Effective nonlinear Ehrenfest hybrid quantum-classical dynamics

Abstract

The definition of a consistent evolution equation for statistical hybrid quantum-classical systems is still an open problem. In this paper we analyze the case of Ehrenfest dynamics on systems defined by a probability density and identify the relations of the non-linearity of the dynamics with the obstructions to define a consistent dynamics for the first quantum moment of the distribution. This first quantum moment represents the physical states as a family of classically-parametrized density matrices $\hat{\rho }(\xi )$, for $\xi$ a classical point; and it is the most common representation of hybrid systems in the literature. Due to this obstruction, we consider higher order quantum moments, and argue that only a finite number of them are physically measurable. Because of this, we propose an effective solution for the hybrid dynamics problem based on approximating the distribution by those moments and representing the states by them.

arXiv comment21 pages. Minor correction in the list of affiliations

References in corpus (16)

• Mixing Quantum and Classical Mechanics
• Hybrid classical-quantum dynamics
• Geometrization of Quantum Mechanics
• Consistent classical and quantum mixed dynamics
• Classical nuclear motion coupled to electronic non-adiabatic transitions
• Hybrid Quantum-Classical Master Equations
• Statistical ensembles in Hamiltonian formulation of hybrid quantum-classical systems
• Statistics and Nosé formalism for Ehrenfest dynamics
• Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence
• Geometrization of some quantum mechanics formalism
• Quantum-classical hybrid dynamics - a summary
• Entropy and canonical ensemble of hybrid quantum classical systems
• Tensorial dynamics on the space of quantum states
• Ehrenfest statistical dynamics in chemistry: study of decoherence effects
• The space of density states in geometrical quantum mechanics
• About the computation of finite temperatureensemble averages of hybrid quantum-classicalsystems with Molecular Dynamics

Cited by in corpus (4)

• Markovian master equations for quantum-classical hybrid systems
• Markovian dynamics for a quantum/classical system and quantum trajectories
• Hybrid quantum-classical systems: statistics, entropy, microcanonical ensemble and its connection to the canonical ensemble
• Heisenberg dynamics of mixed quantum-classical systems