Exactly solvable PT\mathcal{PT}-symmetric models in two dimensions

Non-hermitian, $\mathcal{PT}$-symmetric Hamiltonians, experimentally realized in optical systems, accurately model the properties of open, bosonic systems with balanced, spatially separated gain and loss. We present a family of exactly solvable, two-dimensional, $\mathcal{PT}$ potentials for a non-relativistic particle confined in a circular geometry. We show that the $\mathcal{PT}$ symmetry threshold can be tuned by introducing a second gain-loss potential or its hermitian counterpart. Our results explicitly demonstrate that $\mathcal{PT}$ breaking in two dimensions has a rich phase diagram, with multiple re-entrant $\mathcal{PT}$ symmetric phases.Comment: 6 pages, 6 figure

High Performance Power Spectrum Analysis Using a FPGA Based Reconfigurable Computing Platform

Power-spectrum analysis is an important tool providing critical information about a signal. The range of applications includes communication-systems to DNA-sequencing. If there is interference present on a transmitted signal, it could be due to a natural cause or superimposed forcefully. In the latter case, its early detection and analysis becomes important. In such situations having a small observation window, a quick look at power-spectrum can reveal a great deal of information, including frequency and source of interference. In this paper, we present our design of a FPGA based reconfigurable platform for high performance power-spectrum analysis. This allows for the real-time data-acquisition and processing of samples of the incoming signal in a small time frame. The processing consists of computation of power, its average and peak, over a set of input values. This platform sustains simultaneous data streams on each of the four input channels.Comment: 5 pages, 3 figures. Published in the Proceedings of the IEEE International conference on Reconfigurable Computing and FPGAs (ReConFig 2006). Article also available at http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=4100006&isnumber=409995