Open dynamics in the Aubry-André-Harper model coupled to a finite bath: the influence of localization in the system and dimensionality of bath

Abstract

The population evolution of single excitation is studied in the Aubry- André- Harper (AAH) model coupled to a $d(=1,2,3)$-dimensional simple lattices bath with a focus on the effect of localization in the system and the dimensionality of bath. By performing a precise evaluation of time-independent Schrödinger equation, the reduced energy levels of the system can be determined. It is found that the reduce energy levels show significant relevance for the bath dimensions. Subsequently, the time evolution of excitation is studied in both the system and bath. It is found that excitation in the system can decay super-exponentially when $d=1$ or exponentially when $d=2,3$. Regarding the finite nature of bath, the spreading of excitation in the lattices bath is also studied. We find that, depending on the dimensions of bath and the initial state, the spreading of excitation in the bath is diffusive or behaves localization.

14 pages, 11 figures. Substantial revivison. Title is changed

References in corpus (9)

• Many-Body Physics with Ultracold Gases
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Quantum States and Phases in Driven Open Quantum Systems with Cold Atoms
• Strongly Correlated Quantum Walks in Optical Lattices
• Dissipative Phase Transition in Central Spin Systems
• Dynamical Phase Transitions and Instabilities in Open Atomic Many-Body Systems
• Subwavelength vacuum lattices and atom-atom interactions in photonic crystals
• Nonexponential quantum decay under environmental decoherence
• Green's function on lattices

Cited by in corpus (1)

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