The falling cat problem and shape effects in small molecules in a random environment: A case study

Carsten Hartmann*, Tomohiro Yanao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)


We study the coupling between shape changes and rotations of molecules in a random environment. As a prototype of molecules or biopolymers that can undergo non-trivial conformational transitions we consider a planar four-atomic molecule, with underdamped dynamics of Langevin-type. In this simplified setting, we can extend the available gauge theory of semi-flexible molecules to the stochastic setting which allows us to analyse and explain geometric phase effects that arise from the internal motion of the molecule. Due to the stochastic nature of the Langevin system, the internal dynamics contains temperature-dependent coriolis forces that arise from the fluctuations of the angular momentum around its mean value zero. All theoretical investigations are supplemented by numerical simulations, in which we specifically investigate the dependence of the orientational shift on the parameters of the Langevin equation, i.e., friction coefficient, atomic masses, temperature and the velocity of deformation of the system. The numerical results confirm our theoretical findings. We further discuss various extension of the analysis, e.g., to the overdamped limit or optimal control.

Original languageEnglish
Pages (from-to)3534-3545
Number of pages12
JournalMolecular Physics
Issue number22-23
Publication statusPublished - 2013 Dec 1


  • Fixman potential
  • Geometric phase
  • Langevin equation
  • Nonlinear dynamics

ASJC Scopus subject areas

  • Biophysics
  • Molecular Biology
  • Condensed Matter Physics
  • Physical and Theoretical Chemistry


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