量子自旋-$1/2$链在最小耗散下的纳米焊接
Nano-welding of quantum spin-$1/2$ chains at minimal dissipation
AI总结：
研究在两个量子自旋-1/2链间开启耦合的最优控制，量化能量代价并发现线性驱动下超额功按τ^{-η}标度，增加J_z各向异性抑制耗散，最优协议对链相敏感。
摘要：
我们考虑在两个量子多体系统之间开启耦合项的最优控制问题。具体而言，我们(i)量化在有限时间$\tau$内在两个量子自旋-$1/2$链之间建立弱结的能量代价，并(ii)确定实现该过程的能量最优协议。对于线性驱动协议，我们发现对于长时间，超额（不可逆）功按$\tau^{-\eta}$标度，其中$\eta=1,2$或一个非普适数，取决于链的相。有趣的是，增加链中的$J_z$各向异性会抑制超额功，从而促进准绝热性。我们采用切比雪夫拟设解决了这一般最优控制问题。我们发现最优控制协议对链的相非常敏感。
英文摘要：
We consider the optimal control of switching on a coupling term between two quantum many-body systems. Specifically, we (i) quantify the energetic cost of establishing a weak junction between two quantum spin-$1/2$ chains in finite time $τ$ and (ii) identify the energetically optimal protocol to realize it. For linear driving protocols, we find that for long times the excess (irreversible) work scales as $τ^{-η}$, where $η=1, 2$ or a nonuniversal number depending on the phase of the chains. Interestingly, increasing a $J_z$ anisotropy in the chains suppresses the excess work thus promoting quasi-adiabaticity. The general optimal control problem is solved, employing a Chebyshev ansatz. We find that the optimal control protocol is intimately sensitive to the chain phases.
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