Schrödinger-Koopman quasienergy states of quantum systems driven by a classical flow

Abstract

We study the properties of the quasienergy states of a quantum system driven by a classical dynamical system. The quasienergies are defined in a same manner as in light-matter interaction but where the Floquet approach is generalized by the use of the Koopman approach of dynamical systems. We show how the properties of the classical flow (fixed and cyclic points, ergodicity, chaos) influence the driven quantum system. This approach of the Schrödinger-Koopman quasienergies can be applied to quantum control, quantum information in presence of noises, and dynamics of mixed classical-quantum systems. We treat the example of a kicked spin ensemble where the kick modulation is governed by discrete classical flows as the Arnold's cat map and the Chirikov standard map.

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Cited by in corpus (8)

• Koopman wavefunctions and classical-quantum correlation dynamics
• Madelung transform and probability densities in hybrid classical-quantum dynamics
• The wave operator representation of quantum and classical dynamics
• Entropy non-conservation and boundary conditions for Hamiltonian dynamical systems
• A Transfer Operator Approach to Relativistic Quantum Wavefunction
• Emergent gravity and D-brane adiabatic dynamics: emergent Lorentz connection
• Effective Hamiltonians for almost-periodically driven quantum systems
• Geometric phases, Everett's many-worlds interpretation of quantum mechanics, and wormholes