论文标题
周期性的利比特不平等
The periodic Lieb-Thirring inequality
论文作者
论文摘要
我们讨论了周期系统的Lieb-Thrir-Thrir-Thrir-Thririte不平等，该不平等与有限系统的原始不平等具有相同的最佳常数。这使我们能够对其最佳常数的价值提出一个新的猜想。为了证明周期性状态的重要性，我们证明了特殊指数上的一维动物不平等$γ= 3/2 $允许一个单参数定期优化者家族，在单一结合状态和统一潜力之间插值。最后，我们在2D中提供数值模拟，以支持我们的猜想，即优化器可能是周期性的。
We discuss the Lieb-Thirring inequality for periodic systems, which has the same optimal constant as the original inequality for finite systems. This allows us to formulate a new conjecture about the value of its best constant. To demonstrate the importance of periodic states, we prove that the 1D Lieb-Thirring inequality at the special exponent $γ=3/2$ admits a one-parameter family of periodic optimizers, interpolating between the one-bound state and the uniform potential. Finally, we provide numerical simulations in 2D which support our conjecture that optimizers could be periodic.
