非平衡Stationary States辅助动力学的方差最小化构造
Constructing Auxiliary Dynamics for Nonequilibrium Stationary States by Variance Minimization
摘要：
提出了一种基于方差最小化的指导分布函数构造策略。通过GDF的辅助动态缓解了方差的指数增长，作为大偏差函数的Monte Carlo估计量中偏差的函数。方差最小化技术利用了倾斜算子本征态的精确性质，该算子定义了非平衡系统中的偏置动力学。我们证明了我们的技术在两类问题。在连续体中，我们表明，GDF可以进行优化，以研究相互作用驱动的扩散系统的效率得到系统的提高，将更高的相关性到GDF。在晶格上，我们用相关积态方法研究了一维WASEP。我们表明，与适度的资源，我们可以捕捉到的大系统，标志着相变从均匀运输到一个行波状态的磁化率的功能。我们的工作扩展了可用于研究现实系统中的非平衡性质的工具库。
英文摘要：
We present a strategy to construct guiding distribution functions (GDFs) based on variance minimization. Auxiliary dynamics via GDFs mitigates the exponential growth of variance as a function of bias in Monte Carlo estimators of large deviation functions. The variance minimization technique exploits the exact properties of eigenstates of the tilted operator that defines the biased dynamics in the nonequilibrium system. We demonstrate our techniques in two classes of problems. In the continuum, we show that GDFs can be optimized to study interacting driven diffusive systems where the efficiency is systematically improved by incorporating higher correlations into the GDF. On the lattice, we use a correlator product state ansatz to study the 1D WASEP. We show that with modest resources we can capture the features of the susceptibility in large systems that marks the phase transition from uniform transport to a traveling wave state. Our work extends the repertoire of tools available to study nonequilibrium properties in realistic systems.
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