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We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle . Such a four-terminal junction with a tunable can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for = 90 there is one proper bound state and one eigenvalue embedded in the continuum. We show that the number of eigenvalues becomes larger with increasing asymmetry and the bound-state energies are increasing as functions of in the interval (0, 90). Moreover, states which are sufficiently strongly bound exist in pairs with a small energy difference and opposite parities. Finally, we discuss how the bound states transform with increasing into quasibound states with a complex wave vector.

Let X = (x_1,..,x_n) and Y = (y_1,...,y_m) be a pair of corresponding plaintext and ciphertext for a cryptosystem. We define an embedded surface of this cryptosystem as any polynomial equation: E(X,Y)=E(x_1,..,x_n,y_1,...,y_m)=0, which is satisfied by all such pairs. In this paper, we present a new attack on the multivariate public key cryptosystems from Diophantine equations developed by Gao and Heindl by using the embedded surfaces associated to this family of multivariate cryptosystems.

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No abstract uploaded!