our analysis to gauge field configurations which are static and uniform in the y-direction. Within this restriction we take a gauge in which $A_{1}=a_{1}=0$.

The Maxwell and Chern-Simons extremum equations are respectively,

$$\partial _{\nu }F^{\nu \mu }=eJ_{ind}^{\mu }  \eqnum{3.10a}$$

$$-\frac{N}{4\pi }\varepsilon ^{\mu \nu \rho }f_{\nu \rho }=J_{ind}^{\mu } 
\eqnum{3.10b}$$

Here, $f_{\mu \nu }$ is the Chern-Simons gauge field strength tensor, defined as $f_{\mu \nu }=\partial _{\mu }a_{\nu }-\partial _{\nu }a_{\mu }$, and $J_{ind}^{\mu }$ is the current density induced by the anyon system at finite temperature and density. Their different components are given by

$$J_{ind}^{0}\left( x\right) ={\it \Pi }_{{\it 0}}\left[ a_{0}\left( x\right)
+eA_{0}\left( x\right) \right] +{\it \Pi }_{{\it 0}}\,^{\prime }\partial
_{x}\left( {\cal E}+eE\right) +{\it \Pi }_{{\it 1}}\left( b+eB\right) 
\eqnum{3.11a}$$

$$J_{ind}^{1}\left( x\right) =0,\qquad J_{ind}^{2}\left( x\right) ={\it \Pi }_{%
{\it 1}}\left( {\cal E}+eE\right) +{\it \Pi }_{\,{\it 2}}\partial _{x}\left(
b+eB\right)  \eqnum{3.11b}$$

in the above expressions we used the following notation: ${\cal E}=f_{01}$, $%
E=F_{01}$, $b=f_{12}$ and $B=F_{12}$. Eqs. (3.11) play the role in the anyon fluid of the London equations in BCS superconductivity. When the induced currents (3.11) are substituted in eqs. (3.10) we find, after some manipulation, the set of independent differential equations,

$$\omega \partial _{x}^{2}B+\alpha B=\gamma \left[ \partial _{x}E-\sigma
A_{0}\right] +\tau 