BASIC NOTIONS SEMINAR (hybrid seminar) - Thursday 30 September, at 16:00 (Jean-Pierre Gazeau)

[ICTP Math Section]

BASIC NOTIONS SEMINAR: Orientations in the plane as quantum states

Starts 30 Sep 2021 16:00
Ends 30 Sep 2021 17:00
Central European Time
Online/Presence

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Speaker: Jean-Pierre Gazeau (Université de Paris)


Abstract: I will introduce and  discuss some of the most basic 
fundamental concepts of  quantum physics by using orientations or angles 
in the plane, illustrated through linear polarisations of the light.
Starting with the Euclidean plane, which is certainly a paradigmatic 
example of a Hilbert space, the orientations in the plane  are 
identified with the pure states.  Associating these quantum orientations 
with linear polarisations of light in the plane normal to its 
propagation constitutes an immediate and nice illustration  of the 
presented formalism. Another  contribution concerns the description of 
the dynamics of quantum states. The pure states form the unit circle 
(actually a half of it) and the mixed states form the unit disk 
(actually a half of it). Rotations in the plane rule time evolution 
through  Majorana-like equations involving only real quantities for 
closed (Heisenberg-Dirac) and open (Lindblad) systems. Interesting 
probabilistic aspects  are developed.  Finally, I revisit light linear 
polarisation as an example of quantum measurement through Stokes 
parameters.

References:

H. Bergeron, E. M. F. Curado, , L. M. C. S. Rodrigues,
Brazilian Journal of Physics,  49,  391-401 (2019)

R. Beneduci, E. Frion, J.-P. G., A. Perri,
Real POVMS on the plane: integral quantization, Naimark theorem and 
linear polarization of the light,
arXiv:2108.04086v1 [quant-ph] (submitted)

/The seminar will be a hybrid seminar, with both in-person and 
Zoom-based options for viewing and participating. If you would like to 
join in person, the seminar will take place in the ICTP Budinich Lecture 
Hall./

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