Modernizing PHCpack through phcpy

PHCpack is a large software package for solving systems of polynomial equations. The executable phc is menu driven and file oriented. This paper describes the development of phcpy, a Python interface to PHCpack. Instead of navigating through menus, users of phcpy solve systems in the Python shell or via scripts. Persistent objects replace intermediate files.Comment: Part of the Proceedings of the 6th European Conference on Python in Science (EuroSciPy 2013), Pierre de Buyl and Nelle Varoquaux editors, (2014

The mass gap and vacuum energy of the Gross-Neveu model via the 2PPI expansion

We introduce the 2PPI (2-point-particle-irreducible) expansion, which sums bubble graphs to all orders. We prove the renormalizibility of this summation. We use it on the Gross-Neveu model to calculate the mass gap and vacuum energy. After an optimization of the expansion, the final results are qualitatively good.Comment: 14 pages,19 eps figures, revtex

Computing Dynamic Output Feedback Laws

The pole placement problem asks to find laws to feed the output of a plant governed by a linear system of differential equations back to the input of the plant so that the resulting closed-loop system has a desired set of eigenvalues. Converting this problem into a question of enumerative geometry, efficient numerical homotopy algorithms to solve this problem for general Multi-Input-Multi-Output (MIMO) systems have been proposed recently. While dynamic feedback laws offer a wider range of use, the realization of the output of the numerical homotopies as a machine to control the plant in the time domain has not been addressed before. In this paper we present symbolic-numeric algorithms to turn the solution to the question of enumerative geometry into a useful control feedback machine. We report on numerical experiments with our publicly available software and illustrate its application on various control problems from the literature.Comment: 20 pages, 3 figures; the software described in this paper is publicly available via http://www.math.uic.edu/~jan/download.htm

The asymmetry of the dimension 2 gluon condensate: the finite temperature case

In this paper, we continue the work begun in a previous article. We compute, in the formalism of local composite operators, the value of the asymmetry in the dimension two condensate for finite temperatures. We find a positive value for the asymmetry, which disappears when the temperature is increased. We also compute the value of the full dimension two condensate for higher temperatures, and we find that it decreases in absolute value, finally disappearing for sufficiently high temperature. We also comment on the temperature dependence of the electric and magnetic components of the condensate separately. We compare our results with the corresponding lattice date found by Chernodub and Ilgenfritz.Comment: 8 pages, 4 figure

Optimal teleportation with a mixed state of two qubits

We consider a single copy of a mixed state of two qubits and derive the optimal trace-preserving local operations assisted by classical communication (LOCC) such as to maximize the fidelity of teleportation that can be achieved with this state. These optimal local operations turn out to be implementable by one-way communication, and always yields a teleportation fidelity larger than 2/3 if the original state is entangled. This maximal achievable fidelity is an entanglement measure and turns out to quantify the minimal amount of mixing required to destroy the entanglement in a quantum state.Comment: 5 pages, expanded version of part II of quant-ph/0203073(v2

Variational principle for non-linear wave propagation in dissipative systems

The dynamics of many natural systems is dominated by non-linear waves propagating through the medium. We show that the dynamics of non-linear wave fronts with positive surface tension can be formulated as a gradient system. The variational potential is simply given by a linear combination of the occupied volume and surface area of the wave front, and changes monotonically in time. Finally, we demonstrate that vortex filaments can be written as a gradient system only if their binormal velocity component vanishes, which occurs in chemical system with equal diffusion of reactants