# RESEARCH OF SERGEJ FLACH

NONLINEAR WAVES - CLASSICAL AND QUANTUM

TOPICS:
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
q-breathers:

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)
ratchets:

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
transport:

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
solitons:

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
HALL OF FAME AND MISC