11. In the Cartesian coordinate system $x O y$, the equation of the hyperbola $C$ is $x^{2}-y^{2}=1$. Find all real numbers $a$ greater than 1 that satisfy the following condition: For any two perpendicular lines $l_{1}$ and $l_{2}$ passing through the point $(a, 0)$, if $l_{1}$ intersects the hyperbola $C$ at points $P, Q$, and $l_{2}$ intersects $C$ at points $R, S$, then $|P Q|=|R S|$ always holds.