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تسجيل مستخدم جديدAnisotropic exceptional points of arbitrary order
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A pair of anisotropic exceptional points (EPs) of arbitrary order are found in a class of non-Hermitian random systems with asymmetric hoppings. Both eigenvalues and eigenvectors exhibit distinct behaviors when these anisotropic EPs are approached from two orthogonal directions in the parameter space. For an order-$N$ anisotropic EP, the critical exponents $ u$ of phase rigidity are $(N-1)/2$ and $N-1$, respectively. These exponents are universal within the class. The order-$N$ anisotropic EPs split and trace out multiple ellipses of EPs of order $2$ in the parameter space. For some particular configurations, all the EP ellipses coalesce and form a ring of EPs of order $N$. Crossover to the conventional order-$N$ EPs with $ u=(N-1)/N$ is discussed.
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