3 papers
math.CO2005
First Order Definability of Trees and Sparse Random Graphs
Tom Bohman, Alan Frieze, Tomasz Luczak +4
Let D(G) be the smallest quantifier depth of a first order formula which is true for a graph G but false for any other non-isomorphic graph. This can be viewed as a measure for the…
quant-ph2004
Quasiperiodic dynamics of coherent diffusion: a quantum walk approach
A. Wojcik, T. Luczak, P. Kurzynski +2
We study the dynamics of a generalization of quantum coin walk on the line which is a natural model for a diffusion modified by quantum or interference effects. In particular, our…
quant-ph2004
Examples of nonuniform limiting distributions for the quantum walk on even cycles
Malgorzata Bednarska, Andrzej Grudka, Pawel Kurzynski +2
In the note we show how the choice of the initial states can influence the evolution of time-averaged probability distribution of the quantum walk on even cycles.