Backup mandate Research Council: Quantum chaos and quantum complexity in quantum resonant systems

Project Details

Description

I will study quantum chaos and quantum complexity in the novel context of quantum resonant systems. Quantum resonant systems arise upon quantizing classical resonant systems. The latter provide controlled approximations to the dynamics of interesting classes of weakly nonlinear systems, including weakly interacting Bose-Einstein condensates in harmonic traps and weakly interacting fields in anti- de Sitter (AdS) spacetime.
Quantum resonant systems are attractive for several reasons. First, their Hamiltonian exhibits a block-diagonal structure, which makes them tractable despite having an infinite-dimensional Hilbert space. Second, the corresponding classical resonant systems provide natural semi-classical limits. Third, classical resonant systems display a rich variety of behaviour (e.g. chaotic vs integrable, turbulent or not). Finally, quantum resonant systems are directly
relevant to the study of physical systems such as bosons in harmonic traps and quantum fields in AdS spacetime.
Quantum chaos will be studied by quantifying how the energy level spacing statistics and out-of-time-order correlators interpolate between integrable and chaotic systems. At the same time, it will be tested to what extent these systems satisfy the Eigenstate Thermalization Hypothesis. Quantum complexity will be studied by quantifying complexity growth of the time-evolution operator and by testing to what extent the Eigenstate Complexity Hypothesis is satisfied in various quantum resonant systems.
AcronymOZR3834
StatusActive
Effective start/end date1/11/2131/10/22

Flemish discipline codes

  • Field theory and string theory
  • Quantum information, computation and communication
  • Nonlineair sciences

Keywords

  • Quantum chaos
  • Quantum complexity
  • Quantum resonant systems