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arXiv 2403.03386quant-phcond-mat.mes-hall
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强耦合下开放量子系统中由浴诱导的相互作用与瞬态动力学:有效哈密顿量方法

Bath-induced interactions and transient dynamics in open quantum systems at strong coupling: Effective Hamiltonian approach

Marlon Brenes, Brett Min, Nicholas Anto-Sztrikacs, Nir Bar-Gill, Dvira Segal

AI总结:

本研究采用有效哈密顿量理论研究强耦合开放量子系统动力学,通过两个经典模型验证,发现其虽忽略瞬态非马尔可夫特征,但能正确捕捉浴诱导的非微扰自旋耦合,为强耦合动力学研究提供有力工具。

摘要:

理解耗散量子系统的动力学,尤其是超出弱耦合近似的情况,是各类量子应用的核心问题。虽然数值精确方法能给出准确解,但它们通常缺乏理论方法所提供的解析洞见。本研究中,我们采用近期发展的名为有效哈密顿量理论(effective Hamiltonian theory)的方法,无需对系统-浴耦合能进行微扰描述,即可理解系统-浴构型的动力学。通过映射步骤与截断的结合,有效哈密顿量理论既能为开放量子系统中的强耦合特征提供解析洞见,也为数值模拟提供了直接路径。为验证该方法的准确性,我们将其应用于两个经典模型:浸入玻色浴的单个自旋,以及处于共同浴中的两个非相互作用自旋。在两种情形下,我们研究了非零温度下的瞬态区域和稳态极限,且覆盖了从弱到强的系统-浴相互作用范围。通过将有效哈密顿量理论的结果与数值精确模拟进行比较,我们表明,尽管前者忽略了瞬态平衡动力学中的非马尔可夫特征,但它正确捕捉到了原本无相互作用的自旋之间由浴产生的非微扰耦合,这一点可从它们的同步动力学和关联中观测到。总体而言,有效哈密顿量理论为理解强耦合动力学与热力学提供了一种强有力的方法,能够捕捉此类相互作用在弛豫动力学和稳态极限中的特征。

英文摘要:

Understanding the dynamics of dissipative quantum systems, particularly beyond the weak coupling approximation, is central to various quantum applications. While numerically exact methods provide accurate solutions, they often lack the analytical insight provided by theoretical approaches. In this study, we employ the recently-developed method dubbed the effective Hamiltonian theory to understand the dynamics of system-bath configurations without resorting to a perturbative description of the system-bath coupling energy. Through a combination of mapping steps and truncation, the effective Hamiltonian theory offers both analytical insights into signatures of strong couplings in open quantum systems and a straightforward path for numerical simulations. To validate the accuracy of the method, we apply it to two canonical models: a single spin immersed in a bosonic bath and two noninteracting spins in a common bath. In both cases, we study the transient regime and the steady state limit at nonzero temperature, and spanning system-bath interactions from the weak to the strong regime. By comparing the results of the effective Hamiltonian theory with numerically exact simulations, we show that although the former overlooks non-Markovian features in the transient equilibration dynamics, it correctly captures non-perturbative bath-generated couplings between otherwise non-interacting spins as observed in their synchronization dynamics and correlations. Altogether, the effective Hamiltonian theory offers a powerful approach to understanding strong coupling dynamics and thermodynamics, capturing the signatures of such interactions in both relaxation dynamics and in the steady state limit.

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