Entanglement entropies of coupled harmonic oscillators

Abstract

We investigate the quantum entanglement of systems of coupled harmonic oscillators on the basis of thermo-field dynamics (TFD). For coupled harmonic oscillators at equilibrium, the extended entanglement entropy is derived using the TFD method, and it is demonstrated to be controlled by temperature and coupling parameters. For non-equilibrium systems, in addition to temperature and coupling parameters, the time dependence of the extended entanglement entropy is calculated in accordance with the dissipative von Neumann equation, and the dissipative dynamics of the systems of coupled harmonic oscillators is discussed. Consequently, based on TFD, the physical parametrization of the entanglement entropies is confirmed in both the equilibrium and non-equilibrium cases of harmonic oscillator systems by means of the laws of thermodynamics.

11 pages, 3 figures. The initial condition in Eq.(28) and Fig.2 were revised

References in corpus (1)

• Zeeman effects on the entanglement of non-equilibrium finite-spin systems

Cited by in corpus (4)

• Inter-universal entanglement in a cyclic multiverse
• Entanglement entropy and Fisher information metric for closed bosonic strings in homogeneous plane wave background
• Entanglement of higher-derivative oscillators in holographic systems
• Shannon Entropic Entanglement Criterion in the Simple Harmonic Oscillator