2 research outputs found
Correlation effects in a discrete quantum random walk
We introduce history-dependent discrete-time quantum random walk models by
adding uncorrelated memory terms and also by modifying Hamiltonian of the
walker to include couplings with memory-keeping agents. We next numerically
study the correlation effects in these models. We also propose a correlation
exponent as a relevant and promising tool for investigation of correlation or
memory (hence non-Markovian) effects. Our analysis can easily be applied to
more realistic models in which different regimes may emerge because of
competition between different underlying physical mechanisms.Comment: 6 pages, 7 figure
Pseudo-Hermitian continuous-time quantum walks
In this paper we present a model exhibiting a new type of continuous-time
quantum walk (as a quantum mechanical transport process) on networks, which is
described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it
pseudo-Hermitian continuous-time quantum walk. We introduce a method to obtain
the probability distribution of walk on any vertex and then study a specific
system. We observe that the probability distribution on certain vertices
increases compared to that of the Hermitian case. This formalism makes the
transport process faster and can be useful for search algorithms.Comment: 13 page, 7 figure