2021/12/07 by Arpan Bhattacharyya, T. Hanif, Tanvir Hanif +2
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Harmonic oscillator #Mathematics #Physics #Quantum #Quantum Information and Cryptography #Quantum harmonic oscillator #Quantum many-body systems #Quantum mechanics #Scalar field #Spectroscopy and Quantum Chemical Studies #hep-th #quant-ph
paper · pdf · doi:10.1103/physrevd.105.046011
published as Phys. Rev. D 105, 046011 (2022) · 22 pages, 4 figures
arxiv created 2021/12/07 · openalex publication_date 2022/02/16 · arxiv updated 2022/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the complexity for an open quantum system. Our system is a harmonic oscillator coupled to a one-dimensional massless scalar field, which acts as the bath. Specifically, we consider the reduced density matrix by tracing out the bath degrees of freedom for both regular and inverted oscillators and compute the complexity of purification (COP) and complexity by using the operator-state mapping. We find that when the oscillator is regular, the COP saturates quickly for both underdamped and overdamped oscillators. Interestingly, when the oscillator is underdamped, we discover a kink-like behavior for the saturation value of the COP with a varying damping coefficient. For the inverted oscillator, we find a linear growth of the COP with time for all values of the bath-system interaction. However, when the interaction is increased the slope of the linear growth decreases, implying that the unstable nature of the system can be regulated by the bath.