The possibility of using nanoelectromechanical systems as a simulation tool for quantum many-body effects is explored. It is demonstrated that an array of electrostatically coupled nanoresonators can effectively simulate the Bose-Hubbard model without interactions, corresponding in the single-phonon regime to the Anderson tight-binding model. Employing a density matrix formalism for the system coupled to a bosonic thermal bath, we study the interplay between disorder and thermalization, focusing on the delocalization process. It is found that the phonon population remains localized for a long time at low enough temperatures; with increasing temperatures the localization is rapidly lost due to thermal pumping of excitations into the array, producing in the equilibrium a fully thermalized system. Finally, we consider a possible experimental design to measure the phonon population in the array by means of a superconducting transmon qubit coupled to individual nanoresonators. We also consider the possibility of using the proposed quantum simulator for realizing continuous-time quantum walks.

中文翻译：

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耦合纳米谐振器阵列对安德森·哈密顿量的量子模拟：离域和热化效应

探索了使用纳米机电系统作为量子多体效应仿真工具的可能性。结果表明，静电耦合的纳米谐振器阵列可以有效地模拟Bose-Hubbard模型而没有相互作用，这在单声子体系中与Anderson紧密结合模型相对应。我们采用密度矩阵形式主义与耦合到玻色热浴的系统，我们研究无序和热化之间的相互作用，重点是离域化过程。发现声子种群在足够低的温度下长时间定位。随着温度的升高，由于将激励热泵送到阵列中，从而使定位迅速消失，从而在平衡状态下产生了完全热化的系统。最后，我们认为可能的实验设计是通过耦合到各个纳米谐振器的超导跨子量子位来测量阵列中的声子总数。我们还考虑了使用提出的量子模拟器来实现连续时间量子游走的可能性。