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It extends across Condensed Matter and makes contact with more than one scientific communities. Major areas have been Magnetic Materials, and atomic Bose-Einstein condensates, and also dynamical systems in condensed matter and biology. It also includes non-equilibrium dynamics in nematic Liquid Crystals, and non-topological solitons. The phenomena studied are those of nonlinear dynamics.

Theory of magnetism and magnetic materials
Monobubble in FePt

Rotating vortex-antivortex pair
  • Magnetic vortices and solitons are prominent examples of topologically nontrivial structures. We study the dynamics of topological magnetic solitons in two and three-dimensional ferromagnets. The framework is the Landau-Lifshitz equation. The surprising dynamics of vortices and solitons in ferromagnets are understood only through the direct link of dynamics in magnets to the topology of the magnetisation configurations [see, e.g., Phys. Rev. Lett. 99, 117202 (2007)].
    Our studies are both field-theoretical and numerical (using our "micromagnetics" code).

    Our work on antiferromagnets includes a derivation of a continuum model (the nonlinear σ-model) and the discovery that a direct link between magnetisation topology and antiforromagnetic vortex dynamics is induced by the presence of an external field as this breaks the Lorentz invariance of the system [ Nonlinearity 11, 265-290 (1998)].
    You may be also interested in more rigorous mathematical work which was motivated by the above results (see "Static Theory for Planar Ferromagnets and Antiferromagnets")

  • For spiral antiferromagnets we discuss the spiral state, the spin-flop state, but we also predict the existence of an intermediate phase, in between these two [ Phys. Rev. B 65, 064433 (2002)].

  • The current intensive experimental activity on mesoscopic ferromagnetic elements has opened promising directions for applications of magnetic materials as well as for theoretical work on the mesoscopic and nanoscopic level.
    In collaboration with the Thin Film Magnehtism (TFM) Group (head Professor J.A.C. Bland) at the Cavendish Laboratory, Cambridge we have extended ideas about topological magnetic solitons to the case of mesoscopic (submicron) magnetic elements. Magnetic bubbles (Skyrmions) exist and have been observed in perpendicular anisotropy ferromagnetic nanostructures of FePt alloy [see, e.g., Phys. Rev. B 74, 214406 (2006), and Phys. Rev. B 76, 104426 (2007), or the PhD Thesis currently carried out in Cambridge].
    Our work is linked in the Virtual Journal of Nanoscale Science & Technology, and it is reviewed in the Nanotechnology Website of the Institute of Physics.

  • Our current project is on magnetisation dynamics in three dimensional systems with a major focus on freely propagating structures in ferromagnetic nanowires.

  • Selected presentations of this work
    [Talk on "vortices and bubbles in nanodots" at the MMM, 10/1/2007, Baltimore (pdf)]
    [Poster on "rotating vortex dipoles", 22/5/2007, Dresden (pdf)]
    [Poster on "Transmutation of momentum into position in magnetic vortices" at the Intermag, 8/5/2008, Madrid (pdf)]
    [Review article on "Dynamics of vortex pairs in ferromagnets"].
  • Nonlinear phenomena in Bose-Einstein Condensates
  • Trapped atomic Bose-Einstein condensates is a physical system which is now widely used as a standard model (both for experimental and theoretical work) of condensed matter systems. It is very closely related to nonlinear optics as both systems are described, to an approximation, by the nonlinear Schrödinger equation.
    We have developed a theory for solitary waves in a confined geometry, which unveils the particulars of nonlinear dynamics in this physical system.
    We have found a superfluid vortex ring mode with a roton-like behaviour, and a propagating quantised vortex mode which has been called a solitonic vortex [see, .e.g., Phys. Rev. A 68, 043617 (2003)].
    Experimental observations of vortex rings and interactions among them have been reported by the group of L.V. Hau (Harvard) [ Phys. Rev. Lett. 94, 040403 (2005)].
    This work in reviewed in a forthcoming volume (pdf).

  • Quantized vortices and superfluidity in a BEC: The detailed features of single (and double) vortex states are important for the understanding of their creation and annihilation, and they are surprising enough [see, e.g., Phys. Rev. A 72, 053624 (2005)].
    The formation of vortex (Abrikosov) lattices is a BEC has given some astonishing experimental pictures. We have studied the profile for a fast rotating dilute condensate (in the lowest Landau level approximation) when a vortex lattice has formed [ Phys. Rev. A 70, 033604 (2004)], and vortex lattice phases in BECs with dipolar interactions [ Phys. Rev. A 75, 023623 (2007)].

  • [Numerical solutions for BEC vortex rings in a cylindrical trap]
  • Selected presentations of this work
    [talk in Conference SOLIQUANTUM, 28/9/2006, Cuenca, Spain (pdf)]
    [Review article on "Vortex rings and solitary waves in trapped Bose-Einstein condensates" published in Eur. Phys. J. Special Topics 147, 133-152 (2007) (also available locally here) .]
  • Dynamical systems (in Condensed Matter and Biology)
  • Energy localisation in disordered systems: While a linear disordered system shows energy localisation (Anderson localisation), it has been observed that an added nonlinearity causes the second moment to increase apparently indefinitely. This puzzle is completed by indications that (contrary to expectations) energy appears to remain localised in a disordered nonlinear system, although the localisation profile is substantially different than that of Anderson states. This is evidence for new nonlinear states which are quasi-periodic and can be understood as KAM torii [see our paper in Phys. Rev. Lett. 100, 084103 (2008) or in arXiv:0710.2621].

  • Charge transport in a DNA chain: Charge transport in DNA macromolecules can be studied by methods of nonlinear dynamics [ Phys. Rev. E 65, 061905 (2002)]. Such methods have helped describe crucial phenomena (e.g., DNA denaturation) in a subject which is becoming increasingly important in current biological physics research [see, e.g., G. Kalosakas, K.L. Ngai, and S. Flach, Physical Review E 71, 061901 (2005).].

  • Chaotic dynamics: I have studied the period-doubling cascade of three-dimensional reversible mappings, which model Hamiltonian systems.

    Pattern formation in nematic liquid crystals
    Nematic liquid crystals under electroconvection are non-equilibrium systems which give pattern formation due to hydrodynamic instabilities. We have been interested in the formation of modulated states observed in Nematic Liquid Crystals and the formation of "chevron states". The latter are periodically modulated defect-states and they are among the most commonly observed patterns in electroconvection [ Phys. Rev. E 67, 031701 (2003)].

    Non-topological solitons
    (31416 bytes) Non-topological solitons (Q-balls and Q-rings) have been proposed to help in the explanation of dark matter in a cosmological setting. We have been interested in the dynamics of Q-balls. Simulations of Q-ball scattering showed that the right angle scattering effect observed for topological solitons in two dimensions persists also in the case of Q-balls.