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Flaviu Cipcigan edited magnetoresistance.tex
over 10 years ago
Commit id: 74e1ec13f02a73444a4714de7debad70b5e73124
deletions | additions
diff --git a/magnetoresistance.tex b/magnetoresistance.tex
index 9ce0d6b..fad1dae 100644
--- a/magnetoresistance.tex
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Substituting the components of $\mathbf{B}$, $\mathbf{E}$ and $\mathbf{j} = n q \mathbf{p} / m^*$ into the equation of motion for the charge carrier in the presence of a magnetic field \eqref{eq:eom-B} gives:
\begin{equation}
\begin{split}
j_x
= &= \frac{\sigma_0}{1 + (\omega_\textrm{c} \tau)^2}
\, E_x + \frac{\sigma_0 \omega_\textrm{c} \tau}{1 + (\omega_\textrm{c} \tau)^2} E_y
\\
j_y &= -\frac{\sigma_0 \omega_\textrm{c} \tau}{1 + (\omega_\textrm{c} \tau)^2} E_x + \frac{\sigma_0}{1 + (\omega_\textrm{c} \tau)^2} E_y \quad \textrm{, where}
\end{split}
\end{equation}
\begin{equation}