Saturation of dephasing time in mesoscopic devices produced by a ferromagnetic state

We consider an exchange model of itinerant electrons in a Heisenberg ferromagnet and we assume that the ferromagnet is in a fully polarized state. Using the Holstein-Primakoff transformation we are able to obtain a boson-fermion Hamiltonian that is well-known in the interaction between light and matter. This model describes the spontaneous emission in two-level atoms that is the proper decoherence mechanism when the number of modes of the radiation field is taken increasingly large, the vacuum acting as a reservoir. In the same way one can see that the interaction between the bosonic modes of spin waves and an itinerant electron produces decoherence by spin flipping with a rate proportional to the size of the system. In this way we are able to show that the experiments on quantum dots, described in D. K. Ferry et al. [Phys. Rev. Lett. {\bf 82}, 4687 (1999)], and nanowires, described in D. Natelson et al. [Phys. Rev. Lett. {\bf 86}, 1821 (2001)], can be understood as the interaction of itinerant electrons and an electron gas in a fully polarized state.Comment: 10 pages, no figure. Changed title. Revised version accepted for publication in Physical Review

Nonperturbative Relations in N=2 SUSY Yang-Mills and WDVV equation

We find the nonperturbative relation between $\langle {\rm tr} \phi^2 \rangle$, $\langle {\rm tr} \phi^3\rangle$ the prepotential ${\cal F}$ and the vevs $\langle \phi_i\rangle$ in $N=2$ supersymmetric Yang-Mills theories with gauge group $SU(3)$. Nonlinear differential equations for ${\cal F}$ including the Witten -- Dijkgraaf -- Verlinde -- Verlinde equation are obtained. This indicates that $N=2$ SYM theories are essentially topological field theories and that should be seen as low-energy limit of some topological string theory. Furthermore, we construct relevant modular invariant quantities, derive canonical relations between the periods and investigate the structure of the beta function by giving its explicit form in the moduli coordinates. In doing this we discuss the uniformization problem for the quantum moduli space. The method we propose can be generalized to $N=2$ supersymmetric Yang-Mills theories with higher rank gauge groups.Comment: 12 pages, LaTex. Expanded version. New results, corrections, references and acknowledgements adde

Synthesis, characterization, and photocatalytic activity of pure and N-, B-, or Ag- Doped TiO2

This article reports the synthesis and characterization of pure and N-, B-, and Ag-doped TiO2 and the ability of these oxides to photodegrade methylene blue (MB) under sunlight or UV-ABC radiation. The compounds were synthesized using the sol-gel method and characterized by scanning electron microscopy, X-ray diffraction, diffuse reflectance spectroscopy, Fourier transform infrared spectroscopy, thermogravimetric analysis, and X-ray photoelectron spectroscopy. Photocatalytic efficiency was significantly increased by N-doping, resulting in 98% MB decomposition under UV-ABC irradiation for 180 min. Ag- and B-doped TiO2 lowered MB degradation rates to 52 and 73%, respectively, compared with pure TiO2. The same behavior was observed with exposure to UV-Vis, with 88, 65, 60, and 42% MB removal with N-doped, pure, B-doped, and Ag-doped TiO2, respectively. Under visible light alone, N-doped TiO2 exhibited higher photocatalytic efficiency than commercial P25-type TiO2. Photocatalysis with N-doped TiO2 proved to be a promising alternative for MB degradation, given the potential of employing solar energy, thus minimizing operating costs

Nonperturbative Renormalization Group Equation and Beta Function in N=2 SUSY Yang-Mills

We obtain the exact beta function for $N=2$ SUSY $SU(2)$ Yang-Mills theory and prove the nonperturbative Renormalization Group Equation $$\partial_\Lambda{\cal F}(a,\Lambda)= {\Lambda\over \Lambda_0}\partial_{\Lambda_0}{\cal F}(a_0,\Lambda_0) e^{-2\int_{\tau_0}^\tau {dx \beta^{-1}(x)}}.$$Comment: LaTex, 10 pg. Expanded introduction, references added, to appear in Phys. Rev. Let

π+\pi^+ photoproduction on the proton for photon energies from 0.725 to 2.875 GeV

Differential cross sections for the reaction $\gamma p \to n \pi^+$ have been measured with the CEBAF Large Acceptance Spectrometer (CLAS) and a tagged photon beam with energies from 0.725 to 2.875 GeV. Where available, the results obtained here compare well with previously published results for the reaction. Agreement with the SAID and MAID analyses is found below 1 GeV. The present set of cross sections has been incorporated into the SAID database, and exploratory fits have been made up to 2.7 GeV. Resonance couplings have been extracted and compared to previous determinations. With the addition of these cross sections to the world data set, significant changes have occurred in the high-energy behavior of the SAID cross-section predictions and amplitudes.Comment: 18 pages, 10 figure

Non-linear Representations of the Conformal Group and Mapping of Galileons

There are two common non-linear realizations of the 4D conformal group: in the first, the dilaton is the conformal factor of the effective metric \eta_{\mu\nu} e^{-2 \pi}; in the second it describes the fluctuations of a brane in AdS_5. The two are related by a complicated field redefinition, found by Bellucci, Ivanov and Krivonos (2002) to all orders in derivatives. We show that this field redefinition can be understood geometrically as a change of coordinates in AdS_5. In one gauge the brane is rigid at a fixed radial coordinate with a conformal factor on the AdS_5 boundary, while in the other one the brane bends in an unperturbed AdS_5. This geometrical picture illuminates some aspects of the mapping between the two representations. We show that the conformal Galileons in the two representations are mapped into each other in a quite non-trivial way: the DBI action, for example, is mapped into a complete linear combination of all the five Galileons in the other representation. We also verify the equivalence of the dilaton S-matrix in the two representations and point out that the aperture of the dilaton light-cone around non-trivial backgrounds is not the same in the two representations.Comment: 16 pages. v2: typos corrected (notably eq 4.5), matches JHEP versio

Inequivalence of coset constructions for spacetime symmetries

Non-linear realizations of spacetime symmetries can be obtained by a generalization of the coset construction valid for internal ones. The physical equivalence of different representations for spacetime symmetries is not obvious, since their relation involves not only a redefinition of the fields but also a field-dependent change of coordinates. A simple and relevant spacetime symmetry is obtained by the contraction of the 4D conformal group that leads to the Galileon group. We analyze two non-linear realizations of this group, focusing in particular on the propagation of signals around non-trivial backgrounds. The aperture of the lightcone is in general different in the two representations and in particular a free (luminal) massless scalar is mapped in a Galileon theory which admits superluminal propagation. We show that in this theory, if we consider backgrounds that vanish at infinity, there is no asymptotic effect: the displacement of the trajectory integrates to zero, as can be expected since the S-matrix is trivial. Regarding local measurements, we show that the puzzle is solved taking into account that a local coupling with fixed sources in one theory is mapped into a non-local coupling and we show that this effect compensates the different lightcone. Therefore the two theories have a different notion of locality. The same applies to the different non-linear realizations of the conformal group and we study the particular case of a cosmologically interesting background: the Galilean Genesis scenarios