flat bands:

  • compact localized states
  • Fano resonances
  • local symmetries and topology
  • flatband generators
  • perturbing flatbands: disorder and interactions

    deep learning:

  • finite size RG
  • dynamics recognition

    cryptography meets nonlinear waves:

  • nonlinear waves close to phase transitions
  • encrypting relevant yet short information (passwords!) with nonlinear waves
  • generation of CAPTCHAs

    wave interactions in localizing media:

  • localizing media: disordered lattices (Anderson), quasiperiodic lattices (Aubry Andre), dc biased lattices (Wannier Stark), quantum kicked rotor, ...
  • spreading of nonlinear waves in localizing media
  • heat transport with nonlinear waves in localizing media
  • localization vs delocalization of few quantum interacting particles in localizing media

    discrete breathers:

  • theory: classical, quantum, dissipation, fluctuations, transients, equilibrium
  • nonlinear optics: localizing light in coupled nonlinear optical waveguides - optical switches, tunable filters
  • Josephson Junction Arrays in the classical and quantum regime - localized excitations, tunable filters etc
  • spins: localized excitations in spin lattices
  • micromechanics: driven micromechanical cantilever arrays
  • molecules,solids: Selective bond excitations in molecules and solids - localization vs. tunneling, dissociation


  • math: classical and quantum
  • solving the FPU problem: q-breathers explain all major observations of FPU (localization, recurrence, equipartition via tail resonances)
  • finite systems: abundant in nature, generically allow for q-breathers and their control
  • scaling: finite system solution scaling to infinite system size, connection to anharmonic phonon theory on rigorous footing
  • applications? under construction (e.g. electronic transport through single molecules, interaction with vibrational modes)


  • symmetries: spatio-temporal symmetries and ways of violating them
  • particles (classical,quantum): single particle transport
  • interactions: effects of particle-particle interactions
  • solitons: field description of many interacting particles: soliton ratchets
  • spins: rectifying magnetization for classical and quantum spins, including interaction effects
  • cold atoms: application to transport of cold atoms (Cs, Rb)
  • BEC: even colder: transport of BEC


  • Fano resonances: wave scattering in 1d, destructive interference, resonant total reflection
  • time-dependent scatterers: serve in 1d the above purpose
  • quantum dots: scattering of electrons by side quantum dots, spin filters
  • tunnel junctions: transport of electrons through tunnel junctions with external ac fields
  • Josephson junctions: scattering of plasmons by rotobreather excitations
  • optical waveguides: scattering of light by discrete solitons in waveguide arrays
  • solitons: resonant scattering

    condensed matter:

  • spin filters: electron scattering by side quantum dots, Kondo and Zeeman
  • quantum dots: see above
  • tunnel junctions: transport of electrons through tunnel junctions with external ac fields
  • electronic correlations: ground state properties of interacting electron systems, incremental expansions
  • Peierls-Hubbard: dimerization, interaction
  • 2d Hubbard: ground state energy
  • Josephson junctions: rotobreather excitations in junction networks
  • electron-phonon interactions: interaction of electrons and nonlinera lattice modes
  • superconductivity: influence of anharmonicity on superconductivity

    statistical physics:

  • discrete breathers: properties in and contribution to equilibrium state, long transients in nonequilibrium
  • solitons: properties in and contribution to equilibrium state, long transients in nonequilibrium
  • out of equilibrium systems: routes to equipartition, influence of periodic orbits


  • dissipative optical cavity solitons: first ratchet with nontopological solitons (discrete breathers)
  • resonant light scattering: scattering of light by solitons, Fano resonances
  • soliton ratchets: ratchets with topological solitons, application to Josephson junctions, pecularities of energy flow
  • discreteness effects: on soliton profiles, mobility
  • movability: the neverending problem of mobility in discrete systems