论文标题
乘法噪声在关键动力学中的作用
The role of multiplicative noise in critical dynamics
论文作者
论文摘要
我们研究了临界点附近订单参数动力学的描述中乘法随机过程的作用。我们研究平衡和平衡性能。通过功能形式主义，我们用$ z_2 $对称性为真实标量订单参数构建了动力学重归其化组方程，该方程是由具有相同对称性的类O乘法随机过程驱动的。我们已经使用受控的$ε$ - expansion计算了磁通图，直至$ε^2 $。我们发现，对于尺寸$ d =4-ε$，添加动态固定点不稳定。 The flux runs to a {\em multiplicative fixed point} driven by a diffusion function $G(ϕ)=1+g^*ϕ^2({\bf x})/2$, where $ϕ$ is the order parameter and $g^*=ε^2/18$ is the fixed point value of the multiplicative noise coupling constant.我们表明，即使固定点的位置取决于随机处方，关键指数也不。因此，由不同的随机处方（例如ITô，Stratonovich，Anti-Itô等）驱动的不同动力学在同一普遍性类别中。
We study the role of multiplicative stochastic processes in the description of the dynamics of an order parameter near a critical point. We study equilibrium, as well as, out-of-equilibrium properties. By means of a functional formalism, we built the Dynamical Renormalization Group equations for a real scalar order parameter with $Z_2$ symmetry, driven by a class o multiplicative stochastic processes with the same symmetry. We have computed the flux diagram, using a controlled $ε$-expansion, up to order $ε^2$. We have found that, for dimensions $d=4-ε$, the additive dynamic fixed point is unstable. The flux runs to a {\em multiplicative fixed point} driven by a diffusion function $G(ϕ)=1+g^*ϕ^2({\bf x})/2$, where $ϕ$ is the order parameter and $g^*=ε^2/18$ is the fixed point value of the multiplicative noise coupling constant. We show that, even though the position of the fixed point depends on the stochastic prescription, the critical exponents do not. Therefore, different dynamics driven by different stochastic prescriptions (such as Itô, Stratonovich, anti-Itô and so on) are in the same universality class.
