论文标题
与三角洲杂质的非互动费米子的动态
Quench dynamics of noninteracting fermions with a delta impurity
论文作者
论文摘要
我们研究了一个维度和连续空间中非相互作用费米子的不平衡动力学，在存在的存在点$ g $时，在时间上有$ g $在时间$ t = 0 $的情况下，其强度$ g $。该系统以$ g = g_0 =+\ infty $为基础，具有两个不同的密度和Fermi Wave向量$ k_l $和$ k_r $，分别为$ x> 0 $ x> 0 $和$ x <0 $。然后，它以$ t> 0 $作为孤立系统的发展而发展，具有有限的杂质强度$ g $。我们准确地计算时间依赖性密度和电流。对于固定位置$ x $，并且在很大的时间内限制$ t \至\ infty $，该系统将达到非平衡固定状态（NESS）。我们从分析中获得了相关核，密度，粒子电流和NES的能量电流，并表征它们的弛豫，这是代数的。特别是，在NES中，我们表明，远离杂质，粒子密度显示为弗里德尔振荡的非平衡类似物的振荡。在“射线”的制度中，$ x/t =ξ$用$ x，t \ to \ infty $固定，我们计算相同的数量，并观察到与费米速度$ k_l $和$ k_r $相关的两个光锥的出现。有趣的是，我们发现两个速度$ξ$和$ - ξ$的相反射线之间的非微不足道量子相关性。我们扩展到连续的设置，并与初始状态相关联的分析方法在Ljubotina，Sotiriadis和Prosen的最新作品中开发的分析方法，在具有杂质的离散费米链的背景下。我们还将结果推广到有限温度下的初始状态，通过显式计算恢复了在低能极限中对共形场理论的一些预测。
We study the out-of-equilibrium dynamics of noninteracting fermions in one dimension and in continuum space, in the presence of a delta impurity potential at the origin whose strength $g$ is varied at time $t=0$. The system is prepared in its ground state with $g=g_0=+\infty$, with two different densities and Fermi wave-vectors $k_L$ and $k_R$ on the two half-spaces $x>0$ and $x<0$ respectively. It then evolves for $t>0$ as an isolated system, with a finite impurity strength $g$. We compute exactly the time dependent density and current. For a fixed position $x$ and in the large time limit $t \to \infty$, the system reaches a non-equilibrium stationary state (NESS). We obtain analytically the correlation kernel, density, particle current, and energy current in the NESS, and characterize their relaxation, which is algebraic in time. In particular, in the NESS, we show that, away from the impurity, the particle density displays oscillations which are the non-equilibrium analog of the Friedel oscillations. In the regime of "rays", $x/t=ξ$ fixed with $x, t \to \infty$, we compute the same quantities and observe the emergence of two light cones, associated to the Fermi velocities $k_L$ and $k_R$ in the initial state. Interestingly, we find non trivial quantum correlations between two opposite rays with velocities $ξ$ and $-ξ$ which we compute explicitly. We extend to a continuum setting and to a correlated initial state the analytical methods developed in a recent work of Ljubotina, Sotiriadis and Prosen, in the context of a discrete fermionic chain with an impurity. We also generalize our results to an initial state at finite temperature, recovering, via explicit calculations, some predictions of conformal field theory in the low energy limit.
