12,796 research outputs found

    Transformations RS42(3){RS}_4^2(3) of the Ranks ≤4\leq4 and Algebraic Solutions of the Sixth Painlev\'e Equation

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    Compositions of rational transformations of independent variables of linear matrix ordinary differential equations (ODEs) with the Schlesinger transformations (RSRS-transformations) are used to construct algebraic solutions of the sixth Painlev\'e equation. RSRS-Transformations of the ranks 3 and 4 of 2×22\times2 matrix Fuchsian ODEs with 3 singular points into analogous ODE with 4 singular points are classified.Comment: 26 page

    Hydrodynamic description of transport in strongly correlated electron systems

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    We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temperatures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, κ\kappa. This is in striking contrast with the Stokes flow, in which the resistance is independent of κ\kappa and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magnetoresistance
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