10 research outputs found
Rings and Coulomb boxes in dissipative environments
We study a particle on a ring in presence of a dissipative Caldeira-Leggett
environment and derive its response to a DC field. We show how this
non-equilibrium response is related to a flux averaged equilibrium response. We
find, through a 2-loop renormalization group analysis, that a large dissipation
parameter \eta flows to a fixed point \eta^R=\hbar/2\pi. We also reexamine the
mapping of this problem to that of the Coulomb box and show that the relaxation
resistance, of recent interest, is quantized for large \eta. For finite
\eta>\eta^R we find that a certain average of the relaxation resistance is
quantized. We propose a Coulomb box experiment to measure a quantized noise.Comment: 23 pages, 4 figures. Appendix E has been added, some detailed
definitions and references were adde
Winding of planar gaussian processes
We consider a smooth, rotationally invariant, centered gaussian process in
the plane, with arbitrary correlation matrix . We study the winding
angle around its center. We obtain a closed formula for the variance
of the winding angle as a function of the matrix . For most stationary
processes the winding angle exhibits diffusion at large time
with diffusion coefficient .
Correlations of with integer , the distribution of the
angular velocity , and the variance of the algebraic area are also
obtained. For smooth processes with stationary increments (random walks) the
variance of the winding angle grows as , with proper
generalizations to the various classes of fractional Brownian motion. These
results are tested numerically. Non integer is studied numerically.Comment: 12 pages, 6 figure