970 research outputs found

    Recurrence and Polya number of general one-dimensional random walks

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    The recurrence properties of random walks can be characterized by P\'{o}lya number, i.e., the probability that the walker has returned to the origin at least once. In this paper, we consider recurrence properties for a general 1D random walk on a line, in which at each time step the walker can move to the left or right with probabilities ll and rr, or remain at the same position with probability oo (l+r+o=1l+r+o=1). We calculate P\'{o}lya number PP of this model and find a simple expression for PP as, P=1ΔP=1-\Delta, where Δ\Delta is the absolute difference of ll and rr (Δ=lr\Delta=|l-r|). We prove this rigorous expression by the method of creative telescoping, and our result suggests that the walk is recurrent if and only if the left-moving probability ll equals to the right-moving probability rr.Comment: 3 page short pape

    Rare Semileptonic Decays of Heavy Mesons with Flavor SU(3) Symmetry

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    In this paper, we calculate the decay rates of D+D0e+νD^+ \to D^0 e^+ \nu, DS+D0e+νD^+_S \to D^0 e^+ \nu, BS0B+eνˉB^0_S \to B^+ e^- \bar{\nu}, DS+D+ee+D^+_S \to D^+ e^- e^+ and BS0B0ee+B^0_S \to B^0 e^-e^+ semileptonic decay processes, in which only the light quarks decay, while the heavy flavors remain unchanged. The branching ratios of these decay processes are calculated with the flavor SU(3) symmetry. The uncertainties are estimated by considering the SU(3) breaking effect. We find that the decay rates are very tiny in the framework of the Standard Model. We also estimate the sensitivities of the measurements of these rare decays at the future experiments, such as BES-III, super-BB and LHC-bb.Comment: 4 pages and 1 figure, accepted by European Physical Journal

    Six low-strain zinc-blende half metals: An ab initio investigation

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    A class of spintronic materials, the zinc-blende (ZB) half metals, has recently been synthesized in thin-film form. We apply all-electron and pseudopotential ab initio methods to investigate the electronic and structural properties of ZB Mn and Cr pnictides and carbides, and find six compounds to be half metallic at or near their respective equilibrium lattice constants, making them excellent candidates for growth at low strain. Based on these findings, we further propose substrates on which the growth may be accomplished with minimum strain. Our findings are supported by the recent successful synthesis of ZB CrAs on GaAs and ZB CrSb on GaSb, where our predicted equilibrium lattice constants are within 0.5% of the lattice constants of the substrates on which the growth was accomplished. We confirm previous theoretical results for ZB MnAs, but find ZB MnSb to be half metallic at its equilibrium lattice constant, whereas previous work has found it to be only nearly so. We report here two low-strain half metallic ZB compounds, CrP and MnC, and suggest appropriate substrates for each. Unlike the other five compounds, we predict ZB MnC to become/remain half metallic with compression rather than expansion, and to exhibit metallicity in the minority-rather than majority-spin channel. These fundamentally different properties of MnC can be connected to substantially greater p-d hybridization and d-d overlap, and correspondingly larger bonding-antibonding splitting and smaller exchange splitting. We examine the relative stability of each of the six ZB compounds against NiAs and MnP structures, and find stabilities for the compounds not yet grown comparable to those already grown

    Current-induced cooling phenomenon in a two-dimensional electron gas under a magnetic field

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    We investigate the spatial distribution of temperature induced by a dc current in a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field. We numerically calculate the distributions of the electrostatic potential phi and the temperature T in a 2DEG enclosed in a square area surrounded by insulated-adiabatic (top and bottom) and isopotential-isothermal (left and right) boundaries (with phi_{left} < phi_{right} and T_{left} =T_{right}), using a pair of nonlinear Poisson equations (for phi and T) that fully take into account thermoelectric and thermomagnetic phenomena, including the Hall, Nernst, Ettingshausen, and Righi-Leduc effects. We find that, in the vicinity of the left-bottom corner, the temperature becomes lower than the fixed boundary temperature, contrary to the naive expectation that the temperature is raised by the prevalent Joule heating effect. The cooling is attributed to the Ettingshausen effect at the bottom adiabatic boundary, which pumps up the heat away from the bottom boundary. In order to keep the adiabatic condition, downward temperature gradient, hence the cooled area, is developed near the boundary, with the resulting thermal diffusion compensating the upward heat current due to the Ettingshausen effect.Comment: 25 pages, 7 figure

    Spin-polarized ballistic transport in a thin superlattice of zinc blende half-metallic compounds

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    We examine theoretically ballistic conduction in thin layers of zinc blende half metals, considering as an example a superlattice consisting of monolayers of GaAs and MnAs, a bilayer of CrAs, and a bilayer of GaAs. By artificially separating bilayers, we show that surface states thwart half metallicity. However, capping the metal-As bilayers restores half metallicity, and ballistic conduction of electrons within ∼0.3 eV of the Fermi level will give nearly 100% spin-polarized transmission in the direction of the superlattice. Recent developments suggest atomic layer epitaxy can be used to produce such thin layers for spintronic applications. ©2005 The American Physical Society

    Theoretical study of electronic Raman scattering of Borocarbide superconductors

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    The electronic Raman scattering of Borocarbide superconductors is studied based on the weak coupling theory with s+gs+g-wave gap symmetry. The low energy behaviors and the relative peak positions can be naturally understood, while the explanation of the detailed shape of the B1gB_{1g} peak seems to require a strong inelastic interaction not present in the weak coupling theory.Comment: Revtex 4 file, 9 pages and 5 figure

    Spin Susceptibility and Superexchange Interaction in the Antiferromagnet CuO

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    Evidence for the quasi one-dimensional (1D) antiferromagnetism of CuO is presented in a framework of Heisenberg model. We have obtained an experimental absolute value of the paramagnetic spin susceptibility of CuO by subtracting the orbital susceptibility separately from the total susceptibility through the 63^{63}Cu NMR shift measurement, and compared directly with the theoretical predictions. The result is best described by a 1D S=1/2S=1/2 antiferromagnetic Heisenberg (AFH) model, supporting the speculation invoked by earlier authors. We also present a semi-quantitative reason why CuO, seemingly of 3D structure, is unexpectedly a quasi 1D antiferromagnet.Comment: 7 pages including 4 tables and 9 figure

    Thermopower and thermal conductivity of superconducting perovskite MgCNi3MgCNi_3

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    The thermopower and thermal conductivity of superconducting perovskite MgCNi3MgCNi_3 (TcT_c \approx 8 K) have been studied. The thermopower is negative from room temperature to 10 K. Combining with the negative Hall coefficient reported previously, the negative thermopower definetly indicates that the carrier in MgCNi3MgCNi_3 is electron-type. The nonlinear temperature dependence of thermopower below 150 K is explained by the electron-phonon interaction renormalization effects. The thermal conductivity is of the order for intermetallics, larger than that of borocarbides and smaller than MgB2MgB_2. In the normal state, the electronic contribution to the total thermal conductivity is slightly larger than the lattice contribution. The transverse magnetoresistance of MgCNi3MgCNi_3 is also measured. It is found that the classical Kohler's rule is valid above 50 K. An electronic crossover occures at T50KT^* \sim 50 K, resulting in the abnormal behavior of resistivity, thermopower, and magnetoresistance below 50 K.Comment: Revised on 12 September 2001, Phys. Rev. B in pres
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