AI 中文总结
本文针对一维Lieb-Liniger玻色气体基态的空区形成概率，提出无参数积分方程形式的速率函数猜想，验证其与相关极限及数值结果吻合，还得到类星状真空区域的空区瞬子。
AI 中文摘要
我们研究排斥性一维Lieb-Liniger玻色气体基态中的空区形成概率（Emptiness Formation Probability，EFP）。对于长度为2R的宏观空区间，其主导渐近行为由速率函数f(γ₀)描述，定义为 -log P(R) ~ (ρ₀R)²f(γ₀)，其中ρ₀为平均密度，γ₀为无量纲相互作用强度。我们提出了一个无参数的f(γ₀)积分方程。从EFP的精确对偶场Fredholm行列式表示出发，我们展示了猜想的核如何形式上产生，并确定了严格推导中仍待证明的均匀渐近表述。该猜想重现了Tonks-Girardeau极限和弱耦合极限，以及在两个极限中独立获得的一阶修正，且在耦合的四个数量级以上范围内，与Lieb-Liniger流体动力学作用量的数值极小化结果吻合至百分之几的水平。数值计算得到了对应的空区瞬子及其类星状真空区域。
英文摘要
We study the emptiness formation probability (EFP) in the ground state of the repulsive one-dimensional Lieb-Liniger Bose gas. For a macroscopic empty interval of length $2R$, its leading asymptotic behavior is described by a rate function $f(γ_0)$, defined by $-\log P(R)\sim(ρ_0R)^2f(γ_0)$, where $ρ_0$ is the mean density and $γ_0$ is the dimensionless interaction strength. We propose a parameter-free integral equation for $f(γ_0)$. Starting from the exact dual-field Fredholm-determinant representation of the EFP, we show how the conjectured kernel arises formally and identify the uniform asymptotic statement that remains to be proven for a rigorous derivation. The conjecture reproduces the Tonks-Girardeau and weak-coupling limits, as well as the first correction obtained independently in both limits. It also agrees at the few-percent level with numerical minimization of the Lieb-Liniger hydrodynamic action over more than four orders of magnitude in coupling. The numerical calculation yields the corresponding emptiness instantons and their astroid-like vacuum regions.
Comments33 pages, 5 figures
