论文标题
驱动驱动问题的新方法：Keldysh-Heisenberg方程
A new method for driven-dissipative problems: Keldysh-Heisenberg equations
论文作者
论文摘要
由于存在新型的物理现象，在平衡情况下没有类似物，因此驱动的脉动系统最近引起了极大的关注。 Keldysh路径综合理论是研究这些系统的强大工具。但是，研究最近实验实现的强大非线性效应仍然是挑战，因为在这种情况下，光子数很少，量子波动在系统动力学中起着至关重要的作用。在这里，我们通过以Fock-State引入Keldysh分区函数，然后将标准的鞍点方程映射到Keldyshheisenberg方程中，从而开发了一种新的方法，用于传达驱动系统系统的精确稳态。我们以/没有非线性驾驶的方式将强大的Kerr非线性谐振器作为两个例子来说明我们的方法。发现在没有非线性驱动的情况下，获得的确切稳态并不能表现出双重性，并且与复杂的p-pressentation解决方案非常吻合。尽管在存在非线性驱动的情况下，多光子共振效应被揭示，并且与定性分析一致。我们的方法提供了一种直观的方式来探索各种驱动的触及系统，尤其是具有较强的相关性。
Driven-dissipative systems have recently attracted great attention due to the existence of novel physical phenomena with no analog in the equilibrium case. The Keldysh path-integral theory is a powerful tool to investigate these systems. However, it has still been challenge to study strong nonlinear effects implemented by recent experiments, since in this case the photon number is few and quantum fluctuations play a crucial role in dynamics of system. Here we develop a new approach for deriving exact steady states of driven-dissipative systems by introducing the Keldysh partition function in the Fock-state basis and then mapping the standard saddle-point equations into KeldyshHeisenberg equations. We take the strong Kerr nonlinear resonators with/without the nonlinear driving as two examples to illustrate our method. It is found that in the absence of the nonlinear driving, the exact steady state obtained does not exhibit bistability and agree well with the complex P-representation solution. While in the presence of the nonlinear driving, the multiphoton resonance effects are revealed and are consistent with the qualitative analysis. Our method provides an intuitive way to explore a variety of driven-dissipative systems especially with strong correlations.
