arXiv subjects
Publications and source records attributed to José Luís Da Silva.
Starting with the overall wave function expression for the electron in an Aharonov-Bohm potential, we derive a version of the Kuramoto Model describing the phase dynamics of the bound state of the quantum mechanical system.
We construct the Feynman integral for the Schrödinger propagator in the polar conjugate momentum space, which describes the bound state Aharonov-Bohm effect, as a well-defined white noise functional.
In this paper we investigate the class of grey Brownian motions $B_{α,β}$ ($0<α<2$, $0<β\leq1$). We show that grey Brownian motion admits different representations in terms of certain known processes, such as fractional Brownian motion, multivariate elliptical distribution or as a subordination. The weak convergence of the increments of $B_{α,β}$ in $t$, $w$-variables are studied. Using the Berman criterium we show that $B_{α,β}$ admits a $λ$-square integrable local time $L^{B_{α,β}}(\cdot,I)$ almost surely ($λ$ Lebesgue measure). Moreover, we prove that this local time can be weak-approximated by the number of crossings $C^{B_{α,β}^{\varepsilon}}(x,I)$, of level $x$, of the convolution approximation $B_{α,β}^{\varepsilon}$ of grey Brownian motion.