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

<table>Size <svg height="10.9125" id="M226" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 20.1 10.9125" width="20.1" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑟</tspan>
<tspan style="font-size: 12.50px; " x="5.1012239" y="0">/</tspan>
<tspan style="font-size: 12.50px; " x="8.5770578" y="0">𝑑</tspan>
</text>
</g>
</g>
</svg> dependence of the fraction <svg height="12.925" id="M227" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 21.225 12.925" width="21.225" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,12.925)">
<g transform="translate(72,-61.66)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑝</tspan>
</text>
<text transform="matrix(1,0,0,-1,-65.84,63.31)">
<tspan style="font-size: 8.75px; " x="0" y="0">𝛼</tspan>
<tspan style="font-size: 8.75px; " x="4.9361281" y="0">𝜇</tspan>
</text>
</g>
</g>
</svg> in the transmission current carried by each propagating mode <svg height="9.6750002" id="M228" style="vertical-align:-2.29482pt" version="1.1" viewbox="0 0 9.6374998 9.6750002" width="9.6374998" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,9.675)">
<g transform="translate(72,-64.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.6)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝜇</tspan>
</text>
</g>
</g>
</svg> when each propagating mode <svg height="7.1750002" id="M229" style="vertical-align:-0.1254pt" version="1.1" viewbox="0 0 8.9375 7.1750002" width="8.9375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,7.175)">
<g transform="translate(72,-66.26)">
<text transform="matrix(1,0,0,-1,-71.95,66.44)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝛼</tspan>
</text>
</g>
</g>
</svg> is injected. The wavenumber is set as <svg height="10.9125" id="M230" style="vertical-align:-0.17555pt" version="1.1" viewbox="0 0 55.362499 10.9125" width="55.362499" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,10.9125)">
<g transform="translate(72,-63.27)">
<text transform="matrix(1,0,0,-1,-71.95,63.5)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝐾</tspan>
<tspan style="font-size: 12.50px; " x="9.5272856" y="0">𝑑</tspan>
<tspan style="font-size: 12.50px; " x="19.642214" y="0">=</tspan>
<tspan style="font-size: 12.50px; " x="31.682602" y="0">1</tspan>
<tspan style="font-size: 12.50px; " x="37.934101" y="0">0</tspan>
</text>
</g>
</g>
</svg>.</table>

Advances in Condensed Matter Physics

fig22

Figure 22

Figure 22: Two-Dimensional Electron Systems in Magnetic Fields: The Current Equipartition Law 