Interaction between a quantum system and its environment can induce stationary coherences—off-diagonal elements in the reduced system density matrix in the energy eigenstate basis—even at equilibrium. This work investigates the “quantumness” of such phenomena by examining the ability of classical and semiclassical models to describe equilibrium stationary coherence in the multilevel spin boson model, a common model for light-harvesting systems. A well justified classical harmonic-oscillator model is found to fail to capture equilibrium coherence. This failure is attributed to the effective weakness of classical system-bath interactions due to the absence of a discrete system energy spectrum and, consequently, of quantized shifts in oscillator coordinates. Semiclassical coherences also vanish for a dimeric model with parameters typical of biological light harvesting, i.e., where both system sites couple to the bath with the same reorganization energy. In contrast, equilibrium coherence persists in a fully quantum description of the same system, suggesting a uniquely quantum-mechanical origin for equilibrium stationary coherence in, e.g., photosynthetic systems. Finally, as a computational tool, a perturbative expansion is introduced that, at third order in $\hslash$, gives qualitatively correct behavior at ambient temperatures for all configurations examined.

中文翻译：

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多级自旋玻色子模型中的平衡平稳相干

量子系统与其环境之间的相互作用甚至在平衡时也可以引起平稳的相干性（在能量本征态的基础上，降低的系统密度矩阵中的非对角元素）。这项工作通过检查经典和半经典模型描述多级自旋玻色子模型（光收集系统的通用模型）中的平衡平稳相干的能力，研究了这种现象的“量子性”。发现一个充分合理的经典谐波振荡器模型无法捕获平衡相干性。该失败归因于经典系统-浴相互作用的有效弱点，这归因于不存在离散的系统能谱，因此缺乏振荡器坐标的量化偏移。对于具有生物光收集典型参数的二聚体模型，半经典相干性也消失了，即，两个系统位点以相同的重组能量耦合到熔池。相反，平衡相干性在同一系统的完整量子描述中仍然存在，这暗示了例如光合系统中平衡静态相干性的唯一量子力学起源。最后，作为一种计算工具，引入了摄动展开式，该展开式在$\hslash$给出了所有配置下在环境温度下的定性正确行为。