A recent highlight are topological lasers, theoretically proposed in Opt. Lett. 38, 1912 (2013) and realized in experimental collaboration in Nat. Commun. 9, 981 (2018), which are part of my studies of topological photonics since 2012. I also work on quantum dissipative systems and quantum noise (since 1993), quantum chaos (since 1994), mesoscopic conductors and superconductors (since 1999), Anderson localization (since 2000), dielectric resonators (since 2002), atoms in strong fields (since 2002), graphene (since 2007), PT-symmetric optics (since 2010), Majorana states (since 2012) and many-body localization (since 2015), where I frequently employ random-matrix theory, scattering approaches, and semiclassical methods.

Below you find a breakdown of fields of activity in terms of different categories; see publications for details and results.

# systems▲

## photonic systems

- topological photonics
- PT symmetric and nonhermitian optics
- structured microlasers
- dielectric microresonators
- random media

## mesoscopic systems

- topological superconductors
- topological insulators
- graphene and Dirac materials
- mesoscopic superconductors
- quantum dots and wires
- quantum information devices
- metameterials

## interacting systems

- interacting fermions
- spin chains
- Coulomb blockaded systems

## quantum and atom optical systems

- mesoscopic light emitters
- exciton polaritons
- quantum condensates
- atoms in pulsed optical fields
- atoms in strong fields (NSDI, ATI, HHG)

## quantum dynamical systems

- quantum billiards
- kicked systems
- quantum walks

## classical dynamical systems

- fully chaotic systems
- mixed chaotic systems
- random dynamical systems

# concepts▲

## topological states

- edge and defect states
- Majorana fermions
- flat bands and compactons
- topological mode selection
- nonhermitian and nonlinear protected states

## quantum coherent transport

- effects of bandstructure topology
- Anderson localization
- weak localization
- coherent backscattering
- sample-to-sample fluctuations
- pseudomagnetic fields
- contacts and interfaces
- confinement mechanisms
- adsorbate functionalization and sensing
- spin and pseudospin effects
- proximity effect
- Josephson effect
- Aharonov-Bohm effect
- quantum pumping
- delay times

## quantum noise

- shot noise
- full counting statistics
- quantum limited noise
- nonmarkovian and nonergodic noise

## interactions

- many-body localization
- entanglement and correlations
- dissipation and decoherence
- amplification and lasing
- light-matter interactions
- Coulomb blockade
- space charge effects
- charge ordering
- nonequilibrium dynamics
- nonlinear wave dynamics

## resonance phenomena

- quantum decay
- exceptional points
- mode nonorthogonality
- fractal Weyl law
- nonhermitian symmetries

## quantum-to-classical correspondence

- quantum chaos
- mixed phase space
- bifurcations
- Ehrenfest time
- scarring
- wave corrections
- Goos-Hänchen shift

# methods▲

## scattering theory

- Landauer-Büttiker formalism
- Green's function methods
- kinetic theory
- non-hermitian operators

## statistical approaches

- random matrices
- large deviation statistics
- fluctuation theorems
- multifractality
- nonergodicity
- universal singular fluctuations

## semiclassics

- uniform approximations
- asymptotic boundary layer method
- phase-space representations

## many-body and field theory

- one-particle density matrix
- Bogoliubov theory
- Master equations
- T matrix and vertex functions
- nonlinear sigma model
- Keldysh techniques
- path integrals

## numerics

- exact diagonalization and propagation
- recursive Green's functions and decimation
- tensor networks and matrix product states
- quantum equations of motion
- tight-binding and coupled-mode approaches
- full-wave modelling

## experimental collaborations

- dielectric resonator chains
- exciton polaritons in structured devices
- photonic lattices
- optical quantum walks
- semiconductor microlasers