Main HomePage
Introduction

Hamiltonian Dynamics of the Landau Model of
Ferroelectric Liquid Crystals

P. Pitanga(a,*), A. Ribeiro Filho(b) and K. C. Mundim(b,c)

Abstract:

We present ferroelectric liquid crystals as a simple non-integrable Hamiltonian system. The disordered-helicoidal phase transition undergoes a Hopf bifurcation. The Poincaré sections of the solutions in the helicoidal phase, shows the existence of spatial chaotic behavior of the molecular structure depending on temperature and external magnetic field. The ordered - helicoidal phase transition is also studied as second order derivative Hamiltonian theory.

Résumé

Nous prèsentons les cristaux liquides ferroélectriques comme un systéme Hamiltonien simple non intégrable. La transition de désordonné-hélicoidal phase reflète une bifurcation de Hopf. La section de Poincaré de la solution , de phase hélicoidal montre l'existence d'un comportament chaotique de la structure moléculaire, dépendant de la température et dun champ magnétique externe. La transition de phase ordonné-hélicodal est aussi etudié comme une théorie Hamiltonien derivative de deuxième ordre.

Keywords: Ferroelectric Liquid Crystals. Landau - Ginzburg Functional. Hopf Bifurcation. Hamiltonian Chaos

• Introduction
• The A - C* transition
• The stability analysis
• Higher Order Hamiltonian Theory and C - C* Transition
• The stability analysis
• Concluding Remarks
• References
• About this document ...

- Pitanga- Instituto de Física. Universidade Federal do Rio de Janeiro.
21944 - Rio de Janeiro, RJ - Brazil. - (*) On leave to the Instituto de Matematicas y Física Fundamental, CSIC,
Madrid, Spain, under a CNPq scholarship n. 200583/84.

- Mundim and Ribeiro- Instituto de Física. Universidade Federal da Bahia.
40210-340 - Salvador, BA - Brazil.

- Mundim- Instituto de Química - Universidade de Brasília
Brasília (DF)   - Brasil