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SUMMARY:PDEs in Mixed Quantum-Classical Dynamics and the Koopmon Method
DTSTART:20251030T101500
DTEND:20251030T111500
DTSTAMP:20261005T005352Z
UID:d6ddb17c0d9d67958ce81f8bd7531c49880a4cde22656f410d54f675
CATEGORIES:Conferences - Seminars
DESCRIPTION:Prof. Paul Bergold\nTo alleviate the computational cost associ
 ated with fully quantum dynamics\, a novel mixed quantum-classical (MQC) p
 article method – the Koopmon method – has recently been introduced [1]
 . Unlike conventional MQC models\, which often suffer from inconsistencies
  such as violations of Heisenberg’s principle\, this new approach resolv
 es these issues by blending Koopman’s formulation of classical mechanics
  on Hilbert spaces with tools from symplectic geometry.\n\nThe resulting c
 ontinuum model\, which can be regarded as a correction to the Ehrenfest PD
 E\, retains both a variational and a Hamiltonian structure\, while its non
 linear character calls for suitable closure schemes. Exploiting the underl
 ying action principle\, we introduce a regularization procedure that enabl
 es a singular-solution ansatz\, thereby defining the trajectories of compu
 tational particles – the so-called Koopmons.\n\nNumerical experiments de
 monstrate the capability of the Koopmon method to reproduce nonadiabatic q
 uantum-classical transitions and to capture Rashba-type spin dynamics in q
 uantum nanowire systems. We conclude by proposing a novel strategy for a h
 ybrid Ehrenfest–Koopman implementation that integrates the advantages of
  both approaches.\n\n[1] Bauer\, W.\; Bergold\, P.\; Gay-Balmaz\, F.\, and
  Tronci\, C. Koopmon trajectories in nonadiabatic quantum-classical dynami
 cs. SIAM Multiscale Model. Simul.\, 22(4):1365-1401 (2024)\n[2] Gay-Balmaz
 \, F.\; Tronci\, C. Evolution of hybrid quantum-classical wavefunctions. P
 hys. D 440\, 133450 (2022)\n[3] Gay-Balmaz\, F.\; Tronci\, C. Koopman wave
 functions and classical states in hybrid quantum-classical dynamics. J. Ge
 om. Mech. 14\, n. 4\, 559-596 (2022)
LOCATION:BCH 3118 https://plan.epfl.ch/?room==BCH%203118
STATUS:CONFIRMED
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