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[Fizinfo] Stat Fiz Szeminarium

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  • From: StatFizSzeminar <statfiz AT>
  • To: fizinfo AT
  • Subject: [Fizinfo] Stat Fiz Szeminarium
  • Date: Wed, 20 Feb 2019 16:23:19 +0100

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ELTE TTK Fizikai Intézet

2019. február 27.


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.

1117, Budapest, Pázmány P. sétány 1/A, Északi tömb 2.54

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