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DTSTAMP:20230327T171318Z
UID:1651760100@ist.ac.at
DTSTART:20220505T161500
DTEND:20220505T171500
DESCRIPTION:Speaker: Marie Fialová\nhosted by Robert Seiringer\nAbstract:
Classically\, if we have a magnetic field that is confined to a region of
space and a charged particle moves outside that region\, the particle cann
ot feel any effect of the field. In quantum mechanics the situation change
s as a particle encircling a solenoid gathers a phase shift dependent on
the magnetic flux enclosed by its trajectory\, despite moving in region wh
ere the magnetic field vanishes. This phenomenon is called the Aharonov--B
ohm effect. We investigate the number of zero modes (i.e. the degeneracy o
f the zero eigenvalue) of the Dirac operator describing a charged particle
with spin confined to a plane with holes that contain such Aharonov--Boh
m solenoids. For the domain of the Dirac operator we consider the global A
tiyah--Patodi--Singer (APS) boundary condition which was introduced in the
70s by APS in connection with the index theorem on manifolds with bounda
ry. We find that the number of zero modes depends only on the flux of the
magnetic field. The result is a generalisation of the Aharonov–Casher
theorem. The talk is based on my PhD project adviced by Jan Philip Solovej
.
LOCATION:Mondi 2 (I01.01.008)\, Central Building\, ISTA
ORGANIZER:birgit.oosthuizen-noczil@ist.ac.at
SUMMARY:Marie Fialová: Aharonov-Casher theorem on manifolds with boundary
URL:https://talks-calendar.ista.ac.at/events/3714
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