An effective Hamiltonian for the simulation of open quantum molecular systems

• Published in: Journal of physics. A, Mathematical and theoretical Mathematical and theoretical, 2024-06, Vol.57 (25), p.255002
• Main Authors: Site, Luigi Delle, Djurdjevac, Ana
• Format: Article
• Language: English
• Subjects: molecular dynamics schemes; open systems; quantum many-particle systems; Von Neumann equation
• ISSN: 1751-8113; 1751-8121
• DOI: 10.1088/1751-8121/ad5088

We discuss the derivation of an effective Hamiltonian for open quantum many-particle systems. The aim is to define an operator that can be used for (molecular) simulations where, through the exchange of energy and matter with the surrounding environment (reservoir), the number of particles, n , becomes a variable of the problem. The Hamiltonian is formally derived from the Von Neumann equation; specifically, we derive an n -hierarchy of equations for the density matrix, ρ ^ n , for near equilibrium situations. Such a hierarchy, in case of stationary equilibrium, delivers the standard grand canonical density matrix as it would be expected. We report that a similar Hamiltonian was conjectured, from empirical considerations, in the field of superconductivity. Thus our result also provide a formal basis for this long-standing hypothesis. Finally, an application is discussed for Path Integral simulations of molecular systems.