发表机构
Dalian University of Technology; Seoul National University（大连理工大学; 首尔大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对具有排斥库仑相互作用的被俘获半经典玻色气体的自由能极小化问题，研究其测度值极小化子的存在唯一性、凝聚判据及变分稳定性等性质。
AI 中文摘要
我们研究具有排斥库仑自相互作用的被俘获半经典玻色气体的自由能极小化问题。由于玻色子熵密度的衰退斜率为零，自然的松弛是在相空间上非负有限拉东测度上提出的，极小化子可能具有奇异分量。我们将该分量解释为松弛半经典模型中的凝聚。我们证明了在所有正温度下的存在性与唯一性，推导了凝聚密度的欧拉-拉格朗日接触条件和障碍型公式，建立了凝聚的低温、高温以及小质量、大质量判据。对于简谐势阱，我们得到了尖锐的束缚强度二分性。我们还证明了关于质量守恒且满足自由能不等式的测度值曲线的抽象条件变分稳定性命题。
英文摘要
We study a free-energy minimization problem for a trapped semiclassical Bose gas with repulsive Coulomb self-interaction. Because the bosonic entropy density has zero recession slope, the natural relaxation is posed over nonnegative finite Radon measures on phase space, and a minimizer may have a singular component. We interpret this component as condensation within the relaxed semiclassical model. We prove existence and uniqueness at every positive temperature, derive the Euler-Lagrange contact condition and an obstacle-type formula for the condensed density, and establish sharp phase boundaries under only the standing continuity assumptions on the trap. At fixed mass there is a unique finite positive critical temperature, with condensation precisely below it. At fixed temperature there is a sharp critical mass, possibly infinite, separating normal and condensed minimizers. For harmonic traps we obtain a sharp confinement-strength dichotomy. We also prove an abstract conditional variational-stability statement for measure-valued curves that conserve mass and satisfy the free-energy inequality.
Comments42 pages, 2 figures
