AI 中文总结
本文研究带阶跃磁场的非均匀XX链非平衡动力学，经Jordan-Wigner变换映射为紧束缚链，通过傅里叶与拉普拉斯变换得到两点关联函数精确表达式，流体极限下给出显式公式，数值模拟验证其吻合性。
AI 中文摘要
我们研究具有阶跃型磁场的XX链中的非平衡动力学，该系统经Jordan-Wigner变换后可映射为非均匀紧束缚链。我们结合傅里叶变换与拉普拉斯变换，将问题转化为单位圆上的标准Riemann-Hilbert问题，从若干初始乘积态（包括均匀与非均匀态）进行量子猝灭后，得到费米子两点关联函数的精确解析表达式。对于任意位置和时间，关联函数无法用初等函数表示；但在流体动力学极限（x、y、t→∞且比值固定）下，我们给出仅依赖原点处有效透射系数的显式公式。我们将解析预测与精确数值模拟对比，发现除有限时间修正外，二者在流体动力学极限下吻合极佳。
英文摘要
We study the out-of-equilibrium dynamics in the XX chain with step-like magnetic field, which maps to an inhomogeneous tight-binding chain after Jordan-Wigner transformation. We obtain exact analytic expressions for the fermionic two-point correlation function after a quantum quench from several initial product states, both homogeneous and inhomogeneous ones. This is achieved by using a combination of Fourier and Laplace transforms, which al low us to map the problem to a standard Riemann-Hilbert problem on the unit circle. For arbitrary positions and times the correlators are not expressed in terms of elementary functions. However, in the hydrodynamic limit $x,y,t\to\infty$ with fixed ratios, we provide explicit formulas that depend only on the effective transmission coefficient across the origin. We benchmark our analytic predictions against exact numerical simulations and find excellent agreement in the hydrodynamic limit, apart from finite-time corrections.
Comments23 pages, 7 figures
