12,796 research outputs found
Transformations of the Ranks and Algebraic Solutions of the Sixth Painlev\'e Equation
Compositions of rational transformations of independent variables of linear
matrix ordinary differential equations (ODEs) with the Schlesinger
transformations (-transformations) are used to construct algebraic
solutions of the sixth Painlev\'e equation. -Transformations of the ranks 3
and 4 of 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
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, . This is in striking contrast with the
Stokes flow, in which the resistance is independent of and
proportional to the fluid viscosity. We also identify a new hydrodynamic
mechanism of spin magnetoresistance
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