Department of Physics, Graduate School of Science, University of Tokyo, Kashiwa 277-8574, Japan.
Advanced Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan.
Phys Rev Lett. 2018 Jun 1;120(22):220602. doi: 10.1103/PhysRevLett.120.220602.
We investigate a heating phenomenon in periodically driven integrable systems that can be mapped to free-fermion models. We find that heating to the high-temperature state, which is a typical scenario in nonintegrable systems, can also appear in integrable time-periodic systems; the amount of energy absorption rises drastically near a frequency threshold where the Floquet-Magnus expansion diverges. As the driving period increases, we also observe that the effective temperatures of the generalized Gibbs ensemble for conserved quantities go to infinity. By the use of the scaling analysis, we reveal that, in the limit of infinite system size and driving period, the steady state after a long time is equivalent to the infinite-temperature state. We obtain the asymptotic behavior L^{-1} and T^{-2} as to how the steady state approaches the infinite-temperature state as the system size L and the driving period T increase.
我们研究了周期性驱动可积系统中的加热现象，该现象可以映射到自由费米子模型。我们发现，向高温状态的加热（在非可积系统中是典型的情况）也可能出现在可积的时变周期系统中；在弗洛埃特-马格纳斯展开发散的频率阈值附近，能量吸收急剧增加。随着驱动周期的增加，我们还观察到守恒量的广义吉布斯系综的有效温度趋于无穷大。通过标度分析，我们揭示了，在系统尺寸和驱动周期无限大的极限下，长时间后的稳态相当于无穷大温度状态。我们得到了稳态如何趋近无穷大温度状态的渐近行为 L^{-1}和 T^{-2}，其中 L 是系统尺寸，T 是驱动周期。
