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SUMMARY:Emergent Dimensions: from Geometry to Topology and Phenomena\, Pro
 f. Chia-Yi Ju [朱家誼]\, NSYSU
DTSTART:20260414T053000Z
DTEND:20260414T073000Z
DTSTAMP:20260412T180300Z
UID:indico-event-181@indico.phys.nthu.edu.tw
DESCRIPTION:Recent studies have shown that the Schrödinger equation can b
 e realized geometrically. In this talk\, we briefly review some basic idea
 s in differential geometry and explore their similarities and connections 
 with quantum physics. We then demonstrate how hidden dimensions can emerge
  naturally from parameter spaces and derive the evolution equations for ar
 bitrary quantum states along these emergent dimensions\, as well as the eq
 uations governing the fiber metric of the associated Hilbert space bundle.
  Next\, we show how Berry connections relate to the state evolution equati
 ons and illustrate that exceptional points act as topological defects in t
 he Hilbert space bundle. Finally\, we demonstrate how these concepts relat
 e to the quantum phase transition.\n\nhttps://indico.phys.nthu.edu.tw/even
 t/181/
LOCATION:Physics/124
URL:https://indico.phys.nthu.edu.tw/event/181/
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