Mathieu-state reordering in periodic thermodynamics

A periodically driven, moderately anharmonic oscillator constitutes an ideal model system for investigating quantum resonances, which are amenable to a quantum pendulum approximation. In the present paper, I study the quasi-stationary Floquet-state occupation probabilities which emerge when such a resonantly driven system is coupled to a heat bath. It is demonstrated that the Floquet state which is associated with the ground state of the pendulum turns into an effective ground state, carrying the highest population in the strong-driving regime. Moreover, the population of this effective Floquet ground state can even exceed that of the undriven system’s true ground state at the same bath temperature. These effects can be optimized by suitably engineering the properties of the bath.

Complex symmetric operators and semiclassical resonances

Unbounded complex symmetric operators on Hilbert space are discussed and various spectral results on these operators are presented in this paper. In addition, we show that the technique of complex scaling allows one to identify the quantum resonances of complex self-adjoint Schrödinger Hamiltonians.

Ruelle and Quantum Resonances for Open Hyperbolic Manifolds

We establish a direct classical-quantum correspondence on convex cocompact hyperbolic manifolds between the spectra of the geodesic flow and the Laplacian acting on natural tensor bundles. This extends previous work detailing the correspondence for cocompact quotients.