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UID:7648@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20170130T100000
DTEND;TZID=Europe/Paris:20170130T110000
DTSTAMP:20241120T204746Z
URL:https://www.i2m.univ-amu.fr/evenements/coherent-states-and-berezin-tra
 nsforms-attached-to-landau-levels/
SUMMARY:Zouhair Mouayn (Faculty of Sciences and Technics (M'Ghila) Béni Me
 llal\, Morocco): Coherent states and Berezin transforms attached to Landau
  levels
DESCRIPTION:Zouhair Mouayn: In general\, coherent states xX are a specific 
 overcomplete family of normalized vectors in the Hilbert space  of the pro
 blem that describes the quantum phenomena and solves the identity of  as 1
  = ∫ Xdμ(x). These states have long been known for the harmonic oscilla
 tor and their properties have frequently been taken as models for defining
  this notion for other models. We review the definition and properties of 
 coherent states with examples. We construct coherent states attached to La
 ndau levels (discrete energies of a uniform magnetic field) on three known
  examples of Kähler manifolds X : the Poincare disk D\, the Euclidean pl
 ane ℂ and the Riemann sphere Cℙ1. After defining their corresponding i
 ntegral transforms\, we obtain characterization theorems for spaces of bou
 nd states of the particle. Generalization to ℂn and to the complex unit 
 ball Bn and Cℙn are also discussed. In these cases\, we apply a coherent
  states quantization method to recover the corresponding Berezin transform
 s and we give formulae representing these transforms as functions of Lapla
 ce-Beltrami operators.\n\n\n\nhttps://arxiv.org/abs/1610.02875\n\n\n\n\n&n
 bsp\;
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 020/01/Zouhair_Mouayn.jpg
CATEGORIES:Séminaire,Analyse et Géométrie
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