< Back to previous page
Project
Quantum chaos and quantum complexity in quantum resonant systems. (FWOTM1147)
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 antide 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
through the calculation of an upper bound on complexity for different
models. I will also quantify how this bound changes when
interpolating between integrable and chaotic systems
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 antide 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
through the calculation of an upper bound on complexity for different
models. I will also quantify how this bound changes when
interpolating between integrable and chaotic systems
Date:1 Nov 2022 → Today
Keywords:Quantum chaos, Quantum complexity, Quantum resonant systems
Disciplines:Field theory and string theory, Quantum information, computation and communication, Nonlinear sciences