On quantum multi-hamiltonian systems

Mich�le Irac-Astaud, Guy Rideau

Jincheng Zhang

Quantum multi-particle systems pose significant challenges in modeling and understanding complex phenomena. Traditional Hamiltonian approaches often struggle to accurately capture the dynamic behavior of such systems, particularly when interactions are variable. This paper introduces a novel approach, utilizing an adaptive Hamiltonian description, to address this challenge. We formulate a new framework for dynamically adjusting the Hamiltonian based on the relative strengths and directions of interactions, resulting in a more efficient and accurate representation of the system's dynamics. This design enhances our ability to predict and control the behavior of quantum multi-particle systems, offering a significant step towards improved simulation and analysis.

Sonia G. Schirmer

Shuang Cong, Fangfang Meng

In closed quantum systems, if controlled systems are not strongly regular or there exists at least one eigenstate that is directly uncoupled to the target state, then such systems control will become degenerate cases. This paper proposes a quantum control method designed by an implicit Lyapunov function to transfer states of the quantum systems in these two degenerate cases, especially the method proposed is suitable for multi-control Hamiltonian systems. The state distance is selected as the Lyapunov function in this paper. Numerical simulation experiments on a 4-level system are done, and the experiment results indicate the effectiveness of the implicit Lyapunov control method proposed for degenerate cases and multi-control Hamiltonians.

Valerij V. Kozlov, Oleg Georgievich Smolyanov

Huai-Xin Lu, Zeng‐Bing Chen, Lei Ma +1 more

We construct a general supersymmetric quantum transformation for studying the supersymmetric quadratic Hamiltonian which contains the interaction of multi-mode fermions with multi-mode bosons. The Hamiltonian can be derived from that of multi-mode radiation field interacting with m two-level atoms. By using the supersymmetric quantum transformation, the diagonolized Hamiltonian is given. We also concisely derive the analytic expression of the super-partition function for the supersymmetric quadratic Hamiltonian without knowing the energy spectrum.