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

<table>Plots of transmission coefficients <svg height="14.9" id="M167" style="vertical-align:-4.74141pt" version="1.1" viewbox="0 0 17.775 14.9" width="17.775" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,14.9)">
<g transform="translate(72,-60.08)">
<text transform="matrix(1,0,0,-1,-71.95,64.86)">
<tspan style="font-size: 12.50px; " x="0" y="0">𝑡</tspan>
</text>
<text transform="matrix(1,0,0,-1,-68.04,61.74)">
<tspan style="font-size: 8.75px; " x="0" y="0">1</tspan>
<tspan style="font-size: 8.75px; " x="4.3759999" y="0">𝜇</tspan>
</text>
</g>
</g>
</svg> of the fundamental, 2nd, and 3rd modes for all samples of shape in the complex plane. The incident wave belongs to the fundamental mode; <svg height="20.4125" id="M168" style="vertical-align:-2.64594pt" version="1.1" viewbox="0 0 79.375 20.4125" width="79.375" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,20.4125)">
<g transform="translate(72,-55.67)">
<text transform="matrix(1,0,0,-1,-71.95,58.36)">
<tspan style="font-size: 12.50px; " x="31.690001" y="-0.60000002">√</tspan>
<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>
</text>
<g>
<path d="m -28.66,70.71 20.11,0" style="fill:none;stroke:#000000;stroke-width:0.82499999;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:10;stroke-opacity:1;stroke-dasharray:none"></path>
</g>
<text transform="matrix(1,0,0,-1,-28.66,58.36)">
<tspan style="font-size: 12.50px; " x="0" y="0">3</tspan>
<tspan style="font-size: 12.50px; " x="6.2515001" y="0">2</tspan>
<tspan style="font-size: 12.50px; " x="12.503" y="0">𝜋</tspan>
</text>
</g>
</g>
</svg> and <svg height="15.3625" id="M169" style="vertical-align:-0.27588pt" version="1.1" viewbox="0 0 38.825001 15.3625" width="38.825001" xmlns="http://www.w3.org/2000/svg">
<g transform="matrix(1.25,0,0,-1.25,0,15.3625)">
<g transform="translate(72,-59.71)">
<text transform="matrix(1,0,0,-1,-70.85,62.57)">
<tspan style="font-size: 12.50px; " x="0" y="0"></tspan>
<tspan style="font-size: 12.50px; " x="-1.1" y="2.54">𝐵</tspan>
<tspan style="font-size: 12.50px; " x="11.565539" y="2.54">=</tspan>
<tspan style="font-size: 12.50px; " x="23.605928" y="2.54">9</tspan>
</text>
</g>
</g>
</svg>.</table>

Advances in Condensed Matter Physics

fig18

Figure 18

Figure 18: Two-Dimensional Electron Systems in Magnetic Fields: The Current Equipartition Law 