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X-ORIGINAL-URL:https://www.lps.u-psud.fr/
X-WR-CALNAME:Laboratoire de physique des Solides
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DTSTART;TZID=Europe/Paris:20260115T110000
DTEND;TZID=Europe/Paris:20260115T180000
DTSTAMP:20260105T101400
UID:MEC-58e16dc760ca166c476403499ff5c59b@lps.u-psud.fr
CREATED:20260105
LAST-MODIFIED:20260105
PRIORITY:5
TRANSP:OPAQUE
SUMMARY:Gilles Montambaux : Ramanujan, Landau and Casimir, divergent series: A physicist’s approach
DESCRIPTION:\nIt is a popular paradoxical exercise to show that the infinite sum of positive integer numbers is equal to -1/12, sometimes called the Ramanujan sum. This result is actually well-defined in a proper mathematical sense.Here we propose a qualitative approach, much like that of a physicist, to show how the value -1/12 can make sense and, in fact, appears in certain physical quantities where this type of summation is involved.In the light of two physical examples, taken respectively from condensed matter — the Landau diamagnetism — and quantum electrodynamics — the Casimir effect — that illustrate this strange sum, we present a systematic way to extract the Ramanujan term from the infinity.In both examples, the ”infinite” appears to be a vacuum energy and the Ramanujan sum is revealed by a response function to an external parameter.\n
URL:https://www.lps.u-psud.fr/events/gilles-montambaux-ramanujan-landau-and-casimir-divergent-series-a-physicists-approach/
ORGANIZER;CN=Andrej Meszaros:MAILTO:
CATEGORIES:Séminaire Matière Quantique (SMQ),Séminaires
LOCATION:Moyen amphi (LPS) + ONLINE (Zoom)
ATTACH;FMTTYPE=image/jpeg:https://www.lps.u-psud.fr/wp-content/uploads/2026/01/GM-hexagones-scaled-1.jpg
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