Relaxation Phenomena in a System of Two Harmonic Oscillators

Abstract

We study the process by which quantum correlations are created when an interaction Hamiltonian is repeatedly applied to a system of two harmonic oscillators for some characteristic time interval. We show that, for the case where the oscillator frequencies are equal, the initial Maxwell-Boltzmann distributions of the uncoupled parts evolve to a new equilibrium Maxwell-Boltzmann distribution through a series of transient Maxwell-Boltzmann distributions. Further, we discuss why the equilibrium reached when the two oscillator frequencies are unequal, is not a thermal one. All the calculations are exact and the results are obtained through an iterative process, without using perturbation theory.

22 pages, 6 Figures, Added contents, to appear in PRA

References in corpus (9)

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• Quantifying Entanglement
• Maximizing the entanglement of two mixed qubits
• Maximal entanglement versus entropy for mixed quantum states
• Decoherence induced by interacting quantum spin baths
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Cited by in corpus (10)

• Quantum collision models: open system dynamics from repeated interactions
• Positivity in the presence of initial system-environment correlation
• Interacting universes and the cosmological constant
• Coupled quantum oscillators within independent quantum reservoirs
• Partly invariant steady state of two interacting open quantum systems
• Dynamics and stationarity of two coupled arbitrary oscillators interacting with separate reservoirs
• Relaxation of two coupled quantum oscillators to quasi-equilibrium states based on path integrals
• Quasi-equilibrium relaxation of two identical quantum oscillators with arbitrary coupling strength
• Dynamics of two externally driven coupled quantum oscillators interacting with separate baths based on path integrals
• Heat exchange and fluctuation in Gaussian thermal states in the quantum realm