Modelling Quantum Subsystem Dynamics

I. A. Nagibarova, E. I. Bogdanov, I. A. Deriugin

Kazutomu Shiokawa, Raymond Kapral

The conditions under which an open quantum-mechanical system may be described by mixed quantum-classical dynamics are investigated. Decoherence is studied using influence functional methods in a model composite quantum system comprising two coupled systems, A and C, interacting with a harmonic bath with Ohmic and super-Ohmic spectral densities. Subsystem A is directly coupled to subsystem C, while C is coupled directly to the bath. Calculations are presented for a model where subsystem A is taken to be a two-level system which is bilinearly coupled to a single harmonic oscillator C subsystem. The loss of quantum coherence in each subsystem is discussed in the extreme nonadiabatic regime where the intrinsic dynamics of subsystem A is essentially frozen. Subsystem C is shown to lose its coherence rapidly, while subsystem A maintains coherence for longer time periods since C modulates the influence of the bath on A. Thus, one may identify situations where the coupled AC system evolution effectively obeys mixed quantum-classical dynamics.

Li, Jia, Hao, Yajiang

We investigate the spatial and temporal scales of dynamical quantum phase transitions in the one-dimensional Bose-Hubbard model in the strong interaction limit. Using Jordan-Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo, and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system Loschmidt echo, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical quantum phase transitions using the subsystem Loschmidt echo. It is expected that the present results provide a reliable foundation for further experimental investigations.

Mohamad M. Toutounji, Raymond Kapral

Jia 李 Li 佳, Yajiang Hao

Abstract We investigate the spatial and temporal scales of dynamical quantum phase transitions (DQPTs) in the one-dimensional Bose–Hubbard model in the strong interaction limit. Using Jordan–Wigner transformation, we obtain the time-dependent wavefunction and therefore the subsystem Loschmidt echo (LE), and systematically investigate how its properties vary with subsystem size. It is found that when the subsystem is sufficiently large, it exhibits logarithmic divergence identical to that of the full system LE, yielding a critical exponent of zero. We also obtain the required subsystem size and temporal resolution for detecting dynamical DQPTs using the subsystem LE. It is expected that the present results provide a reliable foundation for further experimental investigations.

Michele Coppola, Zala Lenarčič

When only local observables of a many-body quantum system are of interest, it is desirable to formulate a reduced description within the Hilbert space of the corresponding subsystem, with the remaining degrees of freedom traced out and acting as an environment. Assuming initially uncorrelated states and Gaussian environments, we develop a framework for reconstructing the local dynamical generator of noninteracting quantum chains, with polynomial computational complexity. As an application, we consider two representative models: a bipartitioned Kitaev chain and a Kitaev chain boundary-coupled to a fully connected free-fermion environment. In both models, strong subsystem-environment coupling leads to non-Markovian dynamics characterized by ballistic spreading of the Lindblad dissipator support within the subsystem. On the other hand, weak coupling to a fully connected environment yields predominantly boundary-localized, Markovian dissipation. Our work highlights the implications of subsystem-environment correlations on the generator of local dynamics, beyond the conventional weak-coupling approximations.