We develop a supersymmetric representation of the Hubbard operators which unifies the Slave Boson and Slave Fermion representations, allowing a second-quantized treatment of Hubbard operators with both symmetric and anti-symmetric character. We provide a simple example of the application of this method to the atomic limit of the Hubbard model and discuss its more general application to the infi...

In this paper we give a mathematically rigorous analysis of the Klein paradox in the many-particle formulation of the Dirac theory. This paradox was meant as an example demonstrating the negative energy problems of the single particle Dirac equation. However, we show that this problem does not disappear in the second quantized version of the Dirac theory. It corresponds with a situation which c...

The correlation functions of two-dimensional anyon fields in a KMS-state are studied. The n-particle wave functions of noncanonical fermions of level ν, ν odd, are shown to be of Laughlin type of order ν. For the first noncanonical Fermi class (ν=3) this is simply the finite-temperature generalization of Laughlin wave function. This relates the first and second quantized pictures of the fractio...

In this paper we discuss estimation of parameters from quantized data. Extending some recent results appeared in the literature we show that, under a regularity assumption on the parametric model describing the data, the Maximum Likelihood estimator can be found, asymptotically, in closed form in two steps. The first is a non-linear (and invertible) mapping of the observed relative frequencies ...

The macroscopic flow properties of pure He II are probed in the limit of zero temperature using an oscillating grid. As the oscillation amplitude passes a first critical threshold, the resonant frequency starts decreasing but the flow remains nondissipative. Beyond a second critical amplitude, the flow undergoes a transition to turbulence and becomes dissipative. Nonlinearity and hysteresis obs...

This paper studies the restoration of color-quantized images. Restoration of color-quantized images is rarely addressed in literature, and direct applications of existing restoration techniques are generally inadequate to deal with this problem. In this paper, we propose a restoration algorithm for restoring color-quantized images. This algorithm makes good use of the available color palette to...

A quantized controller is a model-free controller which can provide a nonlinear control. This paper conduct a preliminary study on using the quantized controller in the Static VAR Compensators (SVC) control to enhance the damping of the power-swing. The test system used is a two area multi-machine system. A severe disturbance is introduced into the power system and the quantized controller cont...

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We examine the quantization of the motion of two charged vortices in a Ginzburg–Landau theory for the fractional quantum Hall effect recently proposed by the first two authors. The system has two second-class constraints which can be implemented either in the reduced phase space or Dirac–Gupta–Bleuler formalism. Using the intrinsic formulation of statistics, we show that these two ways of imple...

This paper provides new error bounds on consistent reconstruction methods for signals observed from quantized random sensing. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a reobservation of the estimated signal under the same sensing model. Focusing on dithered uniform scalar quantization of resolution δ > 0, we prove first that, given...