Events in Physics
Christoph Uiberacker
Location: PS128
Current Conservation in Non-Equilibrium Networks
For Quantum-Hall-Systems network models have been successfully used to investigate questions of localizations as well as the distribution of electro-chemical potentials. While the well-known Chalker-Coddington network model [1] , which uses elastic single particle quantum tunneling at saddle points to obtain critical exponents, was used for the former task, in the latter the nonequilibrium network model [2-4], which describes quantities of nonquilibrium thermodynamics via the Landauer-Büttiker approach, was used. In case of local linear transport at saddles we show that the chemical potential distribution can be obtained, respecting the boundary condition of injected currents, from an inhomogeneous system of linear equations. It turns out that the solution is uniquely determined by the boundary condition, no matter how many current contacts we have. The seaming contradiction can be resolved by the fact that current is automatically conserved due to the formulation of the network.
[1] J. T. Chalker and P. D. Coddington, “Percolation, quantum tunnelling and the integer Hall effect“, J. Phys. C: Solid State Phys. 21, 2665 (1988).
[2] J. Oswald, “A new model for the transport regime of the integer quantum Hall effect: The role of bulk transport in the edge channel picture”, Physica E 3, 30 (1998).
[3] J. Oswald and M. Oswald, “Circuit type simulations of magneto-transport in the quantum Hall effect regime“, J. Phys.: Condens. Matter *18*, R101 (2006).
[4] C. Uiberacker, C. Stecher, and J. Oswald, “/Systematic study of nonideal contacts in integer quantum Hall systems/”, Phys. Rev. B *80*,
235331 (2009).
For Quantum-Hall-Systems network models have been successfully used to investigate questions of localizations as well as the distribution of electro-chemical potentials. While the well-known Chalker-Coddington network model [1] , which uses elastic single particle quantum tunneling at saddle points to obtain critical exponents, was used for the former task, in the latter the nonequilibrium network model [2-4], which describes quantities of nonquilibrium thermodynamics via the Landauer-Büttiker approach, was used. In case of local linear transport at saddles we show that the chemical potential distribution can be obtained, respecting the boundary condition of injected currents, from an inhomogeneous system of linear equations. It turns out that the solution is uniquely determined by the boundary condition, no matter how many current contacts we have. The seaming contradiction can be resolved by the fact that current is automatically conserved due to the formulation of the network.
[1] J. T. Chalker and P. D. Coddington, “Percolation, quantum tunnelling and the integer Hall effect“, J. Phys. C: Solid State Phys. 21, 2665 (1988).
[2] J. Oswald, “A new model for the transport regime of the integer quantum Hall effect: The role of bulk transport in the edge channel picture”, Physica E 3, 30 (1998).
[3] J. Oswald and M. Oswald, “Circuit type simulations of magneto-transport in the quantum Hall effect regime“, J. Phys.: Condens. Matter *18*, R101 (2006).
[4] C. Uiberacker, C. Stecher, and J. Oswald, “/Systematic study of nonideal contacts in integer quantum Hall systems/”, Phys. Rev. B *80*,
235331 (2009).
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