Two-Dimensional Electron Systems in Magnetic Fields: The Current Equipartition Law

We consider two-dimensional randomly deformed circular quantum dots with two attached waveguides (an emitter and a collector) in magnetic fields as an electronic analogy of the blackbody radiation. Transport properties through them are numerically investigated. The fraction of the current carried by each propagating mode in the collector is computed for transmission currents when each propagating mode is incident. By taking the statistical average in shape, it is shown that a universal frequency distribution is obtained for a sufficiently deformed system even though magnetic fields are so strong that electron waves form edge states. Then, the transmission currents are randomly distributed over all propagating modes. On average, each propagating mode carries the same current as in the absence of a magnetic field. It is also confirmed that a finite size dot cannot be a model of a reservoir even if it is chaotic.