Институт теоретической физики им. Л.Д. Ландау РАН
L.D. Landau Institute for Theoretical Physics RAS
International conference dedicated to the 100th anniversary of I. M. Khalatnikov
"Quantum Fluids, Quantum Field Theory, and Gravity"
October, 17-20, 2019
Inverted pendulum driven by a random force: statistics of the non-falling trajectory and supersymmetry
Date/Time: 15:10 19-Oct-2019
We study stochastic dynamics of an inverted pendulum subject to a random force in the horizontal direction. Considered at the entire time axis, the problem admits a unique solution which always remains in the upper half plane. We develop a new technique for treating statistical properties of this unique non-falling trajectory. In our approach based on the supersymmetric formalism of Parisi and Sourlas, statistics of the non-falling trajectory is expressed in terms of the zero mode of a corresponding transfer-matrix Hamiltonian. The emerging mathematical structure is similar to that of the Fokker-Planck equation, but it is rather written for the ``square root'' of the distribution function. Our results for the statistics of the non-falling trajectory are in perfect agreement with direct numerical simulations of the stochastic pendulum equation.
Skvortsov Mikhail A.
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