Phase diagrams for quantum Brownian motion models on two-dimensional Bravais lattices

We study quantum Brownian motion (QBM) models for a particle in a dissipative environment coupled to a periodic potential. We review QBM for a particle in a one-dimensional periodic potential and extend the study to that for a particle in two-dimensional (2D) periodic potentials of four Bravais lattice types: square, rectangular, triangular (hexagonal), and centered rectangular. We perform perturbative renormalization group analyses to derive the zero temperature flow diagrams and phase boundaries for a particle in these potentials, and observe localization behavior dependent on the anisotropy of the lattice parameters.Comment: 16 pages, 5 figure

Frequency domain criteria for lp-robust stability of systems with fuzzy parameters

The paper deals with the problem of determining stability margin of linear continuous-time system with fuzzy parametric uncertainty. Non-symmetric multivariate membership functions with lp -constraints describing the uncertainty of characteristic polynomial parameters are considered. An elegant solution, graphical in nature, based on generation of Tsypkin-Polyak plot is presented