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DTSTAMP:20210125T174427Z
LAST-MODIFIED:20201110T192552Z
DTSTART:20201117T203000Z
DTEND:20201117T213000Z
UID:event2372@bu.edu
URL:http://physics.bu.edu/events/show/2372
SUMMARY:General Methods and Properties for Evaluation of Continuum Limits o
f Discrete Time Quantum Walks in One and Two Dimensions
DESCRIPTION:Featuring Michael Manighalam\, Boston University\, Physics Depa
rtment\n\nPart of the PhD Final Oral Exams.\n\nModels of quantum walks whic
h admit continuous time and continuous spacetime limits have recently led t
o quantum simulation schemes for simulating fermions in relativistic and no
n relativistic regimes. This work continues the study of relationships betw
een discrete time quantum walks (DTQW) and their ostensive continuum counte
rparts by developing a more general framework than was done in Di Molfettaâ
€™s 2019 work to evaluate the continuous time limit of these discrete quant
um systems. Under this framework\, we prove two constructive theorems conce
rning which internal discrete transitions ("coins") admit nontrivial contin
uum limits in 1D + 1. We additionally prove that the continuous space limit
of the continuous time limit of the DTQW can only yield massless states wh
ich obey the Dirac equation. We also demonstrate that for general coins the
continuous time limit of the DTQW can be identified with the canonical con
tinuous time quantum walk (CTQW) when the coin is allowed to transition thr
ough the continuum limit process. Finally\, we introduce the Plastic Quantu
m Walk\, or a quantum walk which admits both continuous time and continuous
spacetime limits and\, as a novel result\, we use our 1D + 1 results to ob
tain necessary and sufficient conditions concerning which DTQWs admit plast
icity in 2D + 1\, showing the resulting Hamiltonians. We consider coin oper
ators as general 4 parameter unitary matrices\, with parameters which are f
unctions of the lattice step size Îµ. This dependence on Îµ encapsulates al
l functions of Îµ for which a Taylor series expansion in Îµ is well defined
\, making our results very general.\n\n---\n\nhttps://bostonu.zoom.us/j/920
62697327?pwd=MCtITjFZeEpudEI5N1hBaTNyWFVpdz09\n\nMeeting ID: 920 6269 7327\
n\nPasscode: 704603
LOCATION: \, \,
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