On the Distribution of Zeroes of Artin-Schreier L-functions

We study the distribution of the zeroes of the L-functions of curves in the Artin-Schreier family. We consider the number of zeroes in short intervals and obtain partial results which agree with a random unitary matrix model

Artin-Schreier L-functions and Random Unitary Matrices

We give a new derivation of an identity due to Z. Rudnick and P. Sarnak about the $n$-level correlations of eigenvalues of random unitary matrices as well as a new proof of a formula due to M. Diaconis and P. Shahshahani expressing averages of trace products over the unitary matrix ensemble. Our method uses the zero statistics of Artin-Schreier L-functions and a deep equidistribution result due to N. Katz and P. Sarnak

Photogalvanic current in a double quantum well

We study the in-plane stationary current caused by phototransitions between the states of a double quantum well. The electric polarization of light has both vertical and in-plane components. The stationary current originates from the periodic vibration of electrons between two non-equivalent quantum wells caused by the normal component of the alternating electric field with simultaneous in-plane acceleration/deceleration by the in-plane component of electric field. The quantum mechanism of the stationary current is conditioned by in-plane transition asymmetry which appears due to the indirect phototransitions with the participation of impurity scattering. The photocurrent has a resonant character corresponding to the equality of the photon energy to the distance between subbands. It is found that the current appears as a response to the linear-polarized light.Comment: 6 pages, 2 figure