Tannakian categories, linear differential algebraic groups, and parameterized linear differential equations

We provide conditions for a category with a fiber functor to be equivalent to the category of representations of a linear differential algebraic group. This generalizes the notion of a neutral Tannakian category used to characterize the category of representations of a linear algebraic group.Comment: 26 pages; corrected misprints; simplified Definition 2; more references adde

Massive liquid Ar and Xe detectors for direct Dark Matter searches

A novel experiment for direct searches of the Dark Matter with liquid argon double-phase chamber with a mass of liquid Ar up to several hundred tons is proposed. To suppress the b-, g- and n0- backgrounds, the comparison of scintillation and ionization signals for every event is suggested. The addition in liquid Ar of photosensitive Ge(CH3)4 or C2H4 and suppression of triplet component of scintillation signals ensures the detection of scintillation signals with high efficiency and provides a complete suppression of the electron background. For the detection of photoelectrons and ionization electrons, highly stable and reliable GEM detectors must be used.Comment: 8 pages, 2 figures, 1 tabl

Topological superconducting phases in disordered quantum wires with strong spin-orbit coupling

Zeeman fields can drive semiconductor quantum wires with strong spin-orbit coupling and in proximity to s-wave superconductors into a topological phase which supports end Majorana fermions and offers an attractive platform for realizing topological quantum information processing. Here, we investigate how potential disorder affects the topological phase by a combination of analytical and numerical approaches. Most prominently, we find that the robustness of the topological phase against disorder depends sensitively and non-monotonously on the Zeeman field applied to the wire.Comment: 6 pages, 3 figures; published versio

Nuclear magnetic susceptibility of metals with magnetic impurities

We consider the contribution of magnetic impurities to the nuclear magnetic susceptibility $\chi$ and to the specific heat $C$ of a metal. The impurity contribution to the magnetic susceptibility has a $1/T^2$ behaviour, and the impurity contribution to the specific heat has a $1/T$ behaviour, both in an extended region of temperatures $T$. In the case of a dirty metal the RKKY interaction of nuclear spins and impurity spins is suppressed for low temperatures and the main contribution to $C$ and $\chi$ is given by their dipole-dipole interaction.Comment: 9 pages, 4 figures, REVTE

Functional renormalization-group approach to the Pokrovsky-Talapov model via modified massive Thirring fermion model

A possibility of the topological Kosterlitz-Thouless~(KT) transition in the Pokrovsky-Talapov~(PT) model is investigated by using the functional renormalization-group (RG) approach by Wetterich. Our main finding is that the nonzero misfit parameter of the model, which can be related with the linear gradient term (Dzyaloshinsky-Moriya interaction), makes such a transition impossible, what contradicts the previous consideration of this problem by non-perturbative RG methods. To support the conclusion the initial PT model is reformulated in terms of the 2D theory of relativistic fermions using an analogy between the 2D sine-Gordon and the massive Thirring models. In the new formalism the misfit parameter corresponds to an effective gauge field that enables to include it in the RG procedure on an equal footing with the other parameters of the theory. The Wetterich equation is applied to obtain flow equations for the parameters of the new fermionic action. We demonstrate that these equations reproduce the KT type of behavior if the misfit parameter is zero. However, any small nonzero value of the quantity rules out a possibility of the KT transition. To confirm the finding we develop a description of the problem in terms of the 2D Coulomb gas model. Within the approach the breakdown of the KT scenario gains a transparent meaning, the misfit gives rise to an effective in-plane electric field that prevents a formation of bound vortex-antivortex pairs.Comment: 12 pages, 3 figure

The Decay Properties of the 1^{-+} Hybrid State

Within the framework of the QCD sum rules, we consider the three-point correlation function, work at the limit q^2 -> 0 and m_\pi -> 0, and pick out the singular term ~ {1\over q^2} to extract the pionic coupling constants of the 1^{-+} hybrid meson. Then we calculate the decay widths of different modes. The decay width of the S-wave modes b_1 \pi, f_1\pi increases quickly as the hybrid meson mass and decay momentum increase. But for the low mass hybrid meson around 1.6 GeV, the P-wave decay mode \rho \pi is very important and its width is around 180 MeV, while the widths of \eta \pi and \eta^\prime \pi are strongly suppressed. We suggest the experimental search of \pi_1(1600) through the decay chains at BESIII: e^+e^- -> J/\psi(\psi') -> \pi_1 +\gamma or e^+e^- -> J/\psi(\psi') -> \pi_1 +\rho where the \pi_1 state can be reconstructed through the decay modes \pi_1 -> \rho\pi -> \pi^+\pi^-\pi^0 or \pi_1 -> f_1(1285)\pi^0. It is also interesting to look for \pi_1 using the available BELLE/BABAR data through the process e^+e^- -> \gamma^\ast -> \rho\pi_1, b_1\pi_1, \gamma \pi_1 etc.Comment: one reference correcte

Semileptonic decays of pseudoscalar mesons to scalar "f_0" meson

The transition form factors of (D_s -> f_0 l nu), (D -> f_0 l nu) and (B_u -> f_0 l nu) decays are calculated in 3-point QCD sum rule method, assuming that "f_0" is a quark-antiquark state with a mixture of strange and light quarks. The branching ratios of these decays are calculated in terms of the mixing angle.Comment: 12 pages, 4 figures, LaTeX formatte