标题： CFT方法在吸引势中旋转场块的应用 显示英文标题

标题： CFT-approach to Rotating Field Lumps in Attractive Potential

摘要： 我们展示了相对论修正在研究低能极限下具有四次自相互作用的$(2+1)$维非拓扑孤子稳定性中的重要性。 这一结果是由于非相对论极限中共形对称性的恢复。 特别是，相应的三次 Gross-Pitaevskii 方程支持无尺度的非拓扑孤子。 未破缺的共形对称性提供了额外的简并性，使得能够得到静态经典解的能量和角动量的精确结果。 我们研究了相对论修正对共形对称性的破坏。 通过解析近似和数值计算，展示了在经典背景上指数增长模式的出现。 显示英文摘要

摘要： We demonstrate the importance of relativistic corrections for the study of the stability of $(2+1)$-dimensional non-topological solitons with quartic self-interaction in the low-energy limit. This result is explained by the restoration of conformal symmetry in the non-relativistic limit. Particularly, the corresponding cubic Gross-Pitaevskii equation supports scale-free non-topological solitons. An unbroken conformal symmetry provides the additional degeneration that allows for the exact result for the energy and angular momentum of the stationary classical solutions. We study the violation of conformal symmetry by relativistic corrections. The emergence of exponentially growing modes on the classical background is demonstrated using analytical approximations and numerical calculations.