BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sheng-Fu Chiu (Institute of Mathematics\, Academia Sinica\, Taiwan ) DTSTART:20220406T111000Z DTEND:20220406T123000Z DTSTAMP:20260423T022742Z UID:GDS/53 DESCRIPTION:Title: Fro m Energy-Time Uncertainty to Symplectic Displacement Energy\nby Sheng- Fu Chiu (Institute of Mathematics\, Academia Sinica\, Taiwan) as part of G eometry and Dynamics seminar\n\n\nAbstract\nHeisenberg's Uncertainty Princ iple is one of the most celebrated features of \nquantum mechanics\, which states that one cannot simultaneously obtain the \nprecise measurements o f two conjugated physical quantities such as the pair \nof position and mo mentum or the pair of electric potential and charge density. \nAmong the d ifferent formulations of this fundamental quantum property\, the \nuncerta inty between energy and time has a special place. This is because the \nti me is rather a variable parametrizing the system evolution than a physical \nquantity waiting for determination. Physicists working on the foundatio n of \nquantum theory have understood this energy-time relation by a unive rsal bound \nof how fast any quantum system with given energy can evolve f rom one state to \nanother in a distinguishable (orthogonal) way. Recently \, there have been many \narguing that this bound is not a pure quantum ph enomenon but a general \ndynamical property of Hilbert space. In this talk \, in contrast to the usual \nHilbert space formalism\, we will provide a homological viewpoint of this \nevolutional speed limit based on a persist ence-like distance of the derived \ncategory of sheaves : during a time pe riod what is the minimal energy needed \nfor a system to evolve from one s heaf to a status that is distinguishable from \na given subcategory? As an application\, we will also discuss its geometric \nincarnation in the dyn amics of classical mechanics\, namely the notion of \nsymplectic displacem ent. We will see how this categorical energy manages to \ncharacterize the symplectic energy for disjointing a Lagrangian from an open set.\n LOCATION:https://researchseminars.org/talk/GDS/53/ END:VEVENT END:VCALENDAR