Steve Simon

Abstract:

We construct a wave function, generalizing the well-known Moore-Read Pfaffian, that describes spinless electrons at filling fraction ν=2/5 (or bosons at filling fraction ν=2/3) as the ground state of a very simple three body potential. We find, analogous to the Pfaffian, that when quasiholes are added there is a ground state degeneracy which can be identified as zero modes of the quasiholes. The zero modes are identified as having semionic statistics. We write this wave function as a correlator of the Virasoro minimal model conformal field theory M (5,3). Since this model is nonunitary, we conclude that this wave function is likely a quantum critical state. Nonetheless, we find that the overlaps of this wave function with exact diagonalizations in the lowest and first excited Landau level are very high, suggesting that this wave function may have experimental relevance for some transition that may occur in that regime. © 2007 The American Physical Society.

Abstract:

Certain well known quantum Hall states-including the Laughlin states, the Moore-Read Pfaffian, and the Read-Rezayi Parafermion states-can be defined as the unique lowest degree symmetric analytic function that vanishes as at least p powers as some number (g+1) of particles approach the same point. Analogously, these same quantum Hall states can be generated as the exact highest density zero energy state of simple angular momentum projection operators. Following this theme we determine the highest density zero energy state for many other values of p and g. © 2007 The American Physical Society.

Abstract:

A promising new method from the field of representations of Lie groups is applied to calculate integrals over unitary groups, which are important for multiantenna communications. To demonstrate the power and simplicity of this technique, a number of recent results are rederived, using only a few simple steps. In particular, we derive the joint probability distribution of eigenvalues of the matrix GG† with G a nonzero mean or a semicor-related Gaussian random matrix. These joint probability distribution functions can then be used to calculate the moment generating function of the mutual information for Gaussian multiple-input multiple-output (MIMO) channels with these probability distribution of their channel matrices G. We then turn to the previously unsolved problem of calculating the moment generating function of the mutual information of MIMO channels, which are correlated at both the receiver and the transmitter. From this moment generating function we obtain the ergodic average of the mutual information and study the outage probability. These methods can be applied to a number of other problems. As a particular example, we examine unitary encoded space-time transmission of MIMO systems and we derive the received signal distribution when the channel matrix is correlated at the transmitter end. © 2006 IEEE.

Abstract:

The dynamics of quantum degenerate two-dimensional dipolar excitons confined in electrostatic traps is analyzed and compared to recent experiments. The model results stress the importance of artificial trapping for achieving and sustaining a quantum degenerate exciton fluid in such systems and suggest that a long-lived, spatially uniform, and highly degenerate exciton system was experimentally produced in those electrostatic traps. © 2006 American Institute of Physics.