the $\pm$s-wave state in the mixed state. We found that it is a generic feature of the two band s-wave state with the unequal sizes of gaps, small $\Delta_S$ and large $\Delta_L$, that Doppler shift of the quasiparticle excitations (Volovik effect) creates a finite density of states, on the extended states outside of vortex cores, proportional to $H$ in contrast to the $\sqrt{H}$ dependence of the d-wave state. Impurity scattering effect on the $\pm$s-wave state, however, makes this generic $H$-linear dependence sublinear approaching to the $\sqrt{H}$ behavior. Our calculations of $\lim_{T \rightarrow 0} \kappa(T ,H)/T$ successfully fit the experimental data of Ba(Fe$_{1-x}$Co$_x )_2$ As$_2$ with different Co-doping $x$ by systematically varying the gap size ratio $R= |\Delta_S | / |\Delta_L |$. We also resolve the dilemma of a substantial value of $\gamma(H \rightarrow 0)$ but almost zero value of $\lim_{T \rightarrow 0} \kappa(T ,H \rightarrow 0)/T$, observed in experiments.Comment: 5 pages, 2 figures accepted to Phys. Rev. Lett

Volovik effect on NMR measurements of unconventional superconuctors

We studied the Volovik effect on the NMR measurements of the two unconventional superconducting (SC) states, the d-wave and $\pm$s-wave states. We showed the generic field dependencies of the spin-lattice relaxation rate $1/T_1$ and Knight shift $K$ at low temperature limit in the pure cases as: $1/T_1 \propto H \log H$, $K \propto \sqrt{H}$ for the d-wave, and $1/T_1 \propto H$, $K \propto H$ for the $\pm$s-wave state, respectively. Performing numerical calculations we showed that these generic power laws survive for the good part of low field region with the realistic amount of impurities. We also found that the Volovik effect acts as an equivalent pair breaker as the unitary impurity scattering, hence induces the same temperature evolutions on $1/T_1$ and $K$, respectively, as the unitary impurities in both SC states. This finding implies that the Volovik effect should always be taken into account for the analysis of the NMR measurements in the mixed state.Comment: 5 pages, 4 figures; The fitting function of the inset of Fig.2(a) is slightly change

Effective potential for composite operators and for an auxiliary scalar field in a Nambu-Jona-Lasinio model

We derive the effective potentials for composite operators in a Nambu-Jona-Lasinio (NJL) model at zero and finite temperature and show that in each case they are equivalent to the corresponding effective potentials based on an auxiliary scalar field. The both effective potentials could lead to the same possible spontaneous breaking and restoration of symmetries including chiral symmetry if the momentum cutoff in the loop integrals is large enough, and can be transformed to each other when the Schwinger-Dyson (SD) equation of the dynamical fermion mass from the fermion-antifermion vacuum (or thermal) condensates is used. The results also generally indicate that two effective potentials with the same single order parameter but rather different mathematical expressions can still be considered physically equivalent if the SD equation corresponding to the extreme value conditions of the two potentials have the same form.Comment: 7 pages, no figur

Unstable states in quantum many-body theory

Unstable states of a general type of many-body system characterized by a combination of outgoing waves and bound states in all channels are investigated. It is seen, that the time-development in general will contain both oscillating and exponentially decaying terms

Nuclear spin-lattice relaxation rate in the D+iD superconducting state: implications for CoO superconductor

We calculated the nuclear spin-lattice relaxation rate $1/T_1$ for the D+iD superconducting state with impurities. We found that small amount of unitary impurities quickly produces the residual density of states inside the gap. As a result, the T-linear behavior in 1/T$_1$ is observed at low temperatures. Our results show that the D+iD pairing symmetry of the superconducting state of Na$_{0.35}$CoO$_{2} \cdot y$H$_2$ O is compatible with recent $^{59}$Co 1/T$_1$ experiments of several groups.Comment: 5 pages, 4 figures, minor change

Collapse arrest and soliton stabilization in nonlocal nonlinear media

We investigate the properties of localized waves in systems governed by nonlocal nonlinear Schrodinger type equations. We prove rigorously by bounding the Hamiltonian that nonlocality of the nonlinearity prevents collapse in, e.g., Bose-Einstein condensates and optical Kerr media in all physical dimensions. The nonlocal nonlinear response must be symmetric, but can be of completely arbitrary shape. We use variational techniques to find the soliton solutions and illustrate the stabilizing effect of nonlocality.Comment: 4 pages with 3 figure