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UID:0-857@lptms.universite-paris-saclay.fr
DTSTART;TZID=Europe/Paris:20221109T110000
DTEND;TZID=Europe/Paris:20221109T120000
DTSTAMP:20221101T185259Z
URL:http://www.lptms.universite-paris-saclay.fr/seminars/seminaire-du-lptm
 s-benjamin-bertrand-lacroix-kcl-london/
SUMMARY:Séminaire du LPTMS : Bertrand Lacroix-A-Chez-Toine (KCL) - Salle d
 es séminaires du FAST et du LPTMS\, bâtiment Pascal n°530 - 9 Nov 22 11
 :00
DESCRIPTION:Superposition of random plane waves in high dimension as a rand
 om landscape\nBertrand Lacroix-A-Chez-Toine (King’s College London)\n\n*
 *SPECIAL DAY**\nHybrid: onsite seminar + zoom.\nRegister in advance for th
 is meeting:\nhttps://cnrs.zoom.us/meeting/register/tJYpcOCqrjwjHNMzYke5j7B
 722dWyNmLVNN3\nAfter registering\, you will receive a confirmation email c
 ontaining information about joining the meeting.\n\nSuperpositions of rand
 om plane waves play important roles in the semi-classical description of q
 uantum billiard as pointed out by Berry’s conjecture [1]. In this contex
 t\, they can describe the eigenfunctions of the Laplacian operator at high
  energy. While their properties have been explored in depth in low spatial
  dimensions\, we consider in this talk a large superposition of M ≫ 1 ra
 ndom plane waves in high dimension N ≫ 1 with M/N = α > 1. Here\, we co
 nsider instead this object as a (random) energy landscape and\, adding an 
 isotropic harmonic confinement of strength μ\, we characterise the ergodi
 city breaking in such a landscape.\nTo characterise this property we consi
 der two quantities: the quenched free-energy and the annealed total comple
 xity\, i.e. the rate of exponential growth of the average number of statio
 nary points of the energy landscape with the spatial dimension N .\nWhile 
 similar high-dimensional random landscapes display topology trivialisation
  transition [2]\, whereby the complexity vanishes above some finite value 
 of the confinement μ\, the complexity vanishes only as μ → ∞ in this
  system [3]. One might thus expect that ergodicity is always broken at zer
 o temperature in this model. This is confirmed and enriched by our quenche
 d free-energy computations.\n\n\nReferences:\n[1] M. V. Berry\, Regular an
 d irregular semiclassical wavefunctions\, J. Phys. A 10 2083 (1977).\n[2] 
 Y. V. Fyodorov\, Complexity of Random Energy Landscapes\, Glass Transition
 \, and Absolute Value of the Spectral Determinant of Random Matrices\, Phy
 s. Rev. Lett. 92\, 240601 (2004) Erratum: Phys. Rev. Lett. 93\, 149901(E) 
 (2004).\n[3] B. Lacroix-A-Chez-Toine\, S. Belga-Fedeli\, Y. V. Fyodorov\, 
 Superposition of Random Plane Waves in High Spatial Dimensions: Random Mat
 rix Approach to Landscape Complexity\, J. Math. Phys. 63 (9)\, 093301 (202
 2)\n
CATEGORIES:seminars
LOCATION:Salle des séminaires du FAST et du LPTMS\, bâtiment Pascal n°53
 0\, rue André Riviere\, Orsay\, 91405\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=rue André Riviere\, Orsay\
 , 91405\, France;X-APPLE-RADIUS=100;X-TITLE=Salle des séminaires du FAST 
 et du LPTMS\, bâtiment Pascal n°530:geo:0,0
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DTSTART:20221030T020000
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