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Четверг 11 апреля 2019 г.<br>
Теоретический семинар в ИФП, 11:30.<br>
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Ян Фёдоров (King's College London)<br>
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<font size="+1"><b>On energy landscape of elastic manifolds pinned
by random potentials</b></font><br>
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We consider an elastic manifold of internal dimension d and length L
pinned in a N dimensional random potential and confined by an
additional parabolic potential of curvature μ. First we consider
N=d=1 case of a directed polymer and show how counting stationary
points of its energy provides an upper bound on the strength of the
depinning force. Then we consider a mean-filed limit: first N→∞ at
fixed L^d, and then L→∞, and find the mean spectral density ρ(λ) of
the Hessian matrix K at the absolute minimum of the energy
functional. We show that for a confinement curvature μ exceeding a
critical value, the so-called "Larkin mass", the system is
replica-symmetric and the Hessian spectrum is always gapped (from
zero). The gap vanishes quadratically at approaching the Larkin
mass. For smaller curvatures the replica symmetry breaking (RSB)
occurs and the Hessian spectrum is either gapped or extends down to
zero, depending on whether RSB is 1-step or full. In the 1-RSB case
the gap vanishes in all d as fourth power of the distance to the
transition. In the full RSB case the gap is identically zero.<br>
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The presentation will be based on Y.V. Fyodorov et al., Ann. Phys.
397, 1–64 (2018) and Y.V. Fyodorov and P. Le Doussal,
arXiv:1903.07159.<br>
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Информация о всех запланированных семинарах:<br>
<a href="http://itp.ac.ru/ru/seminars/kapitza-institute/">http://itp.ac.ru/ru/seminars/kapitza-institute/</a><br>
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