On possible SS-wave bound states for a NNˉN \bar N system within a constituent quark model

We try to apply a constituent quark model (a variety chiral constituent quark model) and the resonating group approach for the multi-quark problems to compute the effective potential between the $N\bar{N}$ in $S$-wave (the quarks in the nucleons $N$ and $\bar{N}$, and the two nucleons relatively as well, are in $S$ wave) so as to see the possibility if there may be a tight bound state of six quarks as indicated by a strong enhancement at threshold of $p\bar{p}$ in $J/\psi$ and B decays. The effective potential which we obtain in terms of the model and approach shows if the experimental enhancement is really caused by a tight $S$-wave bound state of six quarks, then the quantum number of the bound state is very likely to be $I=1, J^{PC}=0^{-+}$.Comment: 8 pages, 9 figure

On Darboux-B\"acklund Transformations for the Q-Deformed Korteweg-de Vries Hierarchy

We study Darboux-B\"acklund transformations (DBTs) for the $q$-deformed Korteweg-de Vries hierarchy by using the $q$-deformed pseudodifferential operators. We identify the elementary DBTs which are triggered by the gauge operators constructed from the (adjoint) wave functions of the hierarchy. Iterating these elementary DBTs we obtain not only $q$-deformed Wronskian-type but also binary-type representations of the tau-function to the hierarchy.Comment: 12 pages, Revtex, no figure

Polarization, plasmon, and Debye screening in doped 3D ani-Weyl semimetal

We compute the polarization function in a doped three-dimensional anisotropic-Weyl semimetal, in which the fermion energy dispersion is linear in two components of the momenta and quadratic in the third. Through detailed calculations, we find that the long wavelength plasmon mode depends on the fermion density $n_e$ in the form $\Omega_{p}^{\bot}\propto n_{e}^{3/10}$ within the basal plane and behaves as $\Omega_{p}^{z}\propto n_{e}^{1/2}$ along the third direction. This unique characteristic of the plasmon mode can be probed by various experimental techniques, such as electron energy-loss spectroscopy. The Debye screening at finite chemical potential and finite temperature is also analyzed based on the polarization function.Comment: 11 page

Infrared behavior of dynamical fermion mass generation in QED3_{3}

Extensive investigations show that QED$_{3}$ exhibits dynamical fermion mass generation at zero temperature when the fermion flavor $N$ is sufficiently small. However, it seems difficult to extend the theoretical analysis to finite temperature. We study this problem by means of Dyson-Schwinger equation approach after considering the effect of finite temperature or disorder-induced fermion damping. Under the widely used instantaneous approximation, the dynamical mass displays an infrared divergence in both cases. We then adopt a new approximation that includes an energy-dependent gauge boson propagator and obtain results for dynamical fermion mass that do not contain infrared divergence. The validity of the new approximation is examined by comparing to the well-established results obtained at zero temperature.Comment: 15 pages, 6 figures, to appear on Phys. Rev.

Connection between in-plane upper critical field Hc2H_{c2} and gap symmetry in layered dd-wave superconductors revisited

Angle-resolved upper critical field $H_{c2}$ provides an efficient tool to probe the gap symmetry of unconventional superconductors. We revisit the behavior of in-plane $H_{c2}$ in $d$-wave superconductors by considering both the orbital effect and Pauli paramagnetic effect. After carrying out systematic analysis, we show that the maxima of $H_{c2}$ could be along either nodal or antinodal directions of a $d$-wave superconducting gap, depending on the specific values of a number of tuning parameters. This behavior is in contrast to the common belief that the maxima of in-plane $H_{c2}$ are along the direction where the superconducting gap takes its maximal value. Therefore, identifying the precise $d$-wave gap symmetry through fitting experiments results of angle-resolved $H_{c2}$ with model calculations at a fixed temperature, as widely used in previous studies, is difficult and practically unreliable. However, our extensive analysis of angle-resolved $H_{c2}$ show that there is a critical temperature $T^{*}$: in-plane $H_{c2}$ exhibits its maxima along nodal directions at $T < T^{*}$ and along antinodal directions at $T^{*} < T < T_c$. The concrete value of $T^{*}$ may change as other parameters vary, but the existence of $\pi/4$ shift of $H_{c2}$ at $T^{\ast}$ appears to be a general feature. Thus a better method to identify the precise $d$-wave gap symmetry is to measure $H_{c2}$ at a number of different temperatures, and examine whether there is a $\pi/4$ shift in its angular dependence at certain $T^{*}$. We further show that Landau level mixing does not change this general feature. However, in the presence of Fulde-Ferrell-Larkin-Ovchinnikov state, the angular dependence of $H_{c2}$ becomes quite complicated, which makes it more difficult to determine the gap symmetry by measuring $H_{c2}$.Comment: 12 pages, 11 figure

Quantum phase transition and unusual critical behavior in multi-Weyl semimetals

The low-energy behaviors of gapless double- and triple-Weyl fermions caused by the interplay of long-range Coulomb interaction and quenched disorder are studied by performing a renormalization group analysis. It is found that an arbitrarily weak disorder drives the double-Weyl semimetal to undergo a quantum phase transition into a compressible diffusive metal, independent of the disorder type and the Coulomb interaction strength. In contrast, the nature of the ground state of triple-Weyl fermion system relies sensitively on the specific disorder type in the noninteracting limit: The system is turned into a compressible diffusive metal state by an arbitrarily weak random scalar potential or $z$ component of random vector potential but exhibits stable critical behavior when there is only $x$ or $y$ component of random vector potential. In case the triple-Weyl fermions couple to random scalar potential, the system becomes a diffusive metal in the weak interaction regime but remains a semimetal if Coulomb interaction is sufficiently strong. Interplay of Coulomb interaction and $x$, or $y$, component of random vector potential leads to a stable infrared fixed point that is likely to be characterized by critical behavior. When Coulomb interaction coexists with the $z$ component of random vector potential, the system flows to the interaction-dominated strong coupling regime, which might drive a Mott insulating transition. It is thus clear that double- and triple-Weyl fermions exhibit distinct low-energy behavior in response to interaction and disorder. The physical explanation of such distinction is discussed in detail. The role played by long-range Coulomb impurity in triple-Weyl semimetal is also considered.Comment: 22 pages, 17 figure

Unconventional non-Fermi liquid state caused by nematic criticality in cuprates

At the nematic quantum critical point that exists in the $d_{x^2-y^2}$-wave superconducting dome of cuprates, the massless nodal fermions interact strongly with the quantum critical fluctuation of nematic order. We study this problem by means of renormalization group approach and show that, the fermion damping rate $\left|\mathrm{Im}\Sigma^R(\omega)\right|$ vanishes more rapidly than the energy $\omega$ and the quasiparticle residue $Z_f\rightarrow 0$ in the limit $\omega \rightarrow 0$. The nodal fermions thus constitute an unconventional non-Fermi liquid that represents an even weaker violation of Fermi liquid theory than a marginal Fermi liquid. We also investigate the interplay of quantum nematic critical fluctuation and gauge-potential-like disorder, and find that the effective disorder strength flows to the strong coupling regime at low energies. Therefore, even an arbitrarily weak disorder can drive the system to become a disorder controlled diffusive state. Based on these theoretical results, we are able to understand a number of interesting experimental facts observed in curpate superconductors.Comment: 29 pages, 6 figure

The Component Connectivity of Alternating Group Graphs and Split-Stars

For an integer $\ell\geqslant 2$, the $\ell$-component connectivity of a graph $G$, denoted by $\kappa_{\ell}(G)$, is the minimum number of vertices whose removal from $G$ results in a disconnected graph with at least $\ell$ components or a graph with fewer than $\ell$ vertices. This is a natural generalization of the classical connectivity of graphs defined in term of the minimum vertex-cut and is a good measure of robustness for the graph corresponding to a network. So far, the exact values of $\ell$-connectivity are known only for a few classes of networks and small $\ell$'s. It has been pointed out in~[Component connectivity of the hypercubes, Int. J. Comput. Math. 89 (2012) 137--145] that determining $\ell$-connectivity is still unsolved for most interconnection networks, such as alternating group graphs and star graphs. In this paper, by exploring the combinatorial properties and fault-tolerance of the alternating group graphs $AG_n$ and a variation of the star graphs called split-stars $S_n^2$, we study their $\ell$-component connectivities. We obtain the following results: (i) $\kappa_3(AG_n)=4n-10$ and $\kappa_4(AG_n)=6n-16$ for $n\geqslant 4$, and $\kappa_5(AG_n)=8n-24$ for $n\geqslant 5$; (ii) $\kappa_3(S_n^2)=4n-8$, $\kappa_4(S_n^2)=6n-14$, and $\kappa_5(S_n^2)=8n-20$ for $n\geqslant 4$

Quantum coherence of double-well BEC: a SU(2)-coherent-state path-integral approach

Macroscopic quantum coherence of Bose gas in a double-well potential is studied based on SU(2)-coherent-state path-integral. The ground state and fluctuations around it can be obtained by this method. In this picture, one can obtain macroscopic quantum superposition states for attractive Bose gas. The coherent gap of degenerate ground states is obtained with the instanton technique. The phenomenon of macroscopic quantum self-trapping is also discussed.Comment: 6 pages, 2 figures, final version to appear in Physcial Review

Distance preserving mappings from ternary vectors to permutations

Distance-preserving mappings (DPMs) are mappings from the set of all q-ary vectors of a fixed length to the set of permutations of the same or longer length such that every two distinct vectors are mapped to permutations with the same or even larger Hamming distance than that of the vectors. In this paper, we propose a construction of DPMs from ternary vectors. The constructed DPMs improve the lower bounds on the maximal size of permutation arrays.Comment: 21 page