dr. De Nittis' seminar

[Emanuele Tuillier Illingworth]

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MATHEMATICAL PHYSICS SECTOR SEMINARS
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Speaker:  Giuseppe De Nittis (SISSA)

Venue: Friday 11 December, 14:30 Room D

Title:  Topological quantum numbers arising from symmetries. Application 
to Quantum Hall Effect

Abstract:

Topological quantum numbers play a prominent role in many fields of 
quantum physics. In particular topological quantum numbers provide a 
very elegant explanation for the Quantum Hall effect. In dealing with 
topological quantum numbers, some aspects need a deeper analysis: 1) 
There exists a general framework in which topological quantum numbers 
emerge? 2) There exists a computable procedure which enables us to 
derive the underlying topology associated to a quantum system? Is this 
topology (and the related topological invariants) unique for a given 
system?

Under general assumptions, a natural topological structure emerges from 
the existence of a symmetry group. This topology can be extracted 
through a procedure that generalizes the usual Bloch-Floquet transform 
and it is a "fingerprint" for the physical system.

This procedure shows that the physics of a Bloch electron in a very weak 
magnetic field (QHE in Hofstadter regime) and that of a Bloch electron 
in a very strong magnetic field (QHE in Harper regime) are apparently 
similar but intimately different. Although the algebraic structure is 
the same, these systems are not unitary equivalent since they produce 
different Chern numbers.

In summary, the "abstract" algebraic structure does not contain all the 
physical information. The "concrete" Hilbert space representations 
provide additional structures (symmetries) which define a topological 
content, thus yielding a richer description than the simple algebraic 
structure.



-- 
Dr. Emanuele Tuillier Illingworth
Secretary of Mathematical Physics and Elementary Particle sectors
Main building, second floor, room n.237
phone (+39) 040 37 87 598
fax (+39) 040 37 87 466
SISSA
Via Beirut 2-4
Trieste, ITALY
emanuele.tuillier at sissa.it