A high-precision numerical method for the dissipative dynamics of the Hamiltonian systems

Abstract

In this paper, an effective spectral-Galerkin method was proposed for the dissipative dynamics of a Hamiltonian system. By introducing a suitable Sobolev space, we establish a weak form and corresponding discrete scheme. Compared with the existing methods, our method can achieve higher accuracy and shorter computational time. We also simulate quantum cooling in an optomechanical system as an example to show the advantage of our method. Our method provides a promising platform for studying the dissipative dynamics of nonlinear and complex Hamiltonian systems.

Keywords:

• Hamiltonian system
• spectral-Galerkin approximation
• iterative algorithm
• numerical experiments

2010 AMS Subject Classifications:

• 17B81
• 17C90
• 81-08
• 81S22

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Research was supported in part by National Natural Science Foundation of China (NSFC) (Grant Nos. 11726604, 11726603, 11704026), the China Postdoctoral Science Foundation funded project (Grant No. 2018T110039), and Guizhou Provincial Education Department Foundation (Qianjiaohe No. KY[2018]041).