Lyapunov inequalities for two-parametric quantum Hamiltonian systems and their applications

Lyapunov inequalities and stability for linear Hamiltonian systems

Lyapunov-type inequalities for the first-order nonlinear Hamiltonian systems

In this paper, we establish several new Lyapunov-type inequalities for the first-order nonlinear Hamiltonian system  x ′ (t) = α(t)x(t) + β(t)|y(t)| µ−2 y(t), y ′ (t) = −γ (t)|x(t)| ν−2 x(t) − α(t)y(t), which generalize or improve all related existing ones.

Analysis of Lyapunov Control for Hamiltonian Quantum Systems

We present detailed analysis of the convergence properties and effectiveness of Lyapunov control design for bilinear Hamiltonian quantum systems based on the application of LaSalle’s invariance principle and stability analysis from dynamical systems and control theory. For a certain class of Hamiltonians, strong convergence results can be obtained for both pure and mixed state systems. The cont...

On Two-parameter Dynamical Systems and Applications

In this note some useful properties of strongly continuous two-parameter semigroups of operators are studied, an exponential formula for two-parameter semigroups of operators on Banach spaces is obtained and some applied examples of two-parameter dynamical systems are discussed

Hamiltonian Engineering for Quantum Systems

We describe different strategies for using a semi-classical controller to engineer quantum Hamiltonians to solve control problems such as quantum state or process engineering and optimization of observables.