Inexactness of the Hydro-Thermal Coordination Semidefinite Relaxation

Hydro-thermal coordination is the problem of determining the optimal economic dispatch of hydro and thermal power plants over time. The physics of hydroelectricity generation is commonly simplified in the literature to account for its fundamentally nonlinear nature. Advances in convex relaxation theory have allowed the advent of Shor's semidefinite programming (SDP) relaxations of quadratic models of the problem. This paper shows how a recently published SDP relaxation is only exact if a very strict condition regarding turbine efficiency is observed, failing otherwise. It further proposes the use of a set of convex envelopes as a strategy to successfully obtain a stricter lower bound of the optimal solution. This strategy is combined with a standard iterative convex-concave procedure to recover a stationary point of the original non-convex problem.Comment: Submitted to IEEE PES General Meeting 201

Dimension minimization of a quantum automaton

A new model of a Quantum Automaton (QA), working with qubits is proposed. The quantum states of the automaton can be pure or mixed and are represented by density operators. This is the appropriated approach to deal with measurements and dechorence. The linearity of a QA and of the partial trace super-operator, combined with the properties of invariant subspaces under unitary transformations, are used to minimize the dimension of the automaton and, consequently, the number of its working qubits. The results here developed are valid wether the state set of the QA is finite or not. There are two main results in this paper: 1) We show that the dimension reduction is possible whenever the unitary transformations, associated to each letter of the input alphabet, obey a set of conditions. 2) We develop an algorithm to find out the equivalent minimal QA and prove that its complexity is polynomial in its dimension and in the size of the input alphabet.Comment: 26 page

High-field Electron Spin Resonance of Cu_{1-x}Zn_{x}GeO_{3}

High-Field Electron Spin Resonance measurements were made on powder samples of Cu_{1-x}Zn_{x}GeO_{3} (x=0.00, 0.01, 0.02, 0.03 and 0.05) at different frequencies (95, 110, 190, 220, 330 and 440 GHz) at low temperatures. The spectra of the doped samples show resonances whose positions are dependent on Zn concentration, frequency and temperature. The analysis of intensity variation of these lines with temperature allows us to identify them as originating in transitions within states situated inside the Spin Peierls gap. A qualitative explanation of the details of the spectra is possible if we assume that these states in the gap are associated with "loose" spins created near the Zn impurities, as recently theoreticaly predicted. A new phenomenon of quenching of the ESR signal across the Dimerized to Incommensurate phase-boundary is observed.Comment: 4 pages, 5 ps figures in the text, submitted to Phys. Rev. Let