论文标题
线性化量子玻尔兹曼操作员的明确施加性估计值
An explicit coercivity estimate of the linearized quantum Boltzmann operator without angular cutoff
论文作者
论文摘要
量子玻尔兹曼 - 骨方程描述了弱偶联方向中的bose-Einstein颗粒系统。如果粒子相互作用受反功法控制，则相应的碰撞内核具有角度奇异性。在本文中，我们给出了线性化量子玻尔兹曼 - 杆算子的强制性估计值的建设性证明，以捕获奇异性和散发性的影响。确切地说，估计值明确揭示了对Bose-Einstein凝结之前的逃逸参数的依赖性。通过矫正估计，可以建立bose-enstein平衡的扰动框架和稳定性中不均匀的量子螺栓骨架方程的全局时间良好。
The quantum Boltzmann-Bose equation describes a large system of Bose-Einstein particles in the weak-coupling regime. If the particle interaction is governed by the inverse power law, the corresponding collision kernel has angular singularity. In this paper, we give a constructive proof of the coercivity estimate for the linearized quantum Boltzmann-Bose operator to capture the effects of the singularity and the fugacity. Precisely, the estimate explicitly reveals the dependence on the fugacity parameter before the Bose-Einstein condensation. With the coercivity estimate, the global in time well-posedness of the inhomogeneous quantum Boltzmann-Bose equation in the perturbative framework and stability of the Bose-Einstein equilibrium can be established.
