AI 中文总结
该研究在经典系统-环境模型中推导了关联高斯噪声下的粒子均方值表达式，发现移除Caldeira-Leggett框架耗散会产生t⁵、t³等非扩散量子输运机制。
AI 中文摘要
我们研究一种经典的系统-环境模型，其中系统粒子与简谐振子环境线性耦合。在受白噪声和关联高斯噪声作用的系统中，我们推导了联合概率密度的表达式，并计算了系统粒子与环境粒子的均方值。对于白噪声，系统粒子与环境粒子的均方值呈现出与正常扩散不同的反常时间依赖关系。特别地，对于关联高斯噪声，当时间远小于环境相关时间τ时，环境粒子的均方位移和均方速度分别呈现t⁵和t³的超扩散增长。当τ=0时，受随机噪声作用的量子粒子的均方速度与t成正比，而存在关联高斯噪声时环境粒子的均方速度则与t²成正比。这种反常输运现象源于主方程的混合导数结构，该结构在相对坐标的扩散动力学中与输运坐标耦合。该结果表明，移除Caldeira-Leggett框架中的耗散会导致以非扩散量子扩散为特征的根本不同的输运机制。
英文摘要
We study a classical system-bath model in which a system particle is linearly coupled to a bath of harmonic oscillators. In a system subject to white and correlated Gaussian noises, we derive an expression for the joint probability density, and the mean squared values of the system-bath particles are calculated. For white noise, the mean squared values of the system-bath particles exhibit an anomalous time dependence, which is different from that of normal diffusion. In particular, for a correlated Gaussian noise, the mean squared displacement and mean squared velocity of the bath particle show superspreading growths of $t^5$ and $t^3$ in $t{\ll}τ$, respectively. When $τ=0$, the mean squared velocity of a quantum particle under random noise is proportional to $t$, while the mean squared velocity of a bath particle in the presence of correlated Gaussian noise increases in proportion to $t^2$. This anomalous transport phenomenon results from the mixed derivative structure of the master equation, which couples with the transport coordinates in the diffusion dynamics of the relative coordinates. This result shows that the removal of dissipation in the Caldeira-Leggett framework leads to fundamentally different transport mechanisms characterized by non-diffusive quantum diffusion.
Comments13 pages, 2 Tables
