论文标题
离散非线性schrödinger方程的相变
Phase Transition for Discrete Non Linear Schrödinger Equation in Three and Higher Dimensions
论文作者
论文摘要
我们在尺寸上分析了焦点离散非线性schrödinger方程的热力学$ d \ ge 3 $，其一般非线性$ p> 1 $，并且在具有两个参数的模型下，分别代表了非线性的逆温度和强度。我们证明存在限制自由能的存在，并分析了一般$ d，p $的相位图。我们还证明了连续的相变曲线的存在，该曲线将参数平面划分为涉及孤子的外观或不表现的两个区域。构建了适当的曲线上限和下边界。我们还研究了从Gibbs选择的相图的某些部分中选择的函数的典型行为。
We analyze the thermodynamics of the focusing discrete nonlinear Schrödinger equation in dimensions $d\ge 3$ with general nonlinearity $p>1$ and under a model with two parameters, representing inverse temperature and strength of the nonlinearity, respectively. We prove the existence of limiting free energy and analyze the phase diagram for general $d,p$. We also prove the existence of a continuous phase transition curve that divides the parametric plane into two regions involving the appearance or non-appearance of solitons. Appropriate upper and lower bounds for the curve are constructed. We also look at the typical behavior of a function chosen from the Gibbs measure for certain parts of the phase diagram.
