ELFT HÍRADÓ

[Szeminárium koordinátor <szfi-seminar AT wigner.mta.hu>]

SZFI SzemináriumSzigeti Balázs EndreWigner FK RMI, ELTEShort-time behavior of 
continuous-time quantum walks on graphs2019. december 10. kedd, 10.00, KFKI 
Telephely, I. épület 1. emeleti TanácsteremDynamical evolution of systems 
with sparse Hamiltonians can always be recognized as continuous-time quantum 
walks (CTQWs) on graphs. In this paper, we analyze the short-time asymptotics 
of CTQWs. In recent studies, it was shown that for the classical diffusion 
process the short-time asymptotics of the transition probabilities follows 
power laws whose exponents are given by the usual combinatorial distances of 
the nodes. Inspired by this result, we perform a similar analysis for CTQWs 
both in closed and open systems, including time-dependent couplings. For 
time-reversal symmetric coherent quantum evolutions, the short-time 
asymptotics of the transition probabilities is completely determined by the 
topology of the underlying graph analogously to the classical case, but with 
a doubled power-law exponent. Moreover, this result is robust against the 
introduction of on-site potential terms. However, we show that time-reversal 
symmetry breaking terms and non-coherent effects can significantly alter the 
short-time asymptotics. The analytical formulas are checked against numerics, 
and excellent agreement is found. Furthermore, we discuss in detail the 
relevance of our results for quantum evolutions on particular network 
topologies. Minden érdeklődőt szívesen látunk! - Everyone is welcome to 
attend.Juhász Róbertszfi-seminar AT wigner.mta.hu