Many-body effects in finite-time quantum thermodynamic processes

正如在经典世界中一样，热力学将对量子技术设备的制造和操作施加限制。传统热力学中的描述和定律在这些技术正在发展的尺度上不再有效。在这个层次上，能量涨落变得很重要，像功、热和熵产生这样的量被当作随机变量。量子多体系统的热力学研究仍然是一项具有挑战性的任务，因为即使是理论研究也可能需要巨大的计算能力。量子多体系统中涌现集体现象的热力学研究无疑是一个令人着迷的课题。对多体非平衡系统的量子热力学性质进行了讨论。最近，我们提出了计算驱动场作用下相互作用系统的量子热力学性质的方法，并应用于含时外势驱动的Hubbard模型的平均量子功和熵的计算。我们还开始分析有限时间量子热力学过程中金属-莫特-绝缘体跃迁（一种多体驱动的量子相变）的特征，并演示了增加相关性如何显著影响能量涨落的统计，从而影响有限哈伯德链的量子功分布。特别是，我们注意到不同的影响，由于所考虑的过程是有限时间-不淬火-过程。在这些初步结果之后，在本项目中，我们希望对量子相变对量子热力学性质的影响有一个更普遍的理解。为了这个目的，我们将考虑不同的量子相变过程中驱动的各种时间依赖的潜力的结果。一个特别的目的是确定如何有限时间的过程修改这样的签名的字符。

As in the classical world, thermodynamics will impose limits in the fabrication and operation of devices for quantum technologies. The descriptions and the laws as formulated within the conventional thermodynamics are no longer valid at the scales where these technologies are being developed. At this level energy fluctuations become important, and quantities such as work, heat, and entropy production are treated as stochastic variables. The study of the thermodynamics of quantum many-body systems remains a challenging task, as even theoretical studies may require an enormous computational power. The investigation of the thermodynamics of the emergent collective phenomena in quantum many-body systems is, without a doubt, a fascinating subject. Some discussions about quantum thermodynamic properties in many-body out-of-equilibrium systems have been reported. Recently we presented methods to calculate quantum thermodynamic properties of interacting systems subject to driving fields, where there were applied to the calculation of the averagequantum work and entropy in a Hubbard model driven by a time-dependent external potential. We also started analysing signatures of the metal- Mott-insulator transition, a many-body-driven quantum-phase transitions, in finite-time quantum thermodynamic processes, and demonstrate how increasing correlations dramatically affect the statistics of energy fluctuations and consequently the quantum work distribution of finite Hubbard chains. In particular we noted distinct effects due to the considered processes being afinite-time - not quenched - processes. Following these initial results, in thisproject we wish to capture a more general understanding of the signatures of quantum phase transitions on quantum thermodynamic properties. To this aim we will consider results from different quantum phase transitions during processes driven by various time-dependent potentials. A particular aim is to identify how finite-time processes modify the character of such signatures.