Grimaldi Andrea, Sergi Alessandro, Messina Antonino
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, 98166 Messina, Italy.
Istituto Nazionale di Fisica Nucleare, Sez. di Catania, 95123 Catania, Italy.
Entropy (Basel). 2021 Jan 25;23(2):147. doi: 10.3390/e23020147.
This work concerns the theoretical description of the quantum dynamics of molecular junctions with thermal fluctuations and probability losses. To this end, we propose a theory for describing non-Hermitian quantum systems embedded in constant-temperature environments. Along the lines discussed in [A. Sergi et al., Symmetry 10 518 (2018)], we adopt the operator-valued Wigner formulation of quantum mechanics (wherein the density matrix depends on the points of the Wigner phase space associated to the system) and derive a non-linear equation of motion. Moreover, we introduce a model for a non-Hermitian quantum single-molecule junction (nHQSMJ). In this model the leads are mapped to a tunneling two-level system, which is in turn coupled to a harmonic mode (i.e., the molecule). A decay operator acting on the two-level system describes phenomenologically probability losses. Finally, the temperature of the molecule is controlled by means of a Nosé-Hoover chain thermostat. A numerical study of the quantum dynamics of this toy model at different temperatures is reported. We find that the combined action of probability losses and thermal fluctuations assists quantum transport through the molecular junction. The possibility that the formalism here presented can be extended to treat both more quantum states (∼10) and many more classical modes or atomic particles (∼103-105) is highlighted.
这项工作涉及具有热涨落和概率损失的分子结量子动力学的理论描述。为此，我们提出了一种用于描述嵌入恒温环境中的非厄米量子系统的理论。沿着[A. Sergi等人，《对称性》10 518 (2018)]中讨论的思路，我们采用量子力学的算符值维格纳表述（其中密度矩阵取决于与系统相关的维格纳相空间的点）并推导了一个非线性运动方程。此外，我们引入了一个非厄米量子单分子结（nHQSMJ）模型。在这个模型中，引线被映射到一个隧穿二能级系统，该系统又与一个谐振模式（即分子）耦合。作用在二能级系统上的一个衰减算符从现象学上描述概率损失。最后，分子的温度通过一个诺西 - 胡佛链恒温器来控制。报告了对这个玩具模型在不同温度下的量子动力学的数值研究。我们发现概率损失和热涨落的联合作用有助于量子通过分子结传输。这里所呈现的形式体系能够扩展以处理更多量子态（约10个）以及更多经典模式或原子粒子（约10³ - 10⁵个）的可能性也得到了强调。
