ELFT HÍRADÓ

[StatFizSzeminar <statfiz AT glu.elte.hu>]

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             ELTE TTK Fizikai Intézet
         STATISZTIKUS FIZIKAI SZEMINÁRIUM


                  2019. február 27.

                       szerda 

                       11.00
                   Balázs Szigeti


  ELTE Department of Atomic Physics, Wigner RMI 

"Locality, short-time behavior and reconstruction
 of Hamiltonians of continuous time quantum walks"

Experimentally realizable dynamical evolution of 
systems with sparse Hamiltonians can always be 
recognized as continuous time quantum walks (CTQWs)
on finite graphs. Here, we analyze the short-time
asymptotics of CTQWs. In two recent studies, it was
shown that for small times, the continuous time 
classical diffusion process uses the graph's shortest
paths for propagation of high probability: The short-
time asymptotics of the transition probabilities 
follow power laws whose exponents are given by the 
usual combinatorial distances of the nodes. Borrowing
their arguments, we analyze the short-time asymptotics
of the CTQW both in closed and open systems. 
Furthermore, we derive explicit error bounds not 
relying on the Lieb-Robinson bound for the Hamiltonian
reconstruction of CTQW via short-time measurements. 
Whenever the measurements of the reconstruction process
are local, these error bounds reproduce the previous 
results concerning their scaling: The error of each 
individual measurement does not grow with growing 
system size. Here, not only the scaling is demonstrated,
but the quantitative relationship between the sparsity
of the Hamiltonian and the error bounds are obtained.



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