论文标题
在存在杂质的情况下淬火后的静电时间相关性
Stationary time correlations for fermions after a quench in the presence of an impurity
论文作者
论文摘要
我们考虑在原点存在有限尺寸的杂质的情况下，在一个维度上，非相互作用费米子的淬火动力学。这种杂质的特征是一般动量依赖性反射和传输系数，这些系数从$ {\ sf r} _0（k），{\ sf t} _0（k）$更改为{\ sf r} $ {\ sf r}（k），{\ sf t}（k）$ time $ t = 0 $ t = 0 $。初始状态与$ {\ sf t} _0（k）= 0 $处于平衡状态，以便将系统切成两个独立的一半，$ {\ sf r} _0^r（k）$，$ {\ sf r} _0^l（k）_0^l（k）$分别在左右左右。我们获得了多时间相关性的确切大时间限制。这些相关性变成了时间翻译的时间不变，并且在两个不同的方向上是非零的：（i）对于$ x = o（1）$，该系统达到非平衡稳态稳态（ness）（ii），对于$ x \ sim t $，即ray-regime。对于排斥性杂质，这些相关性独立于$ {\ sf r} _0^r（k）$，$ {\ sf r} _0^l（k）$，而在有界状态的情况下，它们振荡和内存效果持续存在。我们表明，这些非平凡的弛豫特性可以从单个粒子波函数的较大时间行为中以简单的方式检索。
We consider the quench dynamics of non-interacting fermions in one dimension in the presence of a finite-size impurity at the origin. This impurity is characterized by general momentum-dependent reflection and transmission coefficients which are changed from ${\sf r}_0(k), {\sf t}_0(k)$ to ${\sf r}(k), {\sf t}(k)$ at time $t=0$. The initial state is at equilibrium with ${\sf t}_0(k)=0$ such that the system is cut in two independent halves with ${\sf r}_0^R(k)$, ${\sf r}_0^L(k)$ respectively to the right and to the left of the impurity. We obtain the exact large time limit of the multi-time correlations. These correlations become time translationally invariant, and are non-zero in two different regimes: (i) for $x=O(1)$ where the system reaches a non-equilibrium steady state (NESS) (ii) for $x \sim t$, i.e., the ray-regime. For a repulsive impurity these correlations are independent of ${\sf r}_0^R(k)$, ${\sf r}_0^L(k)$, while in the presence of bound states they oscillate and memory effects persist. We show that these nontrivial relaxational properties can be retrieved in a simple manner from the large time behaviour of the single particle wave functions.
